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    "(assurance_planning)=\n",
    "# Assurance Planning via Simulation\n",
    "\n",
    ":::{post} May 2026\n",
    ":tags: experimentation, decision analysis, power analysis, assurance, simulation\n",
    ":category: intermediate, reference\n",
    ":author: Nathaniel Forde\n",
    ":::\n",
    "\n",
    ":::{figure} experimentation_triptych.jpeg\n",
    ":name: experimentation-triptych\n",
    ":width: 100%\n",
    ":align: center\n",
    "\n",
    "The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance (this notebook):* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis:* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis:* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery.\n",
    ":::\n",
    "\n",
    "Experimental questions are seeded in the science that preceded them. Answers are stress-tested and refined. New experiments spawn further questions again. This is the cycle. \n",
    "\n",
    "## The question planners are actually asking\n",
    "\n",
    "When we experiment, we encode questions. Implicitly we assume an answer will be useful. Our hypotheses are \"operationalised\" as power heuristics: given an effect size, what is the probability we cross a fixed threshold? This is an indirect and contorted gauge of efficacy. Instead of asking whether the treatment is effective, we often ask whether the results are surprising assuming a degree of effectiveness. The slippage between these two questions has produced a generation of experimental plans calibrated to invented effect sizes rather than to the beliefs the planners actually hold.\n",
    "\n",
    "An alternative is Bayesian Assurance. The construction is mechanical: draw from the priors, generate a dataset, fit the treatment model, apply the decision rule, repeat. The result is a single number: the probability the experiment will conclude what its stakeholders need. The process is the same whether the response is continuous (like revenue per visitor) or binary (like conversion); we develop it on the Gaussian case first and confirm the process is invariant to the response scale. This notebook is the first of three on the lifecycle of a Bayesian experiment; see {ref}`sensitivity_confounding` for the interpretation counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The same inferential machinery serves all three panels of the triptych, but what changes is the problem put to it.\n",
    "\n",
    ":::{admonition} Where this lands in regulatory practice\n",
    ":class: note\n",
    "\n",
    "We are going to apply Bayesian assurance to a question in product-analytics but the technique has a wider application. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials defines *Bayesian power* as the probability of meeting the success criterion averaged over a prior distribution {cite:p}`fda2026bayesian`, which is assurance under another name. The FDA guidance formalises the success rule as $\\Pr(\\text{effect} > a) > c$ (the rule used below, with $a = 0$ and $c = 0.95$). The same guidance separates the *design prior* that generates the synthetic trials from the *analysis prior* used in inference. The generative and inference models below are distinct objects for this reason. Below we'll runs the assurance loop with the two priors deliberately mismatched. The clinical trial setting in the FDA report differs from product experimentation; the machinery is identical.\n",
    ":::"
   ]
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   "id": "1d31774d",
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   "source": [
    "import warnings\n",
    "\n",
    "from dataclasses import dataclass\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as mticker\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "\n",
    "from scipy import stats\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7b97cc23",
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    "execution": {
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   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "az.style.use(\"arviz-variat\")\n",
    "rng = np.random.default_rng(42)\n",
    "RANDOM_SEED = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "565c8ac0",
   "metadata": {},
   "source": [
    "### The scenario\n",
    "\n",
    "An e-commerce team is evaluating a redesigned checkout flow. We cover two outcomes: the continuous outcome is revenue per visitor, the binary outcome is conversion. We will not commit to a particular vertical or product; the structure is generic to any A/B test with one of these outcome types. What matters is that the same prior beliefs and the same decision rule will be asked of two different likelihoods. The Gaussian case will carry the argument; the Bernoulli case will confirm it travels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "85d2d6a4",
   "metadata": {
    "execution": {
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   "source": [
    "@dataclass\n",
    "class EffectPrior:\n",
    "    \"\"\"Prior beliefs about a treatment effect, on the scale of the outcome.\"\"\"\n",
    "\n",
    "    mu: float\n",
    "    sigma: float\n",
    "\n",
    "    def sample(self, rng, size=1):\n",
    "        return rng.normal(self.mu, self.sigma, size=size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "541c0d41",
   "metadata": {},
   "source": [
    "## Power and assurance: two questions, different focus\n",
    "\n",
    "Power and assurance share an interface and answer different questions. Power conditions on a specific effect size $\\theta_0$ that the planner has been pressed into naming, and computes the probability of rejecting the null at that value:\n",
    "\n",
    "$$\n",
    "\\text{Power}(N) = P\\!\\left(\\text{reject } H_0 \\mid \\theta = \\theta_0,\\; N\\right).\n",
    "$$\n",
    "\n",
    "The conditioning bar is the load-bearing part. The planner who has confidently named $\\theta_0$ has implicitly used up the uncertainty that motivated the experiment in the first place. Assurance refuses the substitution. Instead it integrates over the planner's prior beliefs about the effect. The decision rule is whether the posterior probability of a positive effect clears a threshold $c$:\n",
    "\n",
    "$$\n",
    "\\text{Assurance}(N) = \\mathbb{E}_{\\substack{\\theta \\,\\sim\\, \\pi(\\theta) \\\\ \\hat{d} \\,\\sim\\, p(\\hat{d} \\mid \\theta,\\, N)}}\\!\\left[\\mathbb{1}\\!\\bigl(P(\\theta > 0 \\mid \\hat{d},\\, N) > c\\bigr)\\right].\n",
    "$$\n",
    "\n",
    "The outer expectation averages over effect sizes drawn from the prior; the inner averages over data generated under each effect ({cite:p}`ohagan2005assurance`, {cite:p}`spiegelhalter2004bayesian`). The integration is the entire move. Where power asks the planner to invent a world, assurance asks them to describe the one they already believe they are in. With that description in place, we can quantify how likely the result is when conditioned on the prior distribution. \n",
    "\n",
    "## The simulation engine\n",
    "\n",
    "Assurance is an expectation over the *prior predictive distribution*: the joint distribution of effect and data that the model generates before any real data arrive. As a Monte Carlo estimator the integral becomes a procedure in three steps, repeated for each candidate sample size:\n",
    "\n",
    "1. **Sample the prior predictive** of an unconditioned generative model. Each draw is a complete synthetic experiment: an effect drawn from the prior, and a dataset of size $N$ generated under it.\n",
    "2. **Fit the analysis model** to each synthetic dataset and apply the decision rule.\n",
    "3. **Record** the fraction of synthetic experiments in which the decision succeeded.\n",
    "\n",
    "Drawing a truth and generating data under it is exactly what `pm.sample_prior_predictive` does on a model with no observed data, so we let PyMC's generative machinery produce the synthetic experiments rather than hand-rolling the sampling with `numpy`. The generative model that produces the data and the inference model that analyses it are separate objects, and keeping them separate is the point: the generative model encodes the worlds we are planning for, the inference model encodes how we will reason once real data arrive. This workflow is defined as a function and passed through a sample size grid to determine how many _N_ is required to achieve surety in the finding. "
   ]
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   "execution_count": 4,
   "id": "8f2c40f5",
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    "execution": {
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   "source": [
    "def assurance_curve(assurance_fn, N_grid, n_sims, rng, **kwargs):\n",
    "    \"\"\"Estimate the assurance curve by evaluating assurance at each sample size.\"\"\"\n",
    "    records = []\n",
    "    for N in N_grid:\n",
    "        a = assurance_fn(N=int(N), n_sims=n_sims, rng=rng, **kwargs)\n",
    "        records.append({\"N\": int(N), \"assurance\": a})\n",
    "    return pd.DataFrame(records)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f49b072",
   "metadata": {},
   "source": [
    "## Gaussian outcome: revenue per visitor\n",
    "\n",
    "The Gaussian case is the cleanest place to make the mechanics explicit. Each arm produces a revenue-per-visitor outcome with known noise scale $\\sigma_{\\text{obs}}$ (we treat this as known here; in practice it is estimated from a pilot or historical data). The team is interested in the treatment effect $\\delta = \\mu_B - \\mu_A$, and holds a prior over $\\delta$ informed by past experiments in similar product surfaces. That prior is not conjured from nothing: {ref}`meta_analysis_experiments` shows how a meta-analysis of past experiments produces exactly this kind of prior, so the synthesis at the end of one experiment's lifecycle is the planning input at the start of the next. Concretely, the meta-analytic predictive there closes on $\\mathcal{N}(0.4, 0.5)$, which is exactly the `EFFECT_PRIOR` defined below: the number that ends that notebook opens this one.\n",
    "\n",
    "Two models do the work. The *generative model* is unconditioned: it places the planning prior on $\\delta$ and generates synthetic datasets, and it is the object we hand to `pm.sample_prior_predictive`. The *inference model* conditions on a dataset and returns the posterior on $\\delta$; the decision rule asks whether the posterior probability of a positive effect exceeds a threshold (0.95 below). For the assurance loop the conjugate Normal–Normal posterior on $\\delta$ admits a closed form, which lets us evaluate the decision on each synthetic experiment without running MCMC every time. \n",
    "\n",
    "We will verify that closed form against the inference model's MCMC posterior at a single sample size before relying on it. This also underwrites the idea that we can use MCMC for this procedure even with more complex models. "
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4f485b3b",
   "metadata": {
    "execution": {
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   "source": [
    "SIGMA_OBS = 4.0\n",
    "DECISION_THRESHOLD = 0.95\n",
    "BASELINE_REVENUE = 10.0\n",
    "# Not free-floating: this is the meta-analytic predictive for a new market from\n",
    "# the synthesis notebook (meta_analysis_experiments), which closes on N(0.4, 0.5).\n",
    "EFFECT_PRIOR = EffectPrior(mu=0.4, sigma=0.5)\n",
    "\n",
    "\n",
    "def gaussian_generative_model(N, prior):\n",
    "    \"\"\"Unconditioned model: planning prior on the effect plus the data-generating likelihood.\"\"\"\n",
    "    with pm.Model() as model:\n",
    "        delta = pm.Normal(\"delta\", mu=prior.mu, sigma=prior.sigma)\n",
    "        pm.Normal(\"y_A\", mu=BASELINE_REVENUE, sigma=SIGMA_OBS, shape=N)\n",
    "        pm.Normal(\"y_B\", mu=BASELINE_REVENUE + delta, sigma=SIGMA_OBS, shape=N)\n",
    "    return model\n",
    "\n",
    "\n",
    "def gaussian_two_arm_model(y_A, y_B, prior):\n",
    "    \"\"\"Inference model: conditions on an observed dataset and returns the posterior on the effect.\"\"\"\n",
    "    with pm.Model() as model:\n",
    "        mu_A = pm.Normal(\"mu_A\", mu=BASELINE_REVENUE, sigma=5.0)\n",
    "        delta = pm.Normal(\"delta\", mu=prior.mu, sigma=prior.sigma)\n",
    "        mu_B = pm.Deterministic(\"mu_B\", mu_A + delta)\n",
    "        pm.Normal(\"obs_A\", mu=mu_A, sigma=SIGMA_OBS, observed=y_A)\n",
    "        pm.Normal(\"obs_B\", mu=mu_B, sigma=SIGMA_OBS, observed=y_B)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be971533",
   "metadata": {},
   "source": [
    "A single synthetic experiment makes the inference model concrete. We use the do-operator to fix the generative effect at a chosen value, draw one dataset from the prior predictive, and condition the inference model on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0a894159",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-06-01T17:16:05.230108Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [y_A, y_B]\n",
      "NUTS[nutpie]: [mu_A, delta]\n"
     ]
    }
   ],
   "source": [
    "demo_true_delta = 0.6\n",
    "demo_model = pm.do(gaussian_generative_model(N=200, prior=EFFECT_PRIOR), {\"delta\": demo_true_delta})\n",
    "demo_draw = pm.sample_prior_predictive(1, model=demo_model, random_seed=RANDOM_SEED)\n",
    "y_A_demo = demo_draw.prior[\"y_A\"].values.reshape(-1)\n",
    "y_B_demo = demo_draw.prior[\"y_B\"].values.reshape(-1)\n",
    "\n",
    "with gaussian_two_arm_model(y_A_demo, y_B_demo, EFFECT_PRIOR):\n",
    "    idata_gauss_demo = pm.sample(\n",
    "        draws=1000,\n",
    "        tune=1000,\n",
    "        chains=2,\n",
    "        target_accept=0.95,\n",
    "        random_seed=RANDOM_SEED,\n",
    "        progressbar=False,\n",
    "    )"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "id": "0b654f32",
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    {
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g9xbBu7egD8oe9Le6M1BaPadVL9jb4ejRo/rLEyc7t6p+tGuvvdaWhF0nvPjiizJq1Cjblo/goq8g2OdPYmnih7p3B9rA4O2boFzHB+U85mXp6en6PorF999/L05I90AZreKbYGnViXXDDTc4tgP27dunvzW8du1acQPV0abeNL7jjjv0t9LcsD9U5rABAwZIYWFhvIsDl1DZOcaOHSt+8ssvv8jx48djmjeIwdJWPHBQD0hjsX//fr3O45XBNRSVvVG9pWXFCzi5ubl6UMW2bdssKRvM4dxszKFDh+SCCy4wlEnOD4LQFlklaMeGwvFhTEFBgd5x9sknnzi2vquuukoPJPYzlRmrUaNG8uyzz9qebX7q1KnSqVOnQL0IES9+vAfzEhW8EenFqFBZm8MFSyuTJk0SJ4Kly5UrJ7Vq1bJkXUC4ByorVqwIW0E1atSQ4sWLx1yJa9asiTiNGgHBCfXq1TNd1qBuoxt4pS+Qe4tg3VvQB2Uf+lvdR408ec4551ie1flkAdNXXHHF/1zPT5gwQe68805xwsMPPyxz5851ZF0IHvoKgnf+DHosTTxR9+5DGxiMfROE6/ggncf8INY+IXXudioreg8PlNEKvgmWfuqppxwfHll1OPbu3VsP5Ig3lZ3LjQ9A33rrLbn11lvjXQy4yJAhQ2TOnDniF7Fm3atcubLUqVNHgsaKIT8yMjJiehtRZTCcN2+euNHOnTvl7LPPNv2wUL1taSSTFJzBudmY/v37+/6N3qC1RVYJ0rGhcHwYd91118lXX30lTtqxY4c8+uij4kfqwa+qU5UZK9S1mrr+OnEd/+qrr+oZ8dQLFuXLl495vaqtUQ9Ndu/ebaL0COI9mJeYydqshk1UwaHhgvWs6I+KVMZQwdyAlSZPnhzxIUqXLl1MrcNIQJVTgcSR1rNr166YgnGDsI1u4IW+QO4tgndvQR+UfehvdZ9rrrlGVq1a5ci61H3rQw89pP97/vz5epvhVBCAerli4MCBehAMYAf6CoJ1/gx6LE08UffuRBvo/30ThOv4IJ3H/CDWvk2VVMypY7mLB8poBV8ES8+ePVtGjBgRtyxBKqV9PD344IPyxhtviFu9+eab8sQTT8S7GHAJ1cHTr18/W4coc9Lvv/8e03xODHvqNupm2Io39yIN5fp36oHrxRdfLH/++ae4mbqAUEGK6m3rWKih7FUmSLgD52Zj3n33XT0wIgiC0hZZJUjHhsLxEZ2PP/5Y4uG1117Th/r1ExUcrYahe//990NOo4ZOUy8uqOuMjh076p1c6jeqroPV/OrBx08//aQPEdyqVauo1r9+/Xo9SNtLb5x7kd/uwbwkUiCyypKrMrqHoq4dQlHZQqZMmWKqfCpQMVKgSahgbsBK6kWcSNQLNmYYCSQO94KClapXrx72e3VeVEPFRisI2+gGbu8L5N4iePcW9EHZh/5Wd/r6668d/72qIc1VVnin76nU/cRnn33m6DoRHEHvKwjS+TPosTTxRN27V9DbQL/vmyBcxwfpPOYXZvqFnBpxpqUHymgFzwdLqwZSDRmiGsx4iee61bCrzzzzjLjd8OHD5eeff453MeASKijipZdeEq9Tv33VSRaLIAZLqyAaK4bbqF27dlTTqw6AadOmiReooehVpsZYAoY++OADfWhAxB/nZuPuuusuCYqgtEVWCdKxoXB8eOfaz41v6cdKZXTu1q1byGz3SUlJMnr0aP1BdLjAqrJly+oBbPfdd5/+5vhvv/0mnTp1iuoa0UiQHMzxyz2Y34Kl1X2h+q2F0qdPn4jXnWao+9lIfVpklobd1Hkg0m8lNTU14u8hkq1bt4b9vkSJEjGNZBVrhuFIYgmiDMI2xpsX+gK5twjWvQV9UPaivxUnnkOrDGtr166NS4U899xz7AjYJqh9BUE6fwY9liaeqHv3C2obGIR94/fr+CCdx/ykatWq+vO0WDiVjM0LZbRCsnjcmDFjXDNUuNNUB/iNN95oejkJCQn6kPC9evXSb/jVwV+mTBl9uD41HPv06dPl888/l19//TXmdahgGzU81bJly/RlI37S0tKkdevW0rZtW2nYsKH+UQ8wKlasKCVLltS/T0lJkezsbP1z8OBB/WJk3bp1euCDOplZMVyOyjw3aNAgfV1etXTp0piHDG3RooUEjVWdevXq1YvqjV01vJGXfPvtt/LKK6/I7bffHtV8ZgIlEhMT5ayzztKzyaq2oWbNmlK+fHkpVqyY/l1OTo5+TlBBVWqoUHXeVW+Dq6EH1UPC3NzcmNftN5ybo3P48GEJgiC1RVYJyrGhcHx4i+pkU51Q4YIbvUBlVujZs6d+Pj8ZdU+g7gEvuOCCqJetArDVfYPqCFND3RkZMlhlGFAPbtS1hx9xDxZckYaei5S1Wf2e1HV5qBEfpk6dqt+3qwzVsYgUoGqkjE7p37+/vPfee+JXQc2wr84R9957b8TpVJZ1s/2JkUZOMRLca5UqVapEnEaN3BCtIGxjvLm9L5B7i2DdW9AHZT/6W3FCPINt1AvOK1askKZNm7JDfIa+gvgI2vkzyLE08Ubdh0cb6F5+2Dd+vo4P2nnMb1TfkKpbNwcit/BAGU3TPOzw4cNaZmameppgyadGjRraPffco33yySfab7/9pi1atEj7/vvvtXHjxmkXX3yxlpaWZtm6/vrZuHFjTNt/2WWXmV732WefrS1btszQ+n788Uetdu3aptZ35513arEaPny4qXUbUatWLVv2sRWfd955x9A2VKtW7R/z1q9fX7v//vu1X375RcvNzdXMyM/P18uilml2myZMmKB52euvvx7zti9YsMCRMpo9ptX8VnjzzTct+R1UrlzZ8DoLCwu1tm3bWvYbPOWUU7R///vf2ty5c7UtW7Zox48f1/bs2aMtXrxYe+utt7Rzzz1XS05OtmRdZcqU0fbv3294W1VZYj1HtWnTRluxYkWMe1bT8vLytFmzZmlPPvmk1qNHDy0pKemk61FteBDaYM7N8d1PgwcPjvu1RJDbIi8fG/HC8WHtflb3hv3799fef/99bdq0afr93HfffaeNGjVKa9q0qWXrUdfUXqbuB7p27Rpy+1JTU/V7Pyu88cYbhutVtWFe5cd7MD9cl8Xb+vXrI26L6m+K5IYbbgi7jM8//zzmMv7rX/8Ku+ySJUtqRUVFmhtcf/31cT/27PwE1QsvvGCofubPn296XeXKlQu7jlNPPVVzyldffRVxm1966aWolxuEbYw3N/cFcm8RvHuLoPVBOc0v/a1u6iOz87pO3cf26dNHe/fdd/XfrOon+/nnn/XfbPPmzS1f398/HTt21K9rVDuh2ovp06fr57n27dtbsvwRI0bEXN9m1qv2lRXM7HOzz6jieazTV+Dsh2c4/xT0WJp4ou5pA93aBvr1/BSk63i/3gcG5XnEoEGDYiqDevafnZ1tWTm8XkazPN0bP3LkSEsO7NKlS+s30JEeAKlgkX79+rniAk9dgFpxcx3tQ69du3bpJ4hY15mSkqKtWbNGc+sN7bp167SVK1ee9PPTTz+ZWv9TTz0VctlGPocOHYrq4kZ1DqkOiNmzZ2t2OHLkiNa7d29TdXLRRRdpXnbbbbfFvO3Hjh0LTLC0ekCmfvtWtJfq4s+o8ePHW7LOKlWqaBMnTjS0TtUJqx4+WrHeu+++2/C2qovZWIPP9+3bp1lJnSvfe++9fwRsGrno93obzLk5/h83BksHqS36K4KlOT6cPD7U+eaRRx7RcnJyIga3FCtWzPT6hg0bpnmZCvoIt32vvvqqpet74oknDNXrWWedpXmVH+/BvH5d5gafffaZJQGgU6ZMCbuMq6++OuYyRnqhq1u3bppbECztP2vXrtWKFy8e8XeiHrqbpfo/Qz2gOvE5/fTTNaeoh4+Rtvvxxx+PaplB2EY3cHNfIPeewbq3CGIflNP80t8ahGDpM844Q9u2bVvYgJ0hQ4ZYus4Tn+rVq+uB0aGo35gK2Da7nu7du8dc32bWS7C0NcHS9BUYO954hmP9+TPIsTTxRt3TBrq5v9SP56egXMf7+T4wKM8jXn755Zi3448//rCsHF4vY2CDpVWmBPX2mtmGoG7dutrWrVujWrdqzBISEkyv28wFnmpMzazzvvvu02KlOh0qVKgQ87pvvvlmz3XeKGo/eSH7lTqmVbDYzp07bV+XeiurRYsWMddJiRIlTL+ZFk+x/g5Vpk6nxDNYWl1MqmPRyvbygw8+MLz+Vq1amV5fkyZNtL1790a13QUFBdqll15qet3q92H0wuubb76JaR0PPPCAZqfdu3drzz33nNaoUSNTnfdeaYM5N1v7qVevnv7m4tdff63f2KrsyerhxsGDB/VMjSpwSL2Zqx4WnHghw43B0kFqi7x8bMQLx4f540FlPZ0zZ47hOledKpECiSJ9nAw0slqk0T5uuukmW9bbs2dPX711HvR7MC9cl7nBQw89FLYe1DnKyL5Q+1ztt1DLUVmiYtmnKtNJpCwrbsr+SLC0v6hjtkOHDhHbC3WMqus7s44ePRpxXRdeeKHmFPWiRKTy3HvvvVEtMwjb6AZu7gvk3iJY9xZB7INymt/7W/0SLD1gwAD9eXEkKiDkvPPOs2y96qP2gdGAmoEDB5pal7omUtfvsTCzXoKlzR3r9BVEd7zxDMfa82fQY2niibr/L9pA97WBQdk3fr6OD+p9oJ+eR3z55ZeOZlr3axkDGyythk8ye2FVvnx5PYtJLJ599lnT64/1Am/58uWmLjDbtWtnehjVjz/+OOb1q6wxsQzpTrC08bd6nKSGXTBz/M+cOVPzqsaNG8e0zeqC0G/B0uoiVV3gLVmyRB9C/dprr9XS09MtayfVJyMjQ3/4Z1UGIyNZIcJlpIh04a+GVjFbBnXBbIQa8iqW5b/22muaU8y+ien2i2DOzdb91tVNusrEGI0DBw5ozz//fMRhnJ2+lghaW+TlYyMeOD7MHxMq84G6L4yWyhRn9j7Si1avXq1fT4XaLtVJp9oNO6hrRCN1q4ao86Kg3YO5/brMLSJ1Xrdu3drwsi6//PKwy1IPAaK1cOHCiPtKZY5yC4Kl/cXocI6PPfaYJetT14RWjmRllpEsR9G+7BeEbXQDt/YFcm8hgbq3CGoflNP83t/qh2Bp1ecVTQCxFZn4/vrCorrHNko9OzGbjV799mNhZp0ES5s71ukriO544xmOtefPIMfSxBt1/1+0ge5qA4O0b/x6HR/k+0A/PY+YN29ezNvxzDPPUEaLJIpHffrpp6aXMXr0aKlfv35M8w4ZMkS6dOki8TB+/Hh1dxbz/C+++KIkJCSYKsPll18uDRs2jGne7OxsmTBhgqn1I7RKlSo5Wj1nnHGGqXUuXLhQvGrLli0xzVetWjXxis2bN+vtRaRPWlqafhy0bNlSbrrpJvnggw/k+PHjlpZlwIABkpGRYWjaDz/80PT6xowZE/O+UvXx5ptvSmpqqqkyfPzxx4amy8vLi2n5mzZtEqeUK1dO/IxzszWuvfZaWblypfTt2zeq+cqUKSODBw+W22+/XdwkaG2Rnfx2bCgcH+Y98sgj+rVotO6++25JTk6Oeb379u2T/fv3i9fcfPPNcuzYsZDfP/PMM3q7YYcWLVoYun9etmyZeBH3YIjlXveUU04xXHGXXHJJ2O8nTZoU9U5YsGBBxGnatGkT9XIBI9dAqm8ykrZt28pDDz1kSYUauWc2c20QLSPrivY+Pwjb6AZu7Qvk3iJY9xb0QTmD/lZ3S0pKknHjxklKSorhedQ9aWZmpiXrV9co0TwjrVixovTs2dPUOletWmVqfjiPvgJ3Cdr5M8ixNPFG3f8XbaB7+X3f+PU6PmjnMb8y0z+kYrecUM0DZTTLuR5Si/3www+m5m/VqpVcd911ppbxn//8Rzp06CBOmzhxYszztm/f3pIyJyYmyhVXXCFPPPFETPN/8cUXctttt5kuB+JPHQtNmzaV3bt3xzT/kiVLxIv27Nmjn9D9HiztFsWKFZMHHnjA0LRFRUXy1VdfmVpf9+7dow7I+zvVgXDHHXfo54pY/fnnn7Jt2zapXr162OnS09NjWv5bb70lgwYNkqpVq8ZYQpzAudm8gQMHyksvvWT6Rs0tgtgW2cVvx4bC8WFerVq15L777otp3rJly+oBgH/88UfM69+xY4enXgRSL7JNnz49bHtz0UUX2VqGCy64QGbNmhV2mp07d9paBr8I6j2Yl2zfvj3i/okmEPn888/XX2bIzc096ffqmqOwsFAPGrEqWFrdYzRp0kTcok6dOnrwLLzt999/11+EjqR48eLy/vvvWxbcG4RA4iBsY7y5tS+Qe4vg3VvQB+UM+lvdTT3fbdCgQdT3Uer3+ssvv5hatwp8Vn1t0VLB0mb6CtU9BhAOfQXhBe38GeRYmnij7uODNtC9nN43fr2OD9p5zK/UiwOqz6ygoMC1Af2VPFDGQAZLb9iwQTZu3GhqGSq7nPohm3GiQZk7d644Rb05vG7dupjn79evn2VlOe2002JuBH/99Vc9q5nRLLFwt8qVK/v+zRIrAznKly9vaVmC4LHHHpMqVaoYfuivHmCZDcyzgrrYMxOgqEydOlXP1h1OrMFae/fulY4dO8qzzz4rffr0cfTBqZ9wbjavc+fOlrzR6iZBbIvs4MdjQ+H4ME8FM8Ta6XUi07GZgAbVsaeW4QUqEOnhhx8OO43KKm23U0891dC1CYwJ4j2YlxjJeBJNsHTJkiXlzDPPlG+//Tbkb2fGjBl6P41VwdJq1CA33R8MHz5c/8C7VEZelSXdyChUr732muPB+k5ebxrpkzaTLSjI2xjEvkDuLYJ1b0EflHPob3W3WIMsGjVqZDpY+pprrtFf7IqW2WubWAOMECz0FZxc0M6fQY6liTfqPr5oA93LyX3jx+v4oJ3H/EydW9VL17HEEDiVbCjRA2U0y9wVTpyo7HZmqEw7kYYwNeqyyy4TJ82ePdvU/NE8OIsk1mFXlPz8fNP7Ee6RmpoauLfhww1hHkksHWlBpgLl7rnnHsPTm73pVhdnvXv3FqvaSbNDVxvZntq1a8e8/K1bt+pvAKo3xK688koZM2aM/Pjjj/pbXyo7ESLj3Gw+c/w777xjuuPNbYLYFlnNr8eGwvFhjuqkUsN9mVGzZk1T82dlZYlXvPnmm2GHjFcBkaoT0G5Gsn5x7WFcEO/BvCRSILI6t6ksTdGI1I81adIkw8tSv7VIWVlOOeUUw8sDIjlw4ICcd955smvXrojT3nzzzZY+xFFSUlIiThNLthQz/aJWt/NB2MZ4c2tfIPcWwbq3oA/KOfS3upfK9mfkZdyTsWLUtFj76+rWrRuYfgjED30FJxe082eQY2nijbqPL9pA93Jy3/jxOj5o5zG/U8+/ne6X8mMZzXDPqxAODhmrHgRblc3hwgsvlHvvvVecYqbzs0SJEvrwBlYxW4dqW3r06GFZeWDc0aNHZenSpfpHveGogifURYZ6eHXw4EE5cuSIfqJSH7sfpHg1e5yZRj7WE0sQqYtZNRxHNMNJm8nkopx++umWPsRSQ2ZHCpYwuz1qSOrSpUvLoUOHYl6P+v1PmDBB/5yghvpWy1bBTSc+KvuGynZDhvT/w7nZnOuvv14aNmwofhPEtshqfj02FI4PMd2xU6FCBVPLMHseM5IV0w1UxkbVoRfODTfc4EhZypQpI0HGPViwRDrnqvNbtBk0LrroIrn11lulsLDwpN+r+6YXXnjBUObY1atXR7ynNfuiFXCCOtYuuOACWbFihaHh6dWoIlbzYiCxkTIHbRvjza19gdxbBOvegj4o59Df6l7nnntuzKMlmP29qr66bt26xTSv6r8PQj8EokNfgTOCdv4McixNvFH30aENdC8v7xs/XscH7Tzmd14IRC7mgTIGLlhaPdQxI9rsPZHemlA3x9nZ2eKElStXmjqhRRNwaDcjD0lgDfWW08yZM+Wrr77ShxhbtGiRa7K25eTkiBe59QGJn9SqVUt++OEHqVixYlTzrV271jXniBPZGs0wsj2qc1hdVE6ePFmslJubqw/roj6hMnh06tRJ7yBWQ2m5aTgaJ3FuNkdljvOjILZFVvPrsaFwfIjpIRzNKlmypO0BQG6gsh6EG55NBSmpIYSdYOQ6wU8jsHAPFmyRgqVjydqsArm6dOkiv/3220m/37Ztm8ybN89QG2nkBSqCpWGFvLw8fejSOXPmRJxW3VOqDOl2ZBs2skxVVi9nXQ7CNsabW/sCubcI1r0FfVDOob/VvVRASrxe4lUvPcbaB272ftcr/RAIj76C+Aja+TPIsTTxRt2HRxvoXn7aN368jg/aeczvvBCIXMwDZTTDk1FNZoeMbdasmWVlUQ1tkyZNZP78+eKEzZs3i1/4aVvcSr1l9corr8gbb7whO3bsEDfyarC0mZs6gqUjU8EDU6ZMkWrVqjnetpjpbLVjeepY27dvX8S39NSQoVZf9Iej2hR1w6Q+SmZmpp4FTA1No7KGpaenS1D46Xzm9Lao34dfh3gPaltkFT8fGwrHhzmtW7c2vQ+izeh6sozNXjB+/PiIWezNZtIzykiAlhrezuu4B8P+/fv1IRvtCERWw+CGCpZWVKCpFcHS6kUKq69FEDwqC/rVV1+tvwQdiTrevvvuOz3bjR3Uw3nVhxvu/K0eHjlFZWCy+lolCNsYb27tC+TeIlj3FvRBOYv+Vndq3Lhx3NpjM+tW2QiD0A+Bk6OvIL6Cdv4McixNvFH3J0cb6F5+3Td+u44P2nnM72J9idLJF4+Ke6CMZiSKB5ltpNUbbFayenmhqDd3zF5guUmkh4cwNxzXk08+KbVr15YRI0a49sLG6SFArWSmY4pOrfA3zYMGDdKzTsUSKK0exu7atUvMUMOnWMmK5akscZH07dtXf2sxXg4fPiyff/65XHbZZXo5HnzwQdm9e7f4Hedmc1R2RD8KcltkFb8eGwrHh3mqg90srw37HmvWqW+++SbisONOBpD6OViaezBEk7U51heCVIbecFSwtBVlVEMzmg3mQLCpfo+bbrpJJk6cGHFaNWypCqg2m+kxHJVBp1SpUqaDe61iZF1ly5aNaplB2MZ4c2NfIPcWwbq3oA/KefS3ulPdunVjntdsoIqZdSOY6CuIvyCeP4MaS+MG1P3/og10L7/vGz9dxwfxPOZ3sfYROZntXfNAGQMXLK0alngOi/Z3kTqiraLSlasOUL8wux8ReuhFNazDsGHDPPPWhheZGTLNq9m07da5c2eZO3eujB07NuYH86qdNHsCtrpNV8PKmh1a1kj2J7WOf//73+IGBw8elGeeeUbvABk9erRnLopiwbnZnHbt2okfBbktsopfjw2F48O80qVLm16G14Z9j4V6+ezQoUNhp1HD0TnFSIdrvXr1xIu4B4NTwdI1a9YMm5VaHYvLli2LuBw1lKYd5QNOuOOOO+S9994zdEz/9NNPUrlyZdsrL1JgrpP9lEbWFUsgcRC2MZ7c2BfIvUWw7i3og3Ie/a3uZKbPzOwQ5FY/X4a/0VfgDkE8fwY1lsYNqPv/QxvoXkHYN366jg/ieczvYu0jcnKEthwPlDFwwdLqLRc3XeDZNUTk3/ntROW37XED9cCzY8eOsmTJkngXxffc+IDEixITE+X888/XH47OmjXLdHCcFXVrR4en2WUabS/79+8fMduck1Rg5f333y+9evXSL+T9yG/nMqe3p2XLluJHQW+LrODXY0Ph+HBHB7vZB6ReoK6tIl3POvliguqEdSKzn9O4B8PfLVy4MGylqIwtZgIEL7nkkrDfR8rku379+ogvUoQLyAYiUfeAagjXSFSAtOoLUAHTTihXrlzY750cGcnIKDSRyhvUbYwnN/YFcm8RrHsL+qDig/5W9zHzAF49j/DC82B4H30F7hHE82dQY2ncgLr/L9pA9wrSvvHLdXwQz2N+F2sdOBmInO2BMgYuWDo3NzduHZvx3Nlmt9ttCBi1friCnj17yoEDByxeMrzygMQr1E32OeecIy+99JKeYfDrr7+WM88805Jl5+XlmV6G2aH4TqZYsWKOtf/jx4+X008/Xdxk6tSpcuGFF8Y0TI7bcW42x2sPx42iLTLPr8eGwvHhjg72hIQE8Ts1Ykc4KlDaqSHDlZUrV4b9vmLFip7LMMk9GGLJLG02a3OkTv5JkyaZznxNsDRipYZuVVlyjFzrqUDpBg0aOFbZ1apVi5jpx4rrNKsCiSOVN6jbGE9u7Avk3iJY9xb0QcUP/a3uEs8H8FY/X3Y7q0aMNBs86DX0FbhLEM+fQY2lcQPqnjbQzYJ4fvLDdXwQz2N+F2sdOHkvkuOBMgYuWNrsA12rf3xO/ZjT0tLETzRNi3cRfFWXV155pezbty/eRQkMMzd2fn5bSmVSUSfAMmXKSN26daVTp0565jP1ltzbb78tf/75p/5w7vvvv5fbb79dKlWq5Lp20o79YzarcjQB3OrY/O677+S2224TN5k2bZo89thj4jecm83JzMwUP6ItMs+vx4bC8WGe2UxQQcksvXz58rDft2jRQpw0Z86csN+3b99evIR7MJzMkSNHZN26dbYGIjdt2lQaNWoU8nuVGUZlj44187VqY1u3bm2qjAgmFSRt5J5PXef98MMP0qxZM3FSnTp1Ik6jXuh2gpH1GClvELcxntzYF8i9RbDuLeiDih/6W93Fit+tF9ft5WDpIA23Tl+B+wTx/BnUWBo3CHrd0wa6V1D3jR+u44N4HvO7WNtmJ18+8kIZzfDkXZ3ZDJ0qvb3VD8Oc4JUIfDjv/fffl9mzZ1P1DlLDxcbKSxehtWrV0i9YjH7UG3AqMFi9kage0KvjUmU2e+aZZ+SGG26Qtm3b2voAwYp20o423ewyo90uddGshj3+9ddf5dRTTxW3GDVqlGzcuFH8hHNz/Ie7dSPaIvP8emwoHB9wgso2EOmcqwIunaIChObNmxd2ms6dO4uXcA+GUIHIkTp8zWaWVtQLqbFml46UWVpl+vVKpybc48UXX9Rfko5EHVvffvttXLKX165dO+I0kV52sEqk9agX0GO5Hg7CNsaTG/sCubcIFvqg4ov+VgSRVSNSZGVlSVDQV+A+QTx/BjWWxg2CXve0ge4V5H3j9ev4IJ7H/KywsDDm7O5m+qX8VkazksWDSpYsaeotVKsvCqy+aAn3QEEFGaoDE/irp556ypIKqV69uj7kQ/fu3fVMVWo4THXcRToB9+/fX957771A7ZQqVapIampqTJ1F27dvt6VM+O/FYnJysuFhS5zIcqDeujJTHjMZVnv06KEHJqm3E19//XX56quv4jrknfq9jBkzRsaOHSt+wbnZHPV79SPaIvP8emwoHB9wwoYNGyLeN9asWdOxnTFr1qyI181du3YVL+EeDLFkbVasCBJVwdJPP/102GDp++67L6YyxiOI1QiVbWXKlCniV2oUJq8aN26cDB482NCISeqeNF4vx9SvX99QgO9ZZ51le1nCZX83WtagbmM8ubEvkHuLYKEPyh3ob0WQWDXs+7Zt2yQo6CtwnyCeP4MaS+MGQa972kD3Yt949zo+iOcxP9u1a1fM+1IlunTCLg+U0SxPRiGoSHQzN1abN2+2tDybNm0Sp4Z3qlq1qmzdutWR9cEbZs6cKatXrza1jHLlyulvLl1//fWBGJLcCgkJCXqASSwZeQiWtredVEH+Ztr5tWvXSqdOnSwrk1qeWTVq1DA1/xlnnKF/1E321KlT9eFmpk+fHvHhpR0+/vhj/cLfL20N52aEOi5oixCu3eD4gN127twZcRp1HDpFdUCGU7p0aUuvv+zGPRhizdpcqVIlPdjOrHbt2ukvO4fqG5s7d67s2LFD70P6KzX9nj17PBksrTKtzJ8/P97FwN+MHz9ebr311ogZ1VWA6cSJE/X70nhp3bp1xGmWLVtmeznUb3Dv3r2myxrUbYwnN/YFcm8RLPRBuQv9rQgCNYqoWSor3ZYtWyQI6CtwpyCeP4MaS+MGQa572kD3Yt94+zo+iOcxPzPTP2RkRLmglNGsRPEgsw91re4UXr58uTjFzIGlHj6rhxdu+sA8NXyp2d/TnDlz5MYbb4w5eNHqTLxeEetbMQRL28tslsSlS5daVhYrlqeySseaWfpkbzT37dtX3nrrLf3hnnorTLUhI0eOlOuuu07P8KUCOOykhp71W5AD52acDG0RwuH4gN12794dcZpSpUo5siPUfd8nn3wSdprzzjvPUxnluQdDrMHSVgUiq4C9iy++OOzv7osvvoi6fG4Olob7fPrpp3pfUlFRUdjpVPuuHv706tVL4kn1f1WsWDHsNEZ+I2YZuR8+5ZRTYlp2ELYx3tzYF8i9RbDQB+U+9LfCz6zIcLpo0SIJCvoK3Cto588gx9LEW5DrnjbQvdg33r+OD9p5zM/M9A85lbV5uwfKGMhg6QYNGrjmIkO9veFkoGjjxo1NbXfQGx4/mjFjhunhUs3+piJli/GrOnXqxDTfwYMHJTs72/Ly4L+aNGli+9DZTnYGmmn3I1EX+Co46cEHH5T33ntPZs2apd8IqGGZVJD3l19+KaNHj9YfgLdo0UJ/c9EKf/zxh/gJ52acDG0RwuH4gN2ysrIiTlOsWDFHdsSPP/4YMYvJpZdeKl7CPRhORg3buGrVKscCkS+55JKw30+aNCmmIEmvBjDCWWqo0muuuSbikIzqHvLdd9+VPn36iBtE+g0uXrxY8vPzbS2Dkfvhtm3bxrz8IGxjPLmxL5B7i2ChD8r96G+F25h5MdmKZ3/qujEo6Ctwr6CdP4McSxNvQa572kD3Yt94/zo+aOcxPzMz+oBTWZu3eaCMgQyWbtmypelhBlSDZgWVkt9JHTp0MPUGcCzDBMLdIj2MDadhw4b6Cd8MdWJdu3atBJGZtsjMfoN97aTy22+/6UPDWcVsZ6DZ7YlFRkaGNG/eXC666CK599579TcqlyxZot8QvPzyy6azFvmtzeDcDKuPC4W2yN84PmC3goKCiNPk5eU5siPefPPNsN+XK1dOevfuLV7CPRhORl0vR/rtWRmI3KNHD/33E+5aYv/+/VEFS6vOzDJlylhWRvjT999/L5dddlnE411lQH/jjTf0oGq3UL+bcFQw6++//25rGaZNmxYxs5GZFyuCsI3x5Ma+QO4tgoU+KO+ivxXxkpaWFvO8O3bsiDiKSDjqxbpII035CX0F7hW082eQY2niLch1TxvoXuwb71/HB+085mex/h5VcL4K0nfCKg+UMZDB0mY7U1W2n2+++caSsnz++efiJJUi34zPPvvMsrIETVJSkqn57QhGUA841NAMserWrZvpMqiMNHv27JEgOvXUU2OeV719Bnt07NjR1Pwqw9LJsrDFmqV6zZo1cd0eK1WoUEEGDhyob5eZC51Yhu5wYxt8AudmnAxtEcLh+IDdjGQKMJJ92qzNmzfL5MmTw05z9dVXS2pqqngF92Duvi6LJyNZm60MDlT7IdyLBiqQ9e8vbkYqo1eDF+GcX375Rc9qbuR3PHbsWLnpppvETXr27GloRAS7qIfekQKVTzvtNFMZIIOwjfHkxr5A7i2ChT4o/4lnfyuCQb2kFKvc3FxTwTUTJkyQ3bt3SxDQV+DuvoKgnT+DHEsTb0Gte9pA97aB7Bt/XMcH7Tzmld9XLFSgfSwaNWpk6rreb2UMZLB006ZN9RT4dma3MmL9+vX6QwKntz3W4f6U999/nxT7cXj7+sRwi1ZTbwGZUbFiRdNl+PTTTyWoWrduHfPDHSuH0YG17eSJh7qRhhM24oUXXjA1vzq+zj77bHGbsmXLyrPPPhvz/LG8Fe3GNvgEzs2w47hQaIv8i+MDditVqpShoRjtdv/994ftiFKdXIMHDxYv4R7M3ddl8RQpELl06dKmrw3+TgWthjNx4sT/GUI7Uuc7wdIIZ/bs2XqAvnp4G8moUaPkjjvucF2Fquzu5cuXj9sDZfUCUaQHNEaCnYO+jfHkxr5A7i2ChT4o/4pHfyuCwezz9Fifg6tjUvUJBAV9Be7uKwja+TPIsTTxFtS6pw10bxvIvvHHdXzQzmNe+X052Tdk5uV9P5YxkMHSahjHs846y9QyfvrpJ33YSDMeeOABQ8MbW+3SSy81lS793XfflXiZPn26PPzww+JFJUqUMDW/HR3iZt+AMXtxpE4qamiJoCpWrJh+YRILMkvbK1LQgJH9o4YLNuPPP/+U8ePHm1pG9+7dww6tHU+dO3eOed5Yzp1ubIP/inMzToa2COFwfMBORq4f7D43zpo1K+KLler8Wa9ePfES7sHcf10WLyqLSKQARqupFyvD7Q/V93Xivt/pzNdWU31ZqlPfrx+3mz9/vvTq1UuOHTsWcdrHH39c7rvvPnEjNRxkpHu3lStXyqJFi2xZ/8cff2y6fJEEYRvjya19gdxbBAt9UP7ldH8rgqF69eqm5h83blxM16t33nlnoDKe01fg/r6CIJ0/gx5LE09BrXvaQPe2gewb/1zHB+k85pXfV7RUAqNDhw7FNG+7du3ECVs9UMbABksrffv2Nb0MlcEq1jcIvvzyy//J0OOkfv36mZpfvcnr9LBHv/76q541RA2zqB6ae1Hx4sX1T6zUkCk5OTmWd9CbsXjxYlPz33vvvY4M3+1mHTp0cHToAhhz3XXXma6qhx56KOb9pM4t/fv3N/3Q+9prr42qjXGy8zE/Pz/meTMyMnzRBv8V52acTBDbIhjH8QE71a5dO+I0M2fOtG39aqjeQYMGhZ1GZZV+9NFHxWu4B3P/dVk8qE7tSEFwdgRLp6eny7nnnhv2t3hi+FavB0sjftSxrQLzDx8+HHHaoUOHyrBhw8TNrrnmmojTvPjii5avV2X2+u6778JOc/rpp0vVqlVNrysI2xhPbuwL5N4iWOiDco7f+1sRDGo4bLMvzQ0fPjzq59DvvPOOBAl9Be7vKwja+TPIsTTxFsS6pw10bxsY1H3jx+v4oJ3HvPD7crJfqH379uKEJR4oY6CDpVU2E5XO3ow1a9bow0dG+6NQP+Krr75a4qVly5am3kjbt2+f3iCpv3ZSD+U++ugjPdW66ghXb8EF+Q1sdUF76623mn5766/KlCkjKSkppoZQ3bBhQ0zzvvXWW/L2229L0MU6dOjOnTtl06ZNlpcH/9WqVSv9ossM9cbUOeeco79pFw31APn888+X5cuXm1p/xYoVozrXqOxNdevW1QMj586dK3Yzc0FboUIFX7TBf8W5GScTxLYIxnF8wE4NGzaMeJ/w448/mh5pJpQ77rgjYpbdm2++WZo1ayZewz2Y+6/L4kGdb1UfSDwCkSNlE500aZKhYOkqVaqYHioW/rN69Wq93+PAgQMRp73rrrvkqaeeErfr2rWrfu8czocffmj5Q7XRo0dLUVGR7QGvQdnGeHJjXyD3FsFCH5RzgtDfCv9r0aKF6WU8+eSTMmLECCksLAw73bZt2/T+SHVNEDT0Fbi/ryBo588gx9LEWxDrnjbQvW1gUPeNH6/jg3Ye88LvK1qxJjBSv2NVn06Y6YEyWkLzsPvuu0+lyTP9adKkiTZnzpyI6ysoKNCeeeYZLT093ZL1nvhs3Lgx6m3/+eefLdnuefPmaVb7888/tTvvvFMrW7bsSdfbo0ePmJY7fPhwU9trhd69e5uu9zp16mgPPPCANmHCBP24W7JkibZy5cqwn6KiopBlatiwoanynH322Vp+fn5U9fDSSy9piYmJlv0GvOzgwYNaUlJSTNv93nvv2V6+WrVqmdo3an6v+u677yw5PosVK6Y9/fTTWl5eXsR1fvnll1q1atUsWe9TTz0V1fZec801/zN/ixYttNGjR8d0jonk6NGjWsuWLWPeNnUu9Usb/Fecm93f/sfjWiJobZGbrtu8gOMjfsfHL7/8YuoYfeeddzS3O/XUUyNux5gxYyxf72uvvRZxvRUqVND27t2reRX3YO6/LnPa22+/HXF7V6xYYcu6Dx8+rKWmpoZcb4kSJbScnBytbt26Yct3/vnn21I+eNeGDRu06tWrG/o933rrrZqXvPjiixG36dprr7VsfcuWLYvYd1S1alUtNzfXsnUGYRvjxa19gdxbBOveIoh9UPHg5/7WePbbXH/99XFbd7z7AsysW9VbLNauXWu6vTjxUcfo2LFj9XubrKws/bN69Wrtiy++0K666iqtePHilq3LqmdUTh7r9BW4v68gaOfPIMfSxFsQ65420L1tYBD3jV+v44N2HvPC7ysanTt3jqncV1xxhWVl8EMZreDpSIQdO3ZoaWlpljSuqqHu2bOn9uabb+o/iH379mnHjx/XNm/erM2cOVN76KGHIj5YivUTa4N8ySWXmF636ti9/fbb9R+5mQdz33zzjXbXXXcZCsz0crD0sGHDbDkGIn3Ug81Q+vXrZ3r5F154oX7MR7Jt2zb9QYrV2+d1Xbp0iWm7b7rpJtvLFuRgaeXcc8+17DgtU6aM3iE5fvx47aefftIWL16szZgxQ/v000/1iyorzxGq3sP97o1c9P/106ZNG+3BBx/Uy60u2M2YP3++dsopp5javl9//dU3bfDfcW52d/sfr2uJILVF8a5rL+L4iM/xEe8HpE4wct6sXLmydujQIcvWOWXKlLBBmyc+kyZN0ryMezBvXJc5adCgQWHLrYIGCgsL43YuUdcNCQkJYadR+xT4a/+PeoBg5HfZv39/177IEMqxY8e0cuXKhd0u9ZtR/Z1mqZcdO3ToYNtLxUHexnhya18g9xbR7xMv31sErQ8qHvzc30qwtLO/1xPiESxtxXOieH68FCxNX4E3+gqCdP4MeixNPAWx7mkD3dsGBnHf+Pk6PkjnMS/8vqLpp0tJSYmpDO+++64lZfBDGa3i+UgE9cOLxw/CDRd46gKoZMmSlpWjU6dO2tChQ7WJEyfqjeLOnTu17Oxs/U20I0eOaLt27dIWLlyoPwBXGchuuOEG/UQSbSYNLwdL//jjj65rgD/88ENL1lG6dGlt8ODB2vfff69fwKuLbLXf1Vvnn3/+uXbdddfZ8la4Vfsmnp588smYtrt+/fq2ly3owdKrVq3Ss7HG43dr5hNLAFG4i/6/flSb3bx5c/03rY5d9ebcrFmz9N/6gQMH9HZfBXKoh50qeGrNmjXa1KlTtSeeeCLmh4F//ZQqVcpQZlyvtMF/x7k5urp1WryuJYLUFsW7rr2I4yM+x0cQgqUXLFhgaFvUNYQV1H2JkUBpJ14YtBv3YN64LnNSpOtk1d9ipzfeeCPs+uvVqxexblU2OEDZvXu31qhRI0O/SZVB0M4XAeyk+jYjbV/58uX1e2Uz1MOnSOtRo8KYfUAX1G2MF7f2BXJvEf0+8fK9RdD6oOLBz/2tBEs7+3s9IV7B0kOGDLGsrXD646VgafoKvNFXELTzZ5BjaeItaHVPG+jeNjCI+8bP1/FBO4+5/fdllArOj2X9KtGB2idO+MkDZbSK5yMRVINUsWLFuPwo3HCB99lnn8W9/NF+vBwsrYaKVBcBbmqA1YMGK0+G8fh43aJFi2Le9u3bt9tatqAHSxsJHHDb55ZbbolpO41e9Mf7c9ttt/mqDT4Zzs3G69Zp8byWCEpb5Ia69iKOD+ePjyAESysdO3Y0tD0qM32sVMeZ0c5/VR7Viep13IN557rMCarDvESJEmHLPXDgQNuDW80Obblp0yZbywhvUA+CWrVqZeiY6dOnT9TDsLqJKrsaejTSdtasWVMPQI2lbbj33nsN1aV6cMk2eoub+wK5twjWvUWQ+qDiwc/9rQRLO/97VeIVLK0ykcb7OA1CsDR9Bd7pKwjS+TPosTTxFLS6pw10bxsYxH3j5+v4oJ3H3P77sjszdrt27SxZv1/KaJVE8bjMzEx5+eWXJaj69u0r999/f7yLERipqaly+eWXi5tkZGTIrbfeGtcyJCUlSZC1atVKmjdvHtO8X3/9teXlwf/617/+Jf379/dEtZx66qkyZswY8auUlBS5++67fdUGnwznZpwMbRHC4fiAXYzeKz7zzDPSp08f2bVrl+Flq+e8n376qbRs2VKef/75iNPXrVtXvvjiC0lLSxOv4x7MO9dlTli7dq0cPXo07DRt2rSxtQwVK1aUzp07xzx/uXLlpFatWpaWCd6jjuPzzjtPFi9eHHHa888/Xz755BNJTk4Wr1Jlf/311yP2aW3ZskXatWsn77zzjn7uM2Ljxo3Sq1cvefbZZyNOe/bZZ8vVV18tdgjCNsaLm/sCubcIFvqgYLa/FcHQokUL6dmzZ9zWX6pUKQkC+gq801cQpPNn0GNp4ilodU8b6N42kH3jv+v4IJ3H3P77MmrKlCkxzXfNNdeIU6Z4oIxW8Xyw9ImG4Oabb47LusuWLRv3Ha8ebN92221xLUOQDBkyxHXBwQ8++KCUL18+Lutu3769XHbZZRJ0/fr1i2m+L7/80vKy4J/GjRsnF110kaurpkmTJvLdd99JsWLFxK/uueceadCgge/a4JPh3IyToS1COBwfsMMll1wiZ5xxhqFpVSBzvXr1ZODAgfLLL79ITk7OP6bJzc2V33//XUaMGKFPe8UVV8i6desiLlsFYU6bNk0qV64sfsE9mHeuy+y2YMGCiNOccsoptpdDvfAQKyfKB/d74YUXZO7cuYam3bx5s3Tq1El/4dfJz2OPPWbpNnfr1k0effTRiNMdOXJEbrzxRmndurX+sHvTpk3/mCY7O1s/1w0YMEC/v586dWrE5arz4vvvvy92CsI2xoub+wK5twgW+qCCzYr+VgTDU089JYmJzocFqOsG1TcRFPQVeKevIEjnz6DH0sRT0OqeNtC9bSD7xn/X8UE6j7n992WkH3XRokUxJUG46qqrxAleKKOlNJ9Qqc+7du3qaLr15ORkbdq0aaaH8LFi6JCioiJtyJAhcUuZ70R6fTcN5z548GDXpfaPx1ALVapU0bZt26YP/+WWfRMvqh5iGfY4LS1Ny8rKsq1caoiyeA5x5iZqyPe+ffs6/jsx8lHDHJsdhtXtw8l07NhRy8vL820bfDKcmyPXrdPccC3h97bITXXtRRwfwRgq22nr1q3TMjMzo95GdW1bs2ZNrWXLllqLFi30f8dyvdusWTNt06ZNmh9xD+ad6zI73XvvvWHLnJqaqg8TaDfVtxRrvd5///22lw/uZ/b6zYmPmeHnQyksLNR69+4ddVnKlCmjNW7cWL+GVn0nSUlJUc2fnp6u/fbbb5ZvT1C3MR7c2hd4AvcWxvaHX+4tgtAHFQ9+7m+NZ79NPJ8nxfv3Gu/roIEDBzp6jF544YVaQUGBqX1u9hlVPI51+gq801cQpPNn0GNp4ilodU8b6N42MEj7xs/X8UE9j7n99xXO888/H9O6e/XqZUmd+aWMVvJFZmklPT1dvvrqq5iHv4slJb4abvL0008XN0hISNCHPVTDJfphWGO3GzlypJ7Rxm1vJqo3wpxSqVIl+fnnn6VatWqOrdPNVD3E0h6o7Hzff/+9LWXC/1JtoxoqfujQoXqb6RZq+OKZM2dK1apVxa/U8LRqmFl17vRrG3wynJtxMrRFCIfjA3ZQGaDfe++9qDNIFRUVyZYtW2TJkiWydOlS/d/q/0Xj7LPPllmzZumZpf2IezDvXJfFM7N0s2bN9GEC7Va7du2YM0S3adPG8vIAXqHOj5999pmceeaZUc138OBBWbVqlSxevFjPvlJYWGh4XnVvPHHiRD3rsxOCsI3x4Pa+QO4tgoU+qOCxur8VwfDcc885NqrMlVdeKZ9//rkns/+ZRV+Bd/oKgnT+DHosTTwFre5pA93bBrJv/HcdH6TzmNt/X+FMnjzZ0RHN/FpGK/kmWFopU6aMTJ8+XTp27GjreooVK6Z3MF966aXiNv3799c7sLt27Spu5YcbY3UMfPvtt9KhQwdx24nhrrvucuQh7K+//qoPuYn/o4YrjYUa8hzOUBeMarg5NVRsjRo14lrtxYsXl7Fjx8qUKVOkRIkS4le9e/fW24ty5cr5vg0OhXMz/o62COFwfMAOF110kYwfP96xezEVGKqGgVOBQJm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      "text/plain": [
       "<Figure size 1200x535.887 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 559,
       "width": 1445
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pc = az.plot_dist(\n",
    "    idata_gauss_demo,\n",
    "    var_names=[\"delta\"],\n",
    "    visuals={\"title\": {\"text\": r\"Posterior on $\\delta$ at $N=200$ (one simulated dataset)\"}},\n",
    ")\n",
    "az.add_lines(\n",
    "    pc,\n",
    "    values=0.0,\n",
    "    visuals={\"ref_line\": {\"color\": \"C1\", \"label\": \"ref = 0.0\"}},\n",
    ")\n",
    "pc.get_viz(\"plot\").legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f515a2e",
   "metadata": {},
   "source": [
    "The posterior concentrates above zero; under the decision rule the team would conclude the new flow lifts revenue. That is a single draw of the experiment. Assurance asks how often this conclusion would arrive if we re-ran the experiment many times under our actual prior.\n",
    "\n",
    "The conjugate posterior on $\\delta$ given $\\hat d = \\bar y_B - \\bar y_A$ has mean and variance:\n",
    "\n",
    "$$\n",
    "\\sigma_d^2 = \\frac{2\\sigma_{\\text{obs}}^2}{N}, \\quad\n",
    "\\tau^2_{\\text{post}} = \\left(\\frac{1}{\\tau_0^2} + \\frac{1}{\\sigma_d^2}\\right)^{-1}, \\quad\n",
    "\\mu_{\\text{post}} = \\tau^2_{\\text{post}}\\left(\\frac{\\mu_0}{\\tau_0^2} + \\frac{\\hat d}{\\sigma_d^2}\\right),\n",
    "$$\n",
    "\n",
    "where $(\\mu_0, \\tau_0)$ is the prior on $\\delta$. We check this matches the PyMC posterior before relying on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42e775d9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:06.029977Z",
     "iopub.status.busy": "2026-06-01T17:16:06.029758Z",
     "iopub.status.idle": "2026-06-01T17:16:06.037195Z",
     "shell.execute_reply": "2026-06-01T17:16:06.036727Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>analytical</th>\n",
       "      <th>MCMC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>posterior mean of delta</th>\n",
       "      <td>0.745</td>\n",
       "      <td>0.728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>posterior sd of delta</th>\n",
       "      <td>0.312</td>\n",
       "      <td>0.303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         analytical   MCMC\n",
       "posterior mean of delta       0.745  0.728\n",
       "posterior sd of delta         0.312  0.303"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def gaussian_posterior_delta(d_hat, N, sigma_obs, prior):\n",
    "    sigma_d_sq = 2 * sigma_obs**2 / N\n",
    "    post_var = 1.0 / (1.0 / prior.sigma**2 + 1.0 / sigma_d_sq)\n",
    "    post_mean = post_var * (prior.mu / prior.sigma**2 + d_hat / sigma_d_sq)\n",
    "    return post_mean, np.sqrt(post_var)\n",
    "\n",
    "\n",
    "d_hat_demo = y_B_demo.mean() - y_A_demo.mean()\n",
    "analytical_mu, analytical_sd = gaussian_posterior_delta(\n",
    "    d_hat_demo, N=200, sigma_obs=SIGMA_OBS, prior=EFFECT_PRIOR\n",
    ")\n",
    "mcmc_mu = idata_gauss_demo.posterior[\"delta\"].mean().item()\n",
    "mcmc_sd = idata_gauss_demo.posterior[\"delta\"].std().item()\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\"analytical\": [analytical_mu, analytical_sd], \"MCMC\": [mcmc_mu, mcmc_sd]},\n",
    "    index=[\"posterior mean of delta\", \"posterior sd of delta\"],\n",
    ").round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb2d9901",
   "metadata": {},
   "source": [
    "The two posteriors agree to within MCMC noise. Now we get to the heart of the technique and push our procedure through different sample values of _N_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "62b0f123",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:06.038338Z",
     "iopub.status.busy": "2026-06-01T17:16:06.038265Z",
     "iopub.status.idle": "2026-06-01T17:16:08.642660Z",
     "shell.execute_reply": "2026-06-01T17:16:08.642201Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N</th>\n",
       "      <th>assurance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100</td>\n",
       "      <td>0.267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>200</td>\n",
       "      <td>0.398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>400</td>\n",
       "      <td>0.501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>800</td>\n",
       "      <td>0.603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1600</td>\n",
       "      <td>0.640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3200</td>\n",
       "      <td>0.681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6400</td>\n",
       "      <td>0.717</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      N  assurance\n",
       "0   100      0.267\n",
       "1   200      0.398\n",
       "2   400      0.501\n",
       "3   800      0.603\n",
       "4  1600      0.640\n",
       "5  3200      0.681\n",
       "6  6400      0.717"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def gaussian_assurance_at_N(N, n_sims, prior, sigma_obs, threshold, rng, analysis_prior=None):\n",
    "    # `prior` is the design prior: it generates the synthetic worlds. `analysis_prior`\n",
    "    # is used to form the posterior; it defaults to the design prior so a single\n",
    "    # argument reproduces the matched-prior case.\n",
    "    analysis_prior = prior if analysis_prior is None else analysis_prior\n",
    "    seed = int(rng.integers(2**31 - 1))\n",
    "    pp = pm.sample_prior_predictive(\n",
    "        n_sims, model=gaussian_generative_model(N, prior), random_seed=seed\n",
    "    )\n",
    "    y_A = pp.prior[\"y_A\"].values.reshape(n_sims, N)\n",
    "    y_B = pp.prior[\"y_B\"].values.reshape(n_sims, N)\n",
    "    d_hat = y_B.mean(axis=1) - y_A.mean(axis=1)\n",
    "    post_mu, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, analysis_prior)\n",
    "    prob_positive = 1.0 - stats.norm.cdf(0.0, loc=post_mu, scale=post_sd)\n",
    "    return float((prob_positive > threshold).mean())\n",
    "\n",
    "\n",
    "N_GRID = np.array([100, 200, 400, 800, 1600, 3200, 6400])\n",
    "N_SIMS = 1000\n",
    "\n",
    "assurance_df = assurance_curve(\n",
    "    gaussian_assurance_at_N,\n",
    "    N_grid=N_GRID,\n",
    "    n_sims=N_SIMS,\n",
    "    rng=np.random.default_rng(RANDOM_SEED),\n",
    "    prior=EFFECT_PRIOR,\n",
    "    sigma_obs=SIGMA_OBS,\n",
    "    threshold=DECISION_THRESHOLD,\n",
    ")\n",
    "assurance_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "191f92bd",
   "metadata": {},
   "source": [
    "For each simulated future dataset, we compute the posterior distribution of the treatment effect and evaluate the posterior probability that the effect is positive, `prob_positive`. A trial is considered decisive if `prob_positive` exceeds the pre-specified `DECISION_THRESHOLD`. The Bayesian assurance is the proportion of simulated trials that satisfy this decision criterion. As the planned sample size increases, posterior uncertainty decreases, leading to a larger proportion of decisive trials and therefore higher assurance.\n",
    "\n",
    "For comparison we compute frequentist power at a single fixed effect size. The convention is to set the effect to the prior mean, which is itself an arbitrary choice, and a revealing one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "87ca67e9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:08.644059Z",
     "iopub.status.busy": "2026-06-01T17:16:08.643954Z",
     "iopub.status.idle": "2026-06-01T17:16:08.957767Z",
     "shell.execute_reply": "2026-06-01T17:16:08.957314Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 3000x1100 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1123,
       "width": 3023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gaussian_power(N, delta_alt, sigma_obs, alpha=0.05):\n",
    "    sigma_d = np.sqrt(2 * sigma_obs**2 / N)\n",
    "    z_crit = stats.norm.ppf(1 - alpha)\n",
    "    return 1.0 - stats.norm.cdf(z_crit - delta_alt / sigma_d)\n",
    "\n",
    "\n",
    "power_at_prior_mean = np.array([gaussian_power(N, EFFECT_PRIOR.mu, SIGMA_OBS) for N in N_GRID])\n",
    "power_at_optimistic = np.array(\n",
    "    [gaussian_power(N, EFFECT_PRIOR.mu + EFFECT_PRIOR.sigma, SIGMA_OBS) for N in N_GRID]\n",
    ")\n",
    "power_at_pessimistic = np.array(\n",
    "    [gaussian_power(N, max(EFFECT_PRIOR.mu - EFFECT_PRIOR.sigma, 0.01), SIGMA_OBS) for N in N_GRID]\n",
    ")\n",
    "\n",
    "prior_prob_positive = 1.0 - stats.norm.cdf(0.0, EFFECT_PRIOR.mu, EFFECT_PRIOR.sigma)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 5.5))\n",
    "ax.plot(N_GRID, assurance_df[\"assurance\"], marker=\"o\", linewidth=2, label=\"Assurance (Bayesian)\")\n",
    "ax.plot(\n",
    "    N_GRID,\n",
    "    power_at_prior_mean,\n",
    "    marker=\"s\",\n",
    "    linestyle=\"--\",\n",
    "    label=r\"Power at $\\theta_0 = \\mu_{\\text{prior}}$\",\n",
    ")\n",
    "ax.plot(\n",
    "    N_GRID,\n",
    "    power_at_optimistic,\n",
    "    marker=\"^\",\n",
    "    linestyle=\":\",\n",
    "    alpha=0.7,\n",
    "    label=r\"Power at $\\mu + \\sigma$\",\n",
    ")\n",
    "ax.plot(\n",
    "    N_GRID,\n",
    "    power_at_pessimistic,\n",
    "    marker=\"v\",\n",
    "    linestyle=\":\",\n",
    "    alpha=0.7,\n",
    "    label=r\"Power at $\\mu - \\sigma$\",\n",
    ")\n",
    "ax.axhline(\n",
    "    prior_prob_positive,\n",
    "    color=\"C0\",\n",
    "    linestyle=\"-.\",\n",
    "    alpha=0.6,\n",
    "    label=rf\"Assurance ceiling $P(\\delta>0)$ = {prior_prob_positive:.2f}\",\n",
    ")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n",
    "ax.set_xlabel(\"Sample size per arm\")\n",
    "ax.set_ylabel(\"Probability of declaring uplift\")\n",
    "ax.set_title(\"Assurance vs frequentist power, Gaussian outcome\")\n",
    "ax.legend(loc=\"lower right\", fontsize=9);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45105766",
   "metadata": {},
   "source": [
    "The three power curves fan out because each conditions on a single assumed world. Power at $\\mu + \\sigma$ assumes an effect of $0.9$ and saturates almost immediately; power at $\\mu - \\sigma$ is pinned near the test's five-percent floor, because $\\mu - \\sigma$ lands at essentially zero effect, where even large samples gain almost no detection. Power at the prior mean is the curve a frequentist planner would actually quote. The assurance curve is the prior-weighted integral across the entire fan, and it tells a different story than any single power calculation.\n",
    "\n",
    "The story is in the crossing. Between $N=400$ and $N=800$ the assurance curve drops below power-at-the-mean, having sat above it at smaller samples. At small samples assurance is buoyed by the optimistic tail of the prior: it counts the plausible draws above $0.4$, effects of $0.8$ or $1.0$ that even a hundred observations have a real chance of detecting, which the single-point power calculation never sees. Quoting power at the mean understates what small experiments can do, because it ignores the optimistic tail of the prior that assurance counts.\n",
    "\n",
    "At large samples the relationship inverts, and the reason is the ceiling drawn above. Power at a fixed positive effect climbs to one: with enough data an effect of $0.4$ is certain to be detected. Assurance cannot reach one: the prior assigns positive probability to a zero or negative effect. Its asymptote is exactly the prior probability that the effect is beneficial, $P(\\delta > 0) \\approx 0.79$. No sample size buys more assurance than $P(\\delta > 0)$. A planner should know that ceiling before committing to more data, and no point on a power curve reveals it.\n",
    "\n",
    ":::{admonition} The minimum detectable effect leads a double life\n",
    ":class: note\n",
    "\n",
    "Power is usually quoted at a \"minimum detectable effect\" (MDE), and that single number carries more weight than it appears to. Read one way, the MDE is a *utility threshold*: an effect smaller than this is not worth shipping, so failing to detect it does not matter, and powering at the MDE is a coherent design target. Read another way, it is a *forecast*: a quiet assumption that the true effect is about this large and positive, sometimes reverse-engineered from the sample size a team can already afford. The frequentist machinery itself is innocent here, because the false-positive rate $\\alpha$ already governs the null case; it is the floor that the $\\mu - \\sigma$ curve traces. What conditions the null away is the reported summary, \"$X\\%$ power to detect the MDE\", which is computed entirely inside the world where the effect is real and exactly the MDE. Assurance does not abolish this assumption. It relocates it from an implicit point to an explicit prior, where the probability that the effect is null or harmful becomes visible and open to argument.\n",
    ":::\n",
    "\n",
    "## The same machinery on a binary outcome\n",
    "\n",
    "The generative model fixes the baseline conversion rate, places the planning prior on the lift, and emits binomial counts per arm. The inference step places Beta priors on the per-arm rates and reads off the posterior probability that the lift is positive ({cite:p}`stucchio2015bayesian`, {cite:p}`kruschke2014doing`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d1c18825",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:08.959292Z",
     "iopub.status.busy": "2026-06-01T17:16:08.959195Z",
     "iopub.status.idle": "2026-06-01T17:16:08.963301Z",
     "shell.execute_reply": "2026-06-01T17:16:08.962866Z"
    }
   },
   "outputs": [],
   "source": [
    "BASELINE_RATE = 0.10\n",
    "RATE_LIFT_PRIOR = EffectPrior(mu=0.005, sigma=0.012)\n",
    "BETA_PRIOR_KAPPA = 200  # prior concentration, in units of pseudo-observations\n",
    "prior_prob_lift_positive = 1.0 - stats.norm.cdf(0.0, RATE_LIFT_PRIOR.mu, RATE_LIFT_PRIOR.sigma)\n",
    "\n",
    "\n",
    "def beta_prior_params(p_mean, kappa):\n",
    "    return kappa * p_mean, kappa * (1 - p_mean)\n",
    "\n",
    "\n",
    "def bernoulli_generative_model(N, rate_prior, baseline_rate):\n",
    "    \"\"\"Unconditioned model: fixed baseline rate, planning prior on the lift, binomial counts per arm.\"\"\"\n",
    "    with pm.Model() as model:\n",
    "        lift = pm.Normal(\"lift\", mu=rate_prior.mu, sigma=rate_prior.sigma)\n",
    "        p_B = pm.Deterministic(\"p_B\", pm.math.clip(baseline_rate + lift, 1e-4, 1 - 1e-4))\n",
    "        pm.Binomial(\"n_A\", n=N, p=baseline_rate)\n",
    "        pm.Binomial(\"n_B\", n=N, p=p_B)\n",
    "    return model\n",
    "\n",
    "\n",
    "def bernoulli_assurance_at_N(\n",
    "    N, n_sims, rate_prior, baseline_rate, kappa, threshold, rng, n_post=2000\n",
    "):\n",
    "    seed = int(rng.integers(2**31 - 1))\n",
    "    pp = pm.sample_prior_predictive(\n",
    "        n_sims,\n",
    "        model=bernoulli_generative_model(N, rate_prior, baseline_rate),\n",
    "        random_seed=seed,\n",
    "    )\n",
    "    n_A = pp.prior[\"n_A\"].values.reshape(-1).astype(int)\n",
    "    n_B = pp.prior[\"n_B\"].values.reshape(-1).astype(int)\n",
    "    actual_sims = len(n_A)  # PyMC v6 may return fewer draws than requested\n",
    "    alpha0, beta0 = beta_prior_params(baseline_rate, kappa)\n",
    "    p_A_post = rng.beta(alpha0 + n_A[:, None], beta0 + N - n_A[:, None], size=(actual_sims, n_post))\n",
    "    p_B_post = rng.beta(alpha0 + n_B[:, None], beta0 + N - n_B[:, None], size=(actual_sims, n_post))\n",
    "    prob_positive = (p_B_post > p_A_post).mean(axis=1)\n",
    "    return float((prob_positive > threshold).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bc3152a4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:08.964993Z",
     "iopub.status.busy": "2026-06-01T17:16:08.964890Z",
     "iopub.status.idle": "2026-06-01T17:16:13.436502Z",
     "shell.execute_reply": "2026-06-01T17:16:13.436021Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n",
      "Sampling: [lift, n_A, n_B]\n"
     ]
    },
    {
     "data": {
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Y0KXbQ3tnnXVW+MUvfhGWLVvW7u/Nzc3hxz/+cfj85z9vlwEFu+yyy8KSJUu2+3t1dXU499xz7dEynvyr78A+oe+APmHj2s3v3TW11aGmrqak629qaApNm5qTn+O64za09jucMn98SdcN9E6C5wGAbg/eGL9qU1jZsKnbj8SQutrQ9NzaEGPwDf4CAAAqneBDAACAriF8AwAAQNurleBDAACgp4VuREseX741dKO7xPCNUTOGJT8L3wAAAHoSwYcAPcOzzz4bLr744pzLd9999zBlypQu3SbaGzBgQHjXu94VvvSlL223a37/+9+H97///WH06NF2G7DDmpqawk9/+tNOl5144olh1qxZ9mYFTf5VVVMVRs0YGqqqqkqy7paWlvDiwmUhbIlbjOtupd8hUCqC5wGAbg/emD64Pty9dFVo6cZjEZt5MwbXb/1dIwwAAKh0gg8BAAC6jvANAAAAbS/BhwAAQG8I3eguwjcAAICeSvAhQOXbtGlTOO+888KqVatyPufkk0/u0m2ic2984xvDJZdcEp566ql2f29oaAgXXnhh+PSnP23XATssTlqxaNGi7f7ev3//8OEPf9ierLDJvzZtbArrV2wM9cP6lWS9sey4jiiuM6470u8QKCXB8wBAtwdvrFu0KoxeuSGs39TcbUdjwKC+oX5cTfKzRhgAANBTCD4EAADoGsI3AAAAtL3mnjArVFdXORUAAIAeHboR1dRWh5q6zeOwSqWpoSk0bRlrJnwDAADo6QQfApTe448/HgYOHBjGjBlT1HI3btwYPvGJT4S77ror53Piel/72tcWdb1kU1dXFz71qU+Ft7/97dstu/TSS8OZZ54ZpkyZYvcCO1T/f+c73+l02bvf/e4wbtw4e7ECx4DF78X6D+0bqqqK2w+wpaVla+Zi6zpb6XcIlJLgeQCgLBpdseNhY3NL2NTc0uXbU1tdFSZMGrz1d40wAACgpxB8CAAA0HWEbwAAAGh7AQAA9Ib+h1U1VWHUjKFFD91oG77x4sJlIWza/LvwDQAAoKcTfAhQenfeeWc4//zzw6mnnpqEjk+ePHmny1y8eHH44Ac/GO67777U55111llh0KBBO70+iuPQQw8NxxxzTLjqqqva/b2xsTF885vfDN/61rfsaiCviy++OLzwwgvb/X3q1KnhrW99qz1Y5rp68q9YZiw7MuEy0JUEzwMAZdPoGtjSElY3bAqbqqtCc21pOh62qt7UEqqaWkJNVQjDh/YP/QbWJX8fPHpAmDJ/fEnXDQAA0JUEHwIAAHQN4RsAAADaXgAAAD1JV4dutBK+AQAA9EaCDwFKr6GhIVx66aXht7/9bZg3b1447rjjwitf+cowYsSIgsp56qmnwkUXXRT+8Ic/JGHlaSZOnBje+c537uSWU2yf+MQnwvXXXx82bNjQ7u9XXnlluPfee8Oee+5ppwM5rVixInkf6MwnP/nJUFe3Oc+O8tWVk3/FCZdjma1MuAx0JcHzAEDZNLo2rl0eBtXVhpUtzWH1qL4hFKnRtZ2WljDwxQ2htjkk6xs2duDWRXNPmBWqq0sbeg8AANCVBB8CAAB0HeEbAAAA2l4AAAA9RVeGbrQSvgEAAPRWgg8Buk5zc3O49dZbk8cFF1wQZsyYEebMmRN23333MGnSpDBo0KAwZMiQUFNTE1atWpUEDC9dujTcdddd4bbbbkuC53dEnz59wpe//OXQr19pJnAkuwkTJoSvfe1r4eGHH95u2ZIlS+xaINUzzzwTzjzzzO3+Pnz48HDYYYfZexWiq8aAmXAZ6E6C5wGAsmt0DQnVoaUhhFV9S7PePuuaQl1TCAPrakP/gXXJuqPBoweEKfPHl2alAAAA3UjwIQAAQNcQvgEAAKDtBQAA0JN0df9D4RsAAEBvJvgQoOs1NTWFhQsXJo/LL7+8aOXGCRs/85nPhHnz5hWtTIrrmGOOSR4AhZo7d27yoLJ1xRgwEy4D3a26uzcAAOi9WhtdrWKjK/l7VVUYvaElTB7YL+xck2t7VS0tYeSGljC4rjZZT+s6o7knzArV1cVeIwAAQPm2v1q/9IpfWBWbL8EAAIDePPArTngctYZvRK3hG8UmfAMAAOiNtL0AAAB6Xv9D/Q4BAIDerivaYNpeAKVXU1MTPve5z4XTTz/d7gaAXtwP0ZgvoLsJngcAyrPR1dAURm6qCnuPHByG1NUWZV2xnF379A19mzf/HtcV1xnFbZgyf3xR1gMAAFCOhG8AAAB0DeEbAAAA2l4AAAA9SVf1PxS+AQAAIPgQoNKNGjUq/PSnPw1nnHFGd28KANCNY8BM+gWUg+KkuAIA7GSj68af3b210bXkieVbG11jhg4Pc0cMCmsbm8Lz6zaGl9Y3hOYCGmLVVVVhdP+6MK6+b6ivrQ4vLlzWaQNv7gmzQnV1leMIAAD02vZX/6F9Q1VVcdpFvgQDAAB6uxi+cf9fHk3aW63hGxvXNm4N36gf1q8o6xG+AQAA9GbaXgAAAD2n/6F+hwAAAKVvg2l7Ab3ZhAkTwsiRI8PSpUtLUn5dXV1485vfHN7znveEQYMGlWQdQPmI91VNjc3tft/2y+Z/avpUJ/d2hdqwetuEr1uLbWnZ+nNdfZ9QW1dTcLlrXl4XWuImd8hva/2136C6pOxCrXpxzeZ9saWcltYftug3qG+oH1r4GJoVz64ODRsaWwvdtq1bNrj/kH5h8JjNk+YWYvkzq8L6VZv38Xah4i2x3L5h+OQhBZe77JmVYc2SdW2OWfvlcWzR2F1HZip3+eLVbbZxc8Fbz4f+tWHyvuMKLnf54lXhpceWJdu53W5oaQm1fWrCrMMmF1zuyhfWhGfufrHd9nYsf+7xMwsud83SdeGxfz+zrdhtJ9xWc46fGfr0LSxied2KDeHlp1aEDasbwoY250Uc/9W4YVNY8tjyMGLq0OR6LpQxX0A5EDwPAFTE4K8BfWrCzCH1Ydqg/mFVw6awZlNTWNPQFNZuagpNLS1JGH0Mma+pqgoDamvCwLqaMLC2Jgyuqw01WwLl1y3fkJQZxXXEdUWDRw8IU+aP79Z9AAAA0BWEbwAAAHQN4RsAAADaXgAAAD1JqfsfCt8AAAAofRtM24tcmhqbtgsEbRvGGvvF1tQWHrbZsK4xNDc1dyhzW1JqTZ+aTAG3MZB3U0NT+6DUNi+gpq4mU8BtDB5tWNvYaXhwDDeNQaaDRhcecLt22fok86ZjEO+2YOKaMGLKkEzlrnpx7ebt3RrIu20d8biN263wgNu4rUufWtFun3YM0Z0yr/CA2/UrN4TnH3p5W2Bu24Vb/jZl3viCw5Q3rmkIT9/xfOfHbcu/0/YfHw466KBw/fXXh9tuuy38/e9/DzfddFN44okntg8dLtCsWbPCiSeeGE4//fQwfPjwHfo/9/xx4bb1ttvszb9MnTc+DJs4uOBtieU2btzUrty2r2/yPmPDmF1GZCo3Hr/tdtWWP0zce2yYtNeYgsu998+PhpXPrdluO1vF83fWoYWHHt9/5eNhSQxTbrt725Q/asbwTKHHD/3jybD4nhdznmvDJw0O81+/R8HlPnrdovDovxd1esyigSPrw+H/sV/B5T5567PhvisebbuZ7c63WP8e94mDCy538b0vhlt/dX+786Hj+fzarx5dcLkvProsXPO923KGdkev/sIRSYh5IVY+vzr86XPXd/hr+8JP/MxhYej4QQXXPb/76NWpzzn6QweEsbMLv+bylXvo2/fNVA//9Us3JNudSzx/Zx8xteByr/3BHUnYeC5zT5gV9jppl4LLvfXX94eXHt18LXdml8OmhP3fOKfgcu/762Nh0Z3P51weQ9wPe+e+BZf72PXPhIXXPZ1z+ehZwzMFz8cQ9/v+vPla7syQsQMzBc/H0Pnbfv1AzuV9B9RlCp5fsXh1uPv3D6c+J1Pw/Mvrw/1XPpb6nN2OnlZw8Hy8X33kmqdC86bmZB1RS1NLaIr3miGE1UvWhaETBxUcPG/SL6BcCJ4HACoqeCOGyA/r1ycMC4V9caARBgAAIPgQAACgKwnfAAAA0PYCAADoKUo58bJxXwC9Q64wx7Z/jm8lhb6fxHKbGptT1xFDUuN7WaE6C2Nru4Y+fWuSkNAsgaabQ1I7394Y/tenX22m4NEYktVue9usIoYW9x1YV3C5a5auS4KON5fX0un2Dhjev+ByY3BXw9r2+7ht8bHcwWMKD3Zd/dLasG7lxu0L3KJP/9owfNKQTNsb98XmYrcPmqztWxNGz9yxoNG21ry8LixfvHr7BW2CfifMHZ3pfFj6xIotm7j99kYxqLDQay4Gjj734NKc25s5MHZtY1jUMTC2gyn7jSv4HI6hxDHIc7vNbbMjpuw7LtM5HANNNxe2JTy3w6ZP3mdMGDKusPDK6IG/Px42bWhqv71tCo/nw6jpwwou98GrnwgbVjXk3N4Y7Dp+j1EFl/vwP58Kq5es3bKh229vvC6mzh9fcLnxuL28aGXO7Y0BzbscPqXgcp+4aXF4/uGlObd38NiBYc8TZhVc7tO3Px+evrOTc3jLrzEAu5Ag2tY22D+/c2tST8T6PQYiRi89tjwMGNEvuX6rqqvDiCmDC257xfLi++eSxze36+oG9AlXf/Pmdtt8zHkHFFxHLFu0Mtzyy/vbrbPjfj76gwsKvpZj3f6v793eab3e+pdXvHd+we8b8b3+z1/4d6fnWev2HvaufcPoGYXX77/58N+3C0TfHLi++U8Hnb1npoDQy/7zH2HDqs3vc+13R8tOBcb+5Qv/Lklg7DU/uL0kgbG3XvJASQJj7//LY3kDY48978CCy33shmfyBsae9NnDCy732fteCrdesu2a6yww9nVfP6bgcmPdcP2P70x9zpR5JxRc7soX1m79bCmX+D5X6H1EnIggbT9EY3cdkdQ91dXVYcGCBckjWrVqVbj77rvDww8/HBYvXhyeffbZ8Pzzz4fVq1eH9evXh3Vr1oXmluZQW90n9KnpEwbUDQqD+w4JI+pHh3GDJoU3fPi0sM9hGUKP/5L7fIiGTxySKXg+nr9podKxnswSPB+vt7Q6on54/0zB8y88vDS1juiXof3S+n707P0v5VweJ6fIYvWLa8OLC1/Oubyq8GZnYt3KDck259KxnbejGtdv2vre35m6Adn2b1ND8+Z2bYr4Plpw+765JTRu2DJxQtHlmWBi5+afSCm3NAVvN5FJ8QqurHJLZGcnJOkpSrkXstQRpRa/56p9qSb5DKx6y2eJcQKlWDdtWNkQ6voXlnlo0i+gXAieBwDKguANAAAA7S8AAICeRPgGAACAthcA0H7weByU3VbHMfvVNVWZBpjHELn25bYUJWSyNcxrW7ntl9f0qS44ACeKoS9tt7FjuTGssE/fwod+bljTEJpTAjfjtmYJmYyhPdtCJrff6Li9/Yf0K7jc9as2hsb1jTnLjcEvA0fUZ9re9a0hk21tKbq6T3US5JSl3LXLtgSpdLJ/q6qrwvDJQzKdD6teXJsaFhIDBQu9NuL5u3zxqm3ldpIOMWrGsOT6KETjxk1bwyu3ld2y3fYWGpTatKk5PP/gktTnjJw+LFPQ0DN3v9D+9XfY3hFTh2YKmXzmnhdDU2Ob+qfDPh4+eXASzl6oxfe+GBrWbcq5vUMnDsoUlBqDyOJ1l6vcweMG5g3S62z8V7zeNjY0hWWLVnVax9T2qQn9BtcVHL4Rr43avrVJ+Q9d/eTmTW6zk2No49R5hYdXvvTYsq1hVp1dF3H9WcIrX35qRVh87/ZhVq3XR6yD5xw3s+By43X85C3P5tzeaN/Tdi24joihjQ//66lOgzZb/7b3qbMLDlKJgVP3/mlh6vbGoML6YYW9b8TAqa0Bch23ecs/c46fGYaOLzzY9bof3ZkzHDTa7ehpmUKEb/jp3UldvLWoDuuYddiUTIFsN/383iR4NNf2Tj9gQphx0KSCy73t1w8kAWfbNrP99k7ae2zY45UzCi73rv97ODz3QO76feyuI8N+r90tU0DfU7c+1+k9RGvdfvA5exdc7kP/eDI8/I/NdU47W4ofOLo+HPOhAwou9/GbFoe7Ln94y6Zuf3H0re8TTj7/iEzvRTf+7J4t29j5/eUZ3zq24Doihuj949u3bvf3tuW+5n+ODP0H9y2o3FUvrAl/+tx1qc858dOHhaETBhUcVv27j1yV+pwYcBvPt0L9Nk+5h7x9n0zvR3++4PrUMMj5Z+wRZr+i8MDYf373trDy+U4CzLeYe/yssNfJu2Sqe9LCFWcdOiUseNOcTHVEWmDspH3GhsPftV+ma3nhtcUPjI3vyfdesfl9rjPx3u/kzxUeGPvc/UtSg1JjGOTpGQJjlz65YgcCYwsPPI7tl5su3lL35DB+TobA2FUbwi2/ui/1OfE9OUvw/B2/ezD1OcMnDs7UJrj795vr9lwGja7PFDz/4N+fSK0jYv2bJXj+8RsWp9YR8ZhlCZ6Pba60OqKlObYlCq8rYzh8Wh3RsL4x07370qdWbL3HzlVHZAmej2G8adubpX0Y22AxEH7DU1vOh5aQBB/G8Nl1yzckk58U8plX27ZXbLfH6yM+4mc78ZxLC/4t5N795afbf27QUXOHzwh3RHzdq15ck/6cDKG88d5s3fL16eVu+bxtZz9b3G7d2YrdHH6ZFoZaYYGxpcp1rbTA2JLth9IUW9LA2JIduhzlDh48OBx22GHJo7PPhH/30atTix03emwoBaHSW/ZDuV3KJcpIznct9Z79kP85Zbcv2KxEAeLlFkyeV77NbSmvOqJk+7fC6ojWcuP+GDx6QFj2zObvV2M7qWHd5pv2+Jn8oDH1O7zPTLgMlBPB8wBAWRC8AQAAoP0FAADQ05Rq8uXOwjei2MlxSoZBelDqAVtZOiV3DCLrrBNwoYFIrQMX8w0yjIFhhW5zLLepQ8BZR7HzcZZyG9e3CRjqRJ/+taG6uqrg/Zs2SHlzuX0y7eMYKpOmrr5PpkC2WG7HcLqO5RYaZpWUu3xDMiAz17lW1782UyDb2mXr24dOdbJ/Cw3jaC1308bc50QMYsoyID7uh41rc58T8ZgNGj2g8HJXbAgb2oRZbRfQV1tdcHhI66C+NUvX56x7Yj+UEVOyBb2tzDNQuRhBb7mC0zIFvT2ZPmB75LShBYcVxqC3Fx9pHwzQcR9lvQOgAACmVElEQVSPnDo007URA87SBvfG0LQs90jP3v9SaG5qyR3INn5QpnP4+YeWbg1B7KTYMGTcwExhVi88vDRsWJ37mhs0qj4JRirUi48uC2tfzj0ofsDwfmHMLiMKLnfJE8vbhSB23BH9BvUNE+aOLrjcZc+sDMueXpmr2CTYLEvgyYrnVqeGIlTXVoeZBxcevhUD2dqGZHV2Ks9+xZSC64hYty+684XU58w8dFLB13Ks0x678ZnU58w4cGJy/AoRwyc6hm913BfTFozPFBAaA8PSBn9N3ntsp+8b+dpesV5raVtHdNB3UF3yfwpte8Xworbvcx2NmT0ijN+98ICWGIgUz7dWLZ28F03Zr/Br4/Ebn0mCILeW22FnD5s4OMw6dHLB5T5123PtAmU6HsMYrLPHsTMyBac9c1fua6P/kL5hn1N3zVS3P3HT4pzBirX9asMBb56bqa5sDcNsq+06DnvnvgXXEbFOu/v3j3RS7rafD37rXsn9cKF1zy2/vC+13AVvnBMGjizsWo5BP9f98M7UMIQYKJglKPXvX7+p3QXR8Vzb86RZYVyGALl/fvfWduEvHcvd/ejpmd6PYnhl22u5o3i9ZQlFikFv7e4BO2xwrJ+yhCLd/psHk3uqbeW2Xz5u95Fh/zcUHiB3zx8XhiduXpyz3BHThibXRqHi9fbgVU9sK7bDfhg0akB45UcPzFRX3nFZ7sCwGAZ5yuezhUHG4NGtOrk8zvh24WGQMTj36m/dklruqV8qPAwyBpD96XPXd/hr+8JP+NShyXtHIRrWNuYNbcwaBvnrD/wtdaR+1jDIP3zmmtTPUOadvkfY9cjCwyCv+sbNSR1f7DDI6y+6c7v2XDHCIG+95IGShEHe/5fHwiPXPJUaKHjsRwq/lhdet2hr6HExwyDjfXspwiDjvVR830jzph8cX3C58bOIeK6lOe0rRxdcR6xbtj7849tt6p5OZKkjNm3YFK75/u0lqSOuTe5P0uuILJ+p3fyLe/PWEVmCBeP9X746Isv91INXP5G3jsgXPN/Z+K/VS9clIXwrnl2dBCJ2fD+L9+5pwfO5wjdi4HxdfXO48/KHctYRWer2Fx55OW8dkSl4/umVSbs2rY7IEjwfP5Npe9+TK3g+y2e3j8Tg+RRzT5wVQoGXRvws7bEb0j+P2O2oaQV/Bhjb9mnhoNHMQyaFkOGzurT3uChLeyB67sElqXXEhDmFf54WxfZAWmBslpD8KNY7sW2by7CJhdc70eol61I/Hx84qvDPkFrriBjumku/IYV/BxPF7+VimzmXODFOFvF7xPjdRrHDoeL3nm0/wy6mtt+fQY8jqBCokDoitsGmzhu39TvKtsGH8Tus+L3njurY9or35PFerfW7r4oL9SyWbnzdJQuVzkpg7Jb9UKrdW2HXWDcGxpZKpskIKu24hRKGdqsjdnAHZ9y/dDt1RGXqNRMR9Ly3o7LVf2jfUPtSzdb2VmyTxc9JmxqaCxoDZswXUE4EzwMAPSJ4I3aQac7Rj2X9ig3JzMjxg/hCgzc2rz/3gO3YOMwyEDwOUImDa3KWW12daRBtLHPjmtzlVlWHTAP64kDlDStzd2xq7eRV6JcdcRBivhmg46ClQmbajuLg/TUpg2ij2Cm40DCDGOqwOs8A8/rh/Qse5BnFDrap5Q7rV/DAsCh2JGw3sLqD/kP7hX4ZBoLHjnlpIQlxQGr90MLP4TjTeOOG3OXG6zfLORwHb6XNCh5DHQaPKXyAeZyNMHZUzCWGUAwZV3in1dhBMQY75FJTV52po/j6lRuSTt25xGs4Dkwt1IYYvvB8+rUxemZ5hS+8nCd8YUTG8IU4iCvN8ImDM4UvxAGvaYaOHxj6D+mXqdN8WrjO4LEDMl1zcT/E9960kIQsgyhiJ+a0jtexbi90kEprJ/94feQS3+uzhDrE83dNyjUXBw+MmTU8Ux28MmUwSRwAnWXgeuwktGzRtlCHzu57Ju01JlOdtvSJ9Gtu8n5jC64jYqfrFx7OPfglmrjXmILf7+P9VAw8STN+j9Gdhg6kie+bT9+RHhYxdtcRmd4/n7j52dRvxUbPGl7wQPDoqdufC02NueuIkVOHZHqfe+buF5L77FzidZwlDCget7RrefDYgZkGUjz/8NKw5qXc1/KAkf0zXXOxrky7B4wDrSbtPbbgcl9+akVSr6WFkE3bf0LB7a84iCLtuMVLeMCI/gV/CRbv0xa3veY6OZV3PWpqpoCWp9sOBOqk3FmHTS6vgJZ/pg/giscsW0DLY6nLJ+09JlMoUhyE2HqsOxOvixholSVIJe0ee/QuwzOFRcSBbGu2dIjNdf+X5X0uBqmk3bPGenL6ARMyhQ4sSbm3jPV6lsGN8b7yubZhER30HdQ3zHlV4cEvLz2+LCxKeZ+LbZh9Xr1rptCpx29oE0LRiXln7F5wHRHrns6CX9ra+9WzC26Hx/ehe6/IPXi0deBvoZ/5xDbMHb95sN3ftgs8OWZapvflGEySdh8x89DJmdqJt136QGow5rQFE8K43Qq/lu/6v4dT28vx/i9L2FKsK9PuseN92sxDCg9biudZ2mDMWE/ufsz0gst97N+LwrNtAs46GjJmYHIOF+rp258PT96ae4BuvFfd/42Fh1DEkJqF1zydc3kMBo2D+LPUPTGIIs0R751fcABrvEe743edD1pvdcjb9i64fR/vT266+N7U5yx489ykzVzo5yfX/vCO1OckIU6Tdz7EqbMB5lnel//1/92W+lndrkdNy3Qtx8Ce1UtyhzjNOHBScg9YqFt/dX/qPXYMUsny/hnrtOcfXJoaTBePXaHuv/Lx8PTtz6W2uQ46e6+Cy330ukWpwS/xc5lXvG9+prbnfSnvn7EN86r/PLjgcuMgq9svfSD1OSd+9vCC64jY5vr3T9qEQ3XilR87sF2bYEcmX44dENPeM6KR04aFPv1qUsM3orknzNr6umI77s8XdAyH2r5Oy9Jevvzj/0i+N9mqQ30Rg4uytGv/9Nlr2wWwdqyG9nn17EwhiH/7yo1hRcrn2PE9ee7xMzPVaS8uzH3vPuPgiWH+GXsUXO4N/+/u8PQdKSFOe40Nh75jn0z3aWnvy6NmDgvHnld4iNO9f340PaBl9IBw8vlHZKp7ShHitPjuF/KGOL3x+8cXPEZmyePLw1Xx/TPFaV8+quDP82MbJl4babIGvf3uo1enPueoDy7I9H5/+cf/mR7i9LZ9wtQMk2T85Qv/Tg3kyBr0FkMm00KcYhDQ3qcUfo9948X35AlxmhwWvKnwQNM7L3s4PH3Hc0UPenvgb4+nvt+PmjE8U2hj/FymFHVEjwx6y1BHxHbyP9qGTBYx6C1eG6UIevvX924vSR0R21z564jC+wXc8dsH8wa9DT258M9l7vvrY3nriCzfUcb3+nx1RJbg+adufS5vGGSW4PnF976Ut47IEuwVQ+fz1RFZgufjtRzvqdLE4PlCxe+V7/hd+88AO/ueoNDvNWJ/jrsuzx2c2/p5fqHfa8SQrLv/sH0Idlujpg/N9L3GPX98NLWOiOdEZ8Hz+dpeSf/ClD5UQ2urt/sOeEfaXo/f8ExqHRG3K8t3ifF7rrQ6IrYjs3x+8uz9S/IGxmZpc8V74UevX5RaR2QJno/XXLuw6g7iMckSPB/vsdM+C411RJbg+dhXNV9YYRbxO8rF976Yt99SoWLf2LaTaXQmrf9PLnGShxceWZq3PZLFS4/G6zr3tZxvcq1c4ud/af93fcoEE2lWvbAmtY5I+140X7/FtJDJ+L19FjF4NC0of+iqwu95ovh5cFpoY+xrkEX8Di2tn0icwCaL2FemIWVSrqxamppT+6RnLncHJtjbidJLVC4Ala5j/8PYV7ehsXnr+1JNn8L67ubqdxjbq30HZXtPB0qhwu4PS7W5vSbNqvv2Raagt+5Uos0tu92Q9/vzctvgbtoPZXfgulGvqSPiSZGyTeqI0u6IXlJHjN5lRBI43zH4cGsbrLYmU9srjq2PYtmxH2OXUkdU4u5l6w4u0a5w4MpyX1T1wPuIrEqWwV9hbY2STSJRYW2Nbp2Tocz2RT4tvaStke+cyNyW62F1RMlO3wqsI+Iml6Qu2cl9EY9h7KO47JlV203+1ToGLP9x3rExXwBdRfA8AFA2diR4I1eja/mzazodPBAbYXGASlV1VRIWVmgj7N4rFoZH/lX8gdUP/+upkgysjoM8UwdN1vcJp3/j2ILLff6BJSUJX4iDdUoRvhBD50sRvtC4rjH86XPXlSR84YrPX1+SgdVXfeOWkoQvXH/RXWHFs6uKHr5wy6/uL0n4wt1/WJg+sHrvseHw/9gvU4BcKeqIx29aXJI64pm7XyxJHfHSDoQvZKkjlj+7umThC1eXKHwhX6hD1jriH9++tSR1xL9/fFdJ6ohbL3mgJHVEHLheijriwb8/UZI6IgaplKKOiIFTpagjnn9wSd46YlKGOiIGsl3/4zx1xL6F1xErX1gb/v2Tu/LWEYUGz8dBvTGsMF8dUWjwfOyU1Xqfm1ZHZAmev/Fn9+StI7IEz99+6YN564gsAbf3/OnRvHVEluD5GIKdr47IEqT32PXP5K0jMoVF3PF83joiS0BfDKHNV0fE4PlC218b1zXmDc2oH96v4C/BYlhEDO1JM/vIGDwfCm4T3JknMHba/uPLK6Dl9+nljpg6JGNAy8LUOiKG22YKnv/bE6l1RBzEnzV4PjXorWVmpvupGB6Sr47IEjwf77HzhThlCZ5/4aGleYPesgTPx+v8oX88mVpHZAnOXbF4dXj4n0+mBrRkCZ6PkwWk7Ydov9Nj8Hxh5a5buTEsvC532GY094QYOlrY+33D+k2pwTpRPG6FBs83NzYn95Zppu4/PtP78uM3Lk6tI8btPipT8HwMME+rI2IAdpbg+TjRTFodEYNJsoQtxQCctDoihh7PPKTgYsPSJ1ekhgxl7TC1fPHq8MxduSd72DCj8HueaOWLa1LDi2IdkcXal9cn4fNpdUQWcaLMfKFIWcT7nucfSi83DtYoVJxoJl/YUpbAmThoJAZj5ntNJQlxahMMXejnwml1xJR5hX/G0XpvmVZHZAnEbL02Xn4694RqwycXPgletGbp+mSSlbRJrrKIAWdpE+PUZpg4NSl39cbU/Zs12Ch+hxMn2St2HRGvp7btk2LZ1NicOsFB63XZUb7Jv+IArrTJ3zYXvK3cHZ70q6Ul7wTAWYLponVJgFnuOiLv68kh7peNKcFeWcuNQXmNKZNCp022m2ZTY1PY1LCp6NdG86b0wLDmXDNy59OSfg/SUqqMMgAA6AJpba/YVot9CAtR6ITLAOWjvAYUd5syG1jdreyLLfuhm49D2bAjNu8G+2HbKWFfuDQKryM69j+ME7e3Ti7UGoS4owFMaeEb4+eMCssW5f5OtbcEtOyIcg1oyV1sue3jygpxKplS5aaVKIms24Leyky3Br1lUarzoSSlti29pYKujVBRuquOKLs6uCcGvVVYHVFup0R31RHldp+mjtgsjsfKFXwY22A70i+0s7ZXa3/oWHaufV1WdUSJdGsdUV6XXM8LjG0ps/uI7rqWMm6w+4gCdnEoLyVrL4cedh/RWz7v6cYNLqv7iIr8PKJn1RHlprvqiIpTbpVayT4Tbl9uzNmofan95F9R6xiwfGPE9TsEys3mWgwAoIwGf7UGGLUO/mrb6CpUDGRoDfgw+AsAAKB07S9fggEAAKSHb3QWmBEHcxXS0T4tfGNHJl0GAADojW2vOBlVz2p7ldmgvu5SboMbu5N9sWU/ZNt9BlbbD3R6Ydgtrg11ZRkGtJSNbqwjymk39PYQp7b9D2vrareGbsQxXNtNrtuSrd/hyKlDS7b9laTi3pYFxrbZFQJju1MZVJVlw77Ysh+6+TiUi3K4j6AHqLgbFHqsXlSlJcGHfWuSn9sGH8Y2WFPj5jZVmlxtr1hmLLur64hMb0fqnja7omsCN8udyagqVKnqCEqvwuqIfEo2mUaFncAl3dwshXdnHVFp5Vaa3rIfelgdUVIlm/i2OPeZrd+BRa1tsR0ZA1b+/Q6B3kjwPADQo4M3Wr8A61iWRhgAANDbCT4EAAAoj8m/Nqza8cm/TPoFADuotwS9dSO7Yct+qLQTokSbW2m7QR3RBbs4lFfbq6Wpk+DDLmh7lVsdkTd8QR3Ru+4jBMZ2u3KrI/JSR/SuOqIb2Q1b9kOlnRDqiPLUw4KAepUKOHYd+x+2Dd2I7akdqcfyhW9UCd8oLUFvlIsKu+0pmXK7/1NHUC7K7NLokXVEGQe9dalK295esh9K1jSqsDDI+P1OWvDhpg3pbbC0tlcsM/X7ozLbF3kJjN28G0p13CrtdCjZfqis74DLLlS6O98zeksdka9bQC+pIyrgI9Z2SjenSGVNVlJhm9sz74XL7Zwo0QZX2jkRv5Op6VOz7VG3+REnBo6P+HMWtXU1oe/AunaPfoP6bn4M7hv6DazLVm7f2jBwRP3mx8jNj0GjBmx7tGnbFKJPv5owdMLgdo9hE9s/qmuqMu2HkdOGJY9R0zc/Ju8zNgwaVR/q6vuE/kP6hro2Y8Bi38JcjPkCylFtd28AAEBng7/u/8ujyRdYrYO/Nq5t3Nroqh/Wb4d2WhwoFmdp3tbIzTb4CwAAoKcqVvurqbFpa/trZ8I3oMcpsw5T3aaMOhJCWXFpbNkPdgSoI3pHHdEavnHjz+7eOnhryRPLk5/XvLw+6cSff/BHevhGtfCN3qPnXBo7pwfVEVBUWS+NChtEUXEqbZQK2zh2W/aDk6KknGdd0vaK339V11YXt+3l2G3ZD8U7hnRC0FvlUkds2Q/dfBx6OnVE5VJHbNkP3Xwc8DErRel/+PLTq5L2VmyTNTdtHssVx3TF8JM0+cI3lj65omd9T1DywNjyqFS79S2u3E6J7gpxKrP9IDC2dT9048WhjtiyH0J5UUdUZKh0xYVBlogwyPb7oiS3ecIgK1KpL+X+Q/uG2pdqtn7n1doGa25uTh0DlqvtVT+8f2jetPnvvbqOKOGBq7g6okQExm7ZDxV23EoWIFwdkjps8yrafvfe+k+29cay6gZsDsfdWkK7r/arMk1yGP/PgOH925XTbnurqkJN3ebXU6hhEwdtHpPbYV+3/tqnf7Z4yBGTh4SNaxu2bmS74quqQv2QHRsz3NGo6UNDv0F1ne6L+OOgMdlChEfPHB7q+m9+b+p4+OM6hk8akq3cWcND1Zbw4c7ut4dPzljujOGhpalN5d7mXIhiuHIWI6cPC7sfM721sO0uwb5t9n0hhk8ZEvY8aZfWYttvdAihpk/G83fCoLDfa3dv/8fkXNhWdpZrLoY8L3jT3Pbb27bMqpCEQBcqBmgf8rZ9tt/eNvtiwIht1/qOqu1XG454z7zt/t72+hg2aXDI4qgPLthS1naFJ38bnPGaO/L98zefw1sK3rafN/9TPzRbHXH4f+yX3Jtuf7lVZT5u0SFv3zs0b2rJUUfEczhb4PqCt8wN+79xztZyO6vfs5h3+u5hv9dtvjbavc3t5PvqnFfNSB7FNv3Aicmj2MbvMSq8+guvKHq58T3hxE8fWvRy43v9q/7zoO3+/sTNz27th7hxTePWfoixb2Fsn3U8rsZ8AeVK8DwAUFGDv3I1ujqKjbDWL8CiOJtaK8EbAAAARW5/bWgKdQM2dzAQfEjv6kVXInYD5Lg2XBzqCEh7/1RHqCMqd/KvpoampJPtzoZvkEIdsWU/OEtAHQEAvbTttbqhaMGHlUzTqHU/aBw5HzpeHF19NZYnl0brfnBCOB86XhxdfTWWJ5dG635wQjgfOl4coVdr7X/41O3PJ7/X9q0JDeuad2jyrx0K36iwsMJKqyMqbHNLqmRhkBWmVGGQlca1YT90dk6oI9QRPcf2dX2m87uzcL92ubE7ERjbNoywk0o5a2Bs/04CVtsGWbYG4BZq4Kj6zYGxOe4H4z1yFjFEsm9reG6HsNjW7y+yGDJ2YKhOCWDNFVyez9AJg0LTpuaOm7n1vBg0Olso5pDxg8LYXUdu9/fWbR82MVuI59Bxg8KEuWPalNdhveO2tU8K3b+T9x3X6bK4zXGMVhaDRteH6QdsDoMcOn5QePLW55Kf4/Wy9uX1yX7OEnwYgys3rGrIEWi6dcML3t4YVrrb0dO3u87aFpXl2oiB0nueuEsnYdLbNrrfkML3cQzc3fe1u20rb7tE0+zBrkmYaWs9uzXEtPX3qjBiSrbQ4/1fv0dyzW13HW8J0B02aVDmoNTGDZs6PexxXfFczGLf1+4aGtY2thbU9p9E/wzHLdrr5F3CbkdP67ihW//p0y9btF68NnY5bPLW8jruj6wBt7OPmLr1Wt5cdPuA29b6uVDTD5wQpszrUPfsZGhuNGnvMeGN3zuutaC2/+yUGNr9xv9vS7lFFN9rTv/6MUUvN9a1p37xyFAKJ3yq+MG50SveN78k5baGgRfbXltC0Yttl8OnJI9ii9fbdtdcEYzbdWTyKLb4XpP1/SbfNbddHVwE8b591qFb6uAiipMbTC1Bn5+a2uowcc9t95XFNHb2iJKUm3Uyhx2ZNKAU+g3Kdp+QT5++pYngTSY68TFrjx8DFr8D62zyr57c7xCobILnAYAe0ejqKA4Qa/2iNnZkrK3b/OG9RhgAAEDx21/NzZs7iPoSDAAAINvkX0UJ3wAAAKDTtteqFza3p7S9AACAYtr8vU7xv6OJQWMdgy/bfocU2z1Z1PapCbUdwlTafjWVJWwz9j+MAXEbVjck29XU2JyE38UA05bmEGrqqkNVJ8FpOxK+EQPi2gaEtg3nS/7foM1BnFkCwwaO3ByC01lIX/3w/pnLHTJuW7hfx4DQPhlDR2O5wycPybm9WcX9O2rG8LabuF25Wc6JGMDXNhy03TZv+bHjebgj4rakhYNGredRoabsNy40dxIY2/pj/fB+mcttXL8p5/KsgaaT9x0bRk0fuuW37bd3xLShmcuNobHbCmy/fNS0YZnKnbjXmDBgRJvramu2YtVO7Yfxe4zaGsjbttxWAzJey2Nmjwj7nLprp+VuF4hcgJHTh4Z5p+/R6bJ47LIGHsf6oW34X2fhxFlCmmO46kFn793pstZ1ZNkXsV4/9B37blfWzh672n614Yj3zOt02dZw4knZwomPPHf/bWXlCEXO4oh3z9vaB39b+dvCR7Oew4e+fe/k/bi1nGIFth1w5tzQ1LD5vbuYwa7zztg97P3q2W3KbL+8dWx4lvDKPV45o+1mttvequps11wMUo6hsZ1Kys325jzj4Ilh2gETOt3enREDsN/8wxNCscXA2Dd891WlCYz9xrFFLzfWV6d9+ahQCqecf0RJyj32vANLUu6h79inJOXGsOpSmHv8zORRbLMOm5w8ii1ec7mC53dGvL9uvcdubmoOV3zuuq19CZdUhczBh6XqdxjbW/u1CXIvln4DY/D8rKKXG99rdt8SlF9spQjOjUpxnlVkwG3GSS125J61swlLivF+lLU9ka8dnjUMP29wbsYwfACAnj4GrOPkX8Z8AeVM8DwAUPGNro5iI6z1C7COMx4L3gAAACi8/ZVLx/aX4EMAAIDCJ/+KQRxxQuU4sVeuwR8bVjXkDd8AAKBybA6PSRugW5U9mC4lfC5r4EkssyYl3KUmYyhS/H9pYTQxLChTuX2qQ13b0KkO+mYczB3Dn/oObF/udn3YYrJegccvHreOA9e3y5HLcOxiUMSAYZ2EE7UNFcwwUDxuy6BRA/IegyyGjB2QtI9yadsXsJC2V22/mq1tqnjM+nQIuGvdDzsSfNgxgKuzboyt50X90GyBBEPGDGz3HVzHdQwYsTkgsVCDxgzoPFRwy79DxmYLeov7J4aydRqSFUL70LoCDBpVn4TI5ZJ1/8bAwIl7bgsr7ChrSFb/of1KEvTRb1BdmNrh/OtY92QJk4ivc/oBE7f7e9uis4RfVPepzhukUj8kW8DZ7FdMCaFjFVHV/pzJIm7vpg2bcu6IrMF0Mw6aGDas2tih3G0/jtklW4BLPG4x3CtXuSOmZAtwmbzfuNSwvFjnZQ2Z7Bh21PYcznotj9tt5HbXa9ty6/pnu5ZHzRwW9n/DnKK/xw2fMiQc8JY9U5+TJU8uCYM8a6/UQrJcy/0G9w2HvK1NEFm7vNiqnQqDPOyd+3a6va0/Dsv4vnHEe/YrSchk3A8x0KttWcW4Ng58y9zQ2Ob9fnP5237OGjI5//Q9QsOGxvbltjmA8X0li71O3iXsdvS09n8swjW3x7EzwsyDJ+VcnjVkcpfDpyRhv221yz3OGDI5Zf64MHa3kTnLzRoAPX7O6HDqF4/sUG7VTtcRI6cNDa/96tGpz0lrO+UycFT+MMgs7bm6AX3C67+THl6ZNZT3Df/fq7bfh53UQYUqVXjl8f91SEnKfcX75he9zPiZwVHnLtja/3Djmsat/Q9jG27MLsO3O593NHxj71NmJ49ii2GxOQNjd8KUeeOSR7HFgMlSnBPDJg4Or/xo8QNN43vY0R9cUPRy473fK97beaj0zjrk7aUJYJ1/Ruch4ztrzxOKH7bZ+v5ZCrFN27FdWwwT5oxOHsUW21vbtbmKdM3FRymCXUsRaBrDyadvCcEu9rXc8T6tGOJnzWmf9+yMcW0m0yimeK9WCm0nQSmmgRk/k8wnCcIvwSaXKtg1aaNkbKfku6eqLn6xQA8k+BAAAKB7x4B1NvlXof0OAbqS4HkAoOIbXR3FUI7WwWfJl+1bOpZqhAEAlKkM4QubVeUvttASq7IPKssnLeQjWXfGcmvqqrcfWN223IwjouJA2bQAkSwhFFFtXXWorast+sCwWGZaAECWgfZJuX1rQp/+fXY63GK7/1dXkzpor0/GwZix3L4p5cbBeVnaX/E86uzYbGpoSq61uDzLl2DxuHQMUilGHREHD9R3FqRSjICWPAN7swa0xIEfabIOXh88uj6tish8Dg8aPSC1M37WjvoxDCItUCYZXJCl3JH1yaDGtCCQLAaO7J86EGjgiGwDweN5NmJK7gElWQeux9CGEVPbl9v2bSLfdZMWOjBy2rCc5WYNh4oBTm0DcIolDngfPWv4Tr1v56qDOwbrdPacQsX6Nw4gTZM1KGv8nFGpN03x2GYN+mhYl/uaG5Dx2oiDkdOuq6yhSHGgYF3K+33WAX9xYFgcLJ3LiKnZgl+GTx4Spuw3vuh1xNDxg1IHeeZ9z07ZnmkLcg9CTLs3TBPDtToLRdpZ/QfXhRkH5Q63yHpvGeuemYekD/LMHuKUPvA3a2jP7COmpJ7DWUOcYnhI48YOIU5tDJuYbSThtAXjw/qVuevhUTPav1ftqKn7jQ/DJ+W+XkdNzzYIdOJeo5N7iWIPAk3CljqE57WVNahm9MzhYe7xuQevdwxe3FExBGvPE3cpehsxBmTFEJw0WZrL8X0oX7hFvnufzgZ+bVyzLNT2rU2WbQ4t3D58Y+2y9QVP+hXb9fuettv2C4oQyDbv9N1Tlw+fnO39c59TZ4emxs0hTsW8lucePzM0rG3MuR+GZwyd2v2Y6WHa/u3f59oevhjqmMUuh08OE+K9Wo6Cc31Pmk987xw1fVjRr+Up+45NgjFziSGfWcSAycPe1Xlg2M58PjVy+rBwxHvmFb2OGDpuYN7Qnizv9/F4x9CeNPk+V8hVXx39oQNSn5P1XvjYj6SXm/WeNQbKNKd8bpD1fe6Qt+0dmhqacp4E/TO2jQ5409zt7nvaBr3l+qwun31P2zWp1zoUvNNBqXOOm5ncAxb7M9bZh08J01LaGlnf72M7I2nXFvmz8Rj09povdQgM6xj+nDHo7bSvHJ1aTpagt/he/rqvHZP6nCyfN8fz8/Rv5gmQyxiqcca3j009Plnr91O/1D6gr1iB68d/8pDM4XNpjv5Q8cO3ooPP2Tt5FNt+r90teRTbHq+ckTyKLbbt87Xvs4jBRfmuuSziPVopwgrjZ/n5ro0s4j3NKZ8/IpTCSZ89vCjldGx7jZ09sl3w4ehdhmUOPmyrXXBuEe3/xtyBxztjr5N2CXudVPxyZ79iavIottje6tjmKudgungtj3pntnZrmvjZd7vw5yKJn/kedHabsOoiiZ9NLXjT3FBJoY3x2iiF3Y7qENBcJDMOLP5n49HkfcaGsE9pAvpKEdKXXHMpn3NkFb8viY9SBPTNPLj4IX2xzTq9BOdE/O6sFOGgsT9HKSbpiEoVMjk2z3fAWXX87r5Ysk74siP3lqUQP/vK+nlnmn4D65JHKa6NtO+Ws4pt7NqMn23lu+ZqMva1SRPvjUsR4hnv0bN+3pBP1gnTKM34L+EbAAAA2Qk+BAAAKJ/Jv1p/LnTMF0BXqWpJGykOUKYeeeSR8KlPfard3y644IIwe3b6IH+g8jxx87NbG10xIK7t4K8YNNU6+Ct2RmyKgfMtLeHlp1aGpsamrQPhY4fW2En08P/YLzXgqDNrXl4X1q/cmHN5HLCdZXDBuuUbwvqVG1IHVmcZxL9h9cawdlnucquqY3BG4YFWMSgs7os0cXsLHbgdB9mveSm93MHjBhbcyTeGX65u0xjP1fm90E7JzU3NYdWL6eXG4LS0UJ9cVj6/Ou8gryyds+N+SLvl7zuwb9Kpt1DxfGje1JI6CD1LZ/14bbRev7kGxGcJmozXRuusgLnCd7IERmxc05AakhXP3SyhbPGaa9ywKXVAfJbAsLitjetzlxtlKTdec43rcwcKtoYVFlpHxHo9X7kxfKHQD9jitdyQZz/EMLhCgybjtbZdcFEnIS5ZBi7Ejvdpuy+ew1nKbcizf5MBJxlCRNKuiygesyzlxnMtTbw2suyH5B4iJagma7nxXMv3qUumcuO25ik4S1DqjnxElDWkBehZ7a+29caLC5dtvc+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      "text/plain": [
       "<Figure size 3000x900 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 923,
       "width": 3023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_GRID_BERN = np.array([500, 1000, 2000, 4000, 8000, 16000, 32000])\n",
    "\n",
    "assurance_bern_df = assurance_curve(\n",
    "    bernoulli_assurance_at_N,\n",
    "    N_grid=N_GRID_BERN,\n",
    "    n_sims=N_SIMS,\n",
    "    rng=np.random.default_rng(RANDOM_SEED),\n",
    "    rate_prior=RATE_LIFT_PRIOR,\n",
    "    baseline_rate=BASELINE_RATE,\n",
    "    kappa=BETA_PRIOR_KAPPA,\n",
    "    threshold=DECISION_THRESHOLD,\n",
    ")\n",
    "\n",
    "\n",
    "def bernoulli_power(N, p_A, lift_alt, alpha=0.05):\n",
    "    p_B = p_A + lift_alt\n",
    "    p_bar = 0.5 * (p_A + p_B)\n",
    "    se_null = np.sqrt(2 * p_bar * (1 - p_bar) / N)\n",
    "    se_alt = np.sqrt(p_A * (1 - p_A) / N + p_B * (1 - p_B) / N)\n",
    "    z_crit = stats.norm.ppf(1 - alpha)\n",
    "    return 1.0 - stats.norm.cdf((z_crit * se_null - lift_alt) / se_alt)\n",
    "\n",
    "\n",
    "power_bern_at_prior_mean = np.array(\n",
    "    [bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu) for N in N_GRID_BERN]\n",
    ")\n",
    "power_bern_at_optimistic = np.array(\n",
    "    [\n",
    "        bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu + RATE_LIFT_PRIOR.sigma)\n",
    "        for N in N_GRID_BERN\n",
    "    ]\n",
    ")\n",
    "power_bern_at_pessimistic = np.array(\n",
    "    [\n",
    "        bernoulli_power(N, BASELINE_RATE, max(RATE_LIFT_PRIOR.mu - RATE_LIFT_PRIOR.sigma, 1e-4))\n",
    "        for N in N_GRID_BERN\n",
    "    ]\n",
    ")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 4.5))\n",
    "ax.plot(\n",
    "    N_GRID_BERN,\n",
    "    assurance_bern_df[\"assurance\"],\n",
    "    marker=\"o\",\n",
    "    linewidth=2,\n",
    "    label=\"Assurance (Bayesian)\",\n",
    ")\n",
    "ax.plot(\n",
    "    N_GRID_BERN,\n",
    "    power_bern_at_prior_mean,\n",
    "    marker=\"s\",\n",
    "    linestyle=\"--\",\n",
    "    label=r\"Power at lift $=\\mu_{\\text{prior}}$\",\n",
    ")\n",
    "ax.plot(\n",
    "    N_GRID_BERN,\n",
    "    power_bern_at_optimistic,\n",
    "    marker=\"^\",\n",
    "    linestyle=\":\",\n",
    "    alpha=0.7,\n",
    "    label=r\"Power at $\\mu + \\sigma$\",\n",
    ")\n",
    "ax.plot(\n",
    "    N_GRID_BERN,\n",
    "    power_bern_at_pessimistic,\n",
    "    marker=\"v\",\n",
    "    linestyle=\":\",\n",
    "    alpha=0.7,\n",
    "    label=r\"Power at $\\mu - \\sigma$\",\n",
    ")\n",
    "ax.axhline(\n",
    "    prior_prob_lift_positive,\n",
    "    color=\"C0\",\n",
    "    linestyle=\"-.\",\n",
    "    alpha=0.6,\n",
    "    label=rf\"Assurance ceiling $P(\\text{{lift}}>0)$ = {prior_prob_lift_positive:.2f}\",\n",
    ")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n",
    "ax.set_xlabel(\"Sample size per arm\")\n",
    "ax.set_ylabel(\"Probability of declaring uplift\")\n",
    "ax.set_title(\"Assurance vs frequentist power, Bernoulli outcome\")\n",
    "ax.legend(loc=\"lower right\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45306fae",
   "metadata": {},
   "source": [
    "The conversion-rate version runs the same loop, and the loop discloses something the Gaussian case conceals. The lift is bounded above: how large a positive effect can even be depends on how much room sits above the baseline conversion rate, a constraint the Normal likelihood never faces. The Beta prior on the per-arm rates is parameterised here by a concentration $\\kappa$, the number of pseudo-observations at the baseline rate that the prior is equivalent to. Setting $\\kappa = 200$ is saying: I am as confident about the baseline as if I had watched 200 trials at that rate. This is a different handle on prior calibration than the Normal's mean and standard deviation pair, and it makes the ceiling claim more precise: the assurance curve asymptotes toward the prior probability that the lift is positive, and what that probability is depends not only on the prior's location and scale but on the scale on which the lift is defined. At a 10\\% baseline with a planning prior mean of 0.5\\%, the prior splits its mass roughly two to one in favour of a positive lift, and the assurance curve asymptotes there, near 0.66. The same machinery produces a lower ceiling than the Gaussian case because the planning prior commits to a more cautious belief about how large a conversion lift can plausibly be. The generative model produced the synthetic experiments; the conjugate Beta posterior supplied the decision, with no MCMC in the loop. We confirm below that this matches a full PyMC fit on a single dataset, so nothing in the assurance machinery depends on the closed form being available; it depends only on a posterior we can compute reliably."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "67f5d44e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:13.438114Z",
     "iopub.status.busy": "2026-06-01T17:16:13.438020Z",
     "iopub.status.idle": "2026-06-01T17:16:16.115505Z",
     "shell.execute_reply": "2026-06-01T17:16:16.115030Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [n_A, n_B]\n",
      "NUTS[nutpie]: [p_A, p_B]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x35447ae90>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x535.887 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 559,
       "width": 1223
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bernoulli_two_arm_model(n_A, n_B, N, baseline_rate, kappa):\n",
    "    alpha0, beta0 = beta_prior_params(baseline_rate, kappa)\n",
    "    with pm.Model() as model:\n",
    "        p_A = pm.Beta(\"p_A\", alpha=alpha0, beta=beta0)\n",
    "        p_B = pm.Beta(\"p_B\", alpha=alpha0, beta=beta0)\n",
    "        pm.Deterministic(\"lift\", p_B - p_A)\n",
    "        pm.Binomial(\"obs_A\", n=N, p=p_A, observed=n_A)\n",
    "        pm.Binomial(\"obs_B\", n=N, p=p_B, observed=n_B)\n",
    "    return model\n",
    "\n",
    "\n",
    "demo_model_bern = pm.do(\n",
    "    bernoulli_generative_model(N=4000, rate_prior=RATE_LIFT_PRIOR, baseline_rate=BASELINE_RATE),\n",
    "    {\"lift\": 0.015},\n",
    ")\n",
    "demo_draw_bern = pm.sample_prior_predictive(1, model=demo_model_bern, random_seed=RANDOM_SEED)\n",
    "n_A_demo = int(demo_draw_bern.prior[\"n_A\"].values.reshape(-1)[0])\n",
    "n_B_demo = int(demo_draw_bern.prior[\"n_B\"].values.reshape(-1)[0])\n",
    "\n",
    "with bernoulli_two_arm_model(\n",
    "    n_A_demo, n_B_demo, N=4000, baseline_rate=BASELINE_RATE, kappa=BETA_PRIOR_KAPPA\n",
    "):\n",
    "    idata_bern_demo = pm.sample(\n",
    "        draws=1000,\n",
    "        tune=1000,\n",
    "        target_accept=0.95,\n",
    "        random_seed=RANDOM_SEED,\n",
    "        progressbar=False,\n",
    "    )\n",
    "\n",
    "pc = az.plot_dist(\n",
    "    idata_bern_demo,\n",
    "    var_names=[\"lift\"],\n",
    "    visuals={\"title\": {\"text\": r\"Posterior on conversion lift at $N=4000$\"}},\n",
    ")\n",
    "az.add_lines(\n",
    "    pc,\n",
    "    values=0.0,\n",
    "    visuals={\"ref_line\": {\"color\": \"C1\", \"label\": \"ref = 0.0\"}},\n",
    ")\n",
    "pc.get_viz(\"plot\").legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "005827fd",
   "metadata": {},
   "source": [
    "The PyMC posterior on lift agrees with the conjugate Beta posterior, as it must under this setup. The decision rule is the same, and the ceiling is lower because the planning prior carries a smaller probability that the lift is positive. That prior probability sets the asymptote that no sample size can exceed.\n",
    "\n",
    "## The cost of an under-informed prior\n",
    "\n",
    "The assurance curve is conditional on the prior. A tightly informative prior centred near the truth produces an optimistic-looking curve; a flat prior produces a curve that requires substantially more data to reach the same assurance. Neither is wrong. They report what each prior commitment buys the planner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "279cd463",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-01T17:16:16.117411Z",
     "iopub.status.busy": "2026-06-01T17:16:16.117300Z",
     "iopub.status.idle": "2026-06-01T17:16:23.592971Z",
     "shell.execute_reply": "2026-06-01T17:16:23.592185Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3000x900 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 923,
       "width": 3023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "INFORMED_PRIOR = EffectPrior(mu=0.4, sigma=0.3)\n",
    "FLAT_PRIOR = EffectPrior(mu=0.4, sigma=1.5)\n",
    "SCEPTICAL_PRIOR = EffectPrior(mu=0.1, sigma=0.5)\n",
    "\n",
    "prior_comparison = {}\n",
    "for name, prior in [\n",
    "    (\"Informed\", INFORMED_PRIOR),\n",
    "    (\"Flat\", FLAT_PRIOR),\n",
    "    (\"Sceptical\", SCEPTICAL_PRIOR),\n",
    "]:\n",
    "    df = assurance_curve(\n",
    "        gaussian_assurance_at_N,\n",
    "        N_grid=N_GRID,\n",
    "        n_sims=N_SIMS,\n",
    "        rng=np.random.default_rng(RANDOM_SEED),\n",
    "        prior=prior,\n",
    "        sigma_obs=SIGMA_OBS,\n",
    "        threshold=DECISION_THRESHOLD,\n",
    "    )\n",
    "    prior_comparison[name] = df\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 4.5))\n",
    "for name, df in prior_comparison.items():\n",
    "    ax.plot(df[\"N\"], df[\"assurance\"], marker=\"o\", linewidth=2, label=name)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n",
    "ax.set_xlabel(\"Sample size per arm\")\n",
    "ax.set_ylabel(\"Assurance\")\n",
    "ax.set_title(\"Assurance under three prior commitments\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84fb1b32",
   "metadata": {},
   "source": [
    "## Design prior and analysis prior\n",
    "\n",
    "The assurance loop carries two priors with distinct jobs. The *design prior* generates the synthetic worlds the experiment will face. The *analysis prior* reads each dataset and forms the posterior the decision rule consults. Every curve so far set the two equal. Separating them measures a sensitivity the FDA guidance asks for directly: how the operating characteristics respond when the inference commitment disagrees with the planning belief {cite:p}`fda2026bayesian`. The generative model already carries the design prior and the inference model the analysis prior, so the loop runs the mismatch with one extra argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "142452a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n",
      "Sampling: [delta, y_A, y_B]\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x900 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 923,
       "width": 3023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "OPTIMISTIC_DESIGN = EffectPrior(mu=0.6, sigma=0.4)\n",
    "SCEPTICAL_ANALYSIS = EffectPrior(mu=0.0, sigma=0.3)\n",
    "\n",
    "design_analysis_cases = {\n",
    "    \"Matched (design = analysis)\": (OPTIMISTIC_DESIGN, OPTIMISTIC_DESIGN),\n",
    "    \"Optimistic design, sceptical analysis\": (OPTIMISTIC_DESIGN, SCEPTICAL_ANALYSIS),\n",
    "    \"Sceptical design, optimistic analysis\": (SCEPTICAL_ANALYSIS, OPTIMISTIC_DESIGN),\n",
    "}\n",
    "\n",
    "design_analysis_curves = {}\n",
    "for name, (design_prior, analysis_prior) in design_analysis_cases.items():\n",
    "    design_analysis_curves[name] = assurance_curve(\n",
    "        gaussian_assurance_at_N,\n",
    "        N_grid=N_GRID,\n",
    "        n_sims=N_SIMS,\n",
    "        rng=np.random.default_rng(RANDOM_SEED),\n",
    "        prior=design_prior,\n",
    "        analysis_prior=analysis_prior,\n",
    "        sigma_obs=SIGMA_OBS,\n",
    "        threshold=DECISION_THRESHOLD,\n",
    "    )\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 4.5))\n",
    "for name, df in design_analysis_curves.items():\n",
    "    ax.plot(df[\"N\"], df[\"assurance\"], marker=\"o\", linewidth=2, label=name)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n",
    "ax.set_xlabel(\"Sample size per arm\")\n",
    "ax.set_ylabel(\"Assurance\")\n",
    "ax.set_title(\"Assurance when the design and analysis priors agree or disagree\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ff8d8a",
   "metadata": {},
   "source": [
    "A sceptical analysis prior lowers assurance at every sample size, because it discounts the same evidence the optimistic design prior expects to see. The reverse pairing recovers most of the matched curve once the data accumulate, since an optimistic analysis prior and a growing dataset agree. The gap between the curves is the price of a mismatch, and it narrows as $N$ grows. Small experiments pay the most for an analysis prior that disagrees with the design belief, which matches the guidance observation that trial characteristics are most sensitive to the analysis prior when the sample size is small {cite:p}`fda2026bayesian`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb131822",
   "metadata": {},
   "source": [
    "## The information content of a prior: effective sample size\n",
    "\n",
    "The three curves above differ because the three priors carry different amounts of information. The *prior effective sample size* (ESS) makes this precise: it is the number of actual experimental observations the prior is equivalent to in terms of information content. A prior with ESS of 128 is, before the first participant is enrolled, already as informative as 128 observed subjects per arm.\n",
    "\n",
    "For the two-arm Gaussian trial the ESS follows from equating information in the prior with information from $n$ observations. The prior $\\mathcal{N}(\\mu_0, \\sigma_0^2)$ carries information $1/\\sigma_0^2$; the effect estimate from $n$ observations carries $n / 2\\sigma_{\\text{obs}}^2$. Setting them equal:\n",
    "\n",
    "$$n_{\\text{ESS}} = \\frac{2\\sigma_{\\text{obs}}^2}{\\sigma_0^2}$$\n",
    "\n",
    "The simulation-based approach recovers the same number without the closed form. For each $N$ in a grid, draw synthetic datasets from the prior predictive and compute the posterior variance under a flat reference prior; the $N^*$ where the average posterior variance crosses the prior variance is the ESS. The machinery is the same prior-predictive loop already running in the assurance calculation; only the inner step changes. In the conjugate case the analytical posterior fills that step. In non-conjugate models such as hierarchical likelihoods or logistic regression, the same loop runs with MCMC posteriors and the ESS estimate generalises without modification. Verifying that analytical and simulation estimates agree for the Gaussian case validates the approach for those more complex settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8518b730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prior_mu</th>\n",
       "      <th>prior_sigma</th>\n",
       "      <th>analytical_ESS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Informed</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>355.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Default</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>128.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Flat</th>\n",
       "      <td>0.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>14.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sceptical</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>128.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           prior_mu  prior_sigma  analytical_ESS\n",
       "Informed        0.4          0.3           355.6\n",
       "Default         0.4          0.5           128.0\n",
       "Flat            0.4          1.5            14.2\n",
       "Sceptical       0.1          0.5           128.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def analytical_ess(prior, sigma_obs):\n",
    "    \"\"\"Prior ESS for a two-arm Gaussian trial: 2σ²_obs / σ²_prior.\"\"\"\n",
    "    return 2 * sigma_obs**2 / prior.sigma**2\n",
    "\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        \"prior_mu\": [p.mu for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]],\n",
    "        \"prior_sigma\": [\n",
    "            p.sigma for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]\n",
    "        ],\n",
    "        \"analytical_ESS\": [\n",
    "            analytical_ess(p, SIGMA_OBS)\n",
    "            for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]\n",
    "        ],\n",
    "    },\n",
    "    index=[\"Informed\", \"Default\", \"Flat\", \"Sceptical\"],\n",
    ").round(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c1190134",
   "metadata": {},
   "outputs": [
    {
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     "output_type": "stream",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prior_sigma</th>\n",
       "      <th>analytical_ESS</th>\n",
       "      <th>simulation_ESS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Informed</th>\n",
       "      <td>0.3</td>\n",
       "      <td>355.6</td>\n",
       "      <td>357.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Default</th>\n",
       "      <td>0.5</td>\n",
       "      <td>128.0</td>\n",
       "      <td>128.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Flat</th>\n",
       "      <td>1.5</td>\n",
       "      <td>14.2</td>\n",
       "      <td>14.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sceptical</th>\n",
       "      <td>0.5</td>\n",
       "      <td>128.0</td>\n",
       "      <td>128.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "           prior_sigma  analytical_ESS  simulation_ESS\n",
       "Informed           0.3           355.6           357.1\n",
       "Default            0.5           128.0           128.1\n",
       "Flat               1.5            14.2            14.3\n",
       "Sceptical          0.5           128.0           128.1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulation_based_ess(prior, sigma_obs, N_grid, n_sims, rng):\n",
    "    \"\"\"\n",
    "    Estimate prior ESS via simulation: find N* where the mean posterior variance\n",
    "    under a flat reference prior crosses the prior variance.\n",
    "\n",
    "    Uses the same prior-predictive sampling as the assurance loop. Replace\n",
    "    gaussian_posterior_delta with an MCMC posterior to extend to non-conjugate models.\n",
    "    \"\"\"\n",
    "    flat_ref = EffectPrior(mu=0.0, sigma=10 * sigma_obs)\n",
    "    target_var = prior.sigma**2\n",
    "    records = []\n",
    "    for N in N_grid:\n",
    "        N = int(N)\n",
    "        seed = int(rng.integers(2**31 - 1))\n",
    "        pp = pm.sample_prior_predictive(\n",
    "            n_sims, model=gaussian_generative_model(N, prior), random_seed=seed\n",
    "        )\n",
    "        y_A = pp.prior[\"y_A\"].values.reshape(n_sims, N)\n",
    "        y_B = pp.prior[\"y_B\"].values.reshape(n_sims, N)\n",
    "        d_hat = y_B.mean(axis=1) - y_A.mean(axis=1)\n",
    "        _, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, flat_ref)\n",
    "        records.append({\"N\": N, \"mean_post_var\": float(np.mean(post_sd**2))})\n",
    "    df = pd.DataFrame(records)\n",
    "    post_vars = df[\"mean_post_var\"].values\n",
    "    N_vals = df[\"N\"].values.astype(float)\n",
    "    # post_var decreases with N; interpolate to find where it crosses the prior variance\n",
    "    ess_sim = float(np.interp(target_var, post_vars[::-1], N_vals[::-1]))\n",
    "    return ess_sim, df\n",
    "\n",
    "\n",
    "N_ESS_GRID = np.unique(np.round(np.geomspace(10, 600, 30)).astype(int))\n",
    "N_ESS_SIMS = 200\n",
    "ess_rng = np.random.default_rng(RANDOM_SEED + 99)\n",
    "\n",
    "ess_results = {}\n",
    "for name, prior in [\n",
    "    (\"Informed\", INFORMED_PRIOR),\n",
    "    (\"Default\", EFFECT_PRIOR),\n",
    "    (\"Flat\", FLAT_PRIOR),\n",
    "    (\"Sceptical\", SCEPTICAL_PRIOR),\n",
    "]:\n",
    "    ess_a = analytical_ess(prior, SIGMA_OBS)\n",
    "    ess_s, df_curve = simulation_based_ess(prior, SIGMA_OBS, N_ESS_GRID, N_ESS_SIMS, ess_rng)\n",
    "    ess_results[name] = {\n",
    "        \"prior\": prior,\n",
    "        \"ess_analytical\": ess_a,\n",
    "        \"ess_sim\": ess_s,\n",
    "        \"curve\": df_curve,\n",
    "    }\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        \"prior_sigma\": {n: v[\"prior\"].sigma for n, v in ess_results.items()},\n",
    "        \"analytical_ESS\": {n: round(v[\"ess_analytical\"], 1) for n, v in ess_results.items()},\n",
    "        \"simulation_ESS\": {n: round(v[\"ess_sim\"], 1) for n, v in ess_results.items()},\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "839ea69e",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 4000x1000 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1023,
       "width": 4023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(20, 5))\n",
    "\n",
    "# Left: ESS crossing picture for the default prior\n",
    "res = ess_results[\"Default\"]\n",
    "curve = res[\"curve\"]\n",
    "prior_d = res[\"prior\"]\n",
    "ess_a_d = res[\"ess_analytical\"]\n",
    "ess_s_d = res[\"ess_sim\"]\n",
    "\n",
    "axes[0].plot(\n",
    "    curve[\"N\"],\n",
    "    curve[\"mean_post_var\"],\n",
    "    marker=\"o\",\n",
    "    color=\"C0\",\n",
    "    markersize=4,\n",
    "    label=\"Mean posterior variance (flat prior)\",\n",
    ")\n",
    "axes[0].axhline(\n",
    "    prior_d.sigma**2,\n",
    "    color=\"C3\",\n",
    "    linestyle=\"--\",\n",
    "    label=rf\"Prior variance $\\sigma_0^2$ = {prior_d.sigma**2:.2f}\",\n",
    ")\n",
    "axes[0].axvline(\n",
    "    ess_a_d,\n",
    "    color=\"C2\",\n",
    "    linestyle=\":\",\n",
    "    linewidth=2,\n",
    "    label=f\"Analytical ESS = {ess_a_d:.0f}\",\n",
    ")\n",
    "axes[0].axvline(\n",
    "    ess_s_d,\n",
    "    color=\"C3\",\n",
    "    linestyle=\":\",\n",
    "    linewidth=2,\n",
    "    alpha=0.7,\n",
    "    label=f\"Simulation ESS ≈ {ess_s_d:.0f}\",\n",
    ")\n",
    "axes[0].set_xlabel(\"N per arm\")\n",
    "axes[0].set_ylabel(\"Mean posterior variance under flat prior\")\n",
    "axes[0].set_title(r\"ESS crossing: default prior ($\\sigma_0 = 0.5$)\")\n",
    "axes[0].legend()\n",
    "\n",
    "# Right: assurance curves with ESS positions annotated\n",
    "for name in [\"Informed\", \"Flat\", \"Sceptical\"]:\n",
    "    res = ess_results[name]\n",
    "    df = prior_comparison[name]\n",
    "    ess_a = res[\"ess_analytical\"]\n",
    "    axes[1].plot(\n",
    "        df[\"N\"],\n",
    "        df[\"assurance\"],\n",
    "        marker=\"o\",\n",
    "        linewidth=2,\n",
    "        label=f\"{name} (ESS ≈ {ess_a:.0f})\",\n",
    "    )\n",
    "    axes[1].axvline(ess_a, linestyle=\":\", alpha=0.35)\n",
    "\n",
    "axes[1].set_xscale(\"log\")\n",
    "axes[1].xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n",
    "axes[1].set_xlabel(\"Sample size per arm\")\n",
    "axes[1].set_ylabel(\"Assurance\")\n",
    "axes[1].set_title(\"Assurance curves with ESS marked\")\n",
    "axes[1].legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95945bca",
   "metadata": {},
   "source": [
    "The left panel is a calibration check. The simulation curve, posterior variance under a flat prior as a function of N, crosses the prior variance at the point the analytical formula predicts. The two estimates agree to within interpolation noise. For non-conjugate models where no closed form for the posterior variance exists, the same loop with MCMC posteriors in place of `gaussian_posterior_delta` gives the correct ESS. The conjugate case validates the simulation approach before the closed form disappears.\n",
    "\n",
    "The right panel reads the ESS against the assurance curves. The dotted vertical lines mark each prior's ESS on the sample-size axis. An ESS of 356 (Informed) means the prior carries more information than 350 subjects per arm before the first participant is enrolled; the curve climbs steeply early because the prior is already doing most of the work. An ESS of 14 (Flat) means the prior contributes almost nothing, and every observation earns its full weight. The ESS converts the abstract question \"how informative is this prior?\" into a number on the same axis as the assurance curve: experiments whose planned N falls well below the ESS are prior-dominated; those well above it are data-dominated.\n",
    "\n",
    "This is the quantitative form of the trade-off the sensitivity analysis in {ref}`sensitivity_confounding` interrogates from the other side. There, the question is what happens when that committed information meets an identification gap, and the tipping point at which the conclusion turns measures how much that committed ESS has put at risk."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fda04dc5",
   "metadata": {},
   "source": [
    "The three curves disagree most where they should: at small sample sizes where the data has not yet overwhelmed the prior. The informed prior reaches high assurance fastest because it is willing to commit to a narrow effect range; the sceptical prior assumes a smaller effect and so needs more data to detect it; the flat prior carries enough probability mass over zero that even moderate datasets do not push the posterior reliably above the decision threshold. The point is to make the dependence of the assurance number on the prior commitment visible, so the prior becomes a subject of negotiation rather than a hidden choice.\n",
    "\n",
    "## Planning as a posterior over future posteriors\n",
    "\n",
    "The experiment we have not yet run is a posterior we have not yet computed. What we have is a prior, a model, and the patience to ask what the experiment will likely say.\n",
    "\n",
    "Statistical power questions answers a conditional: given a specific effect, what probability of detection? Bayesian assurance answers a marginal question: given everything currently believed, what probability that the inference about to be drawn will be useful? The operation that produces assurance is the same one that will produce the posterior at the end of the experiment - only the data are still hypothetical. Assurance makes explicit the assumption power leaves buried, a believed distribution of effects, and derives from that assumption a posterior to evaluate.\n",
    "\n",
    "The Gaussian case and the Bernoulli case ran the same inference machinery. What changed was the likelihood, and with it the ceiling its geometry sets on how much assurance any sample size can buy. The next notebook, {ref}`sensitivity_confounding`, keeps the machinery and changes the question: not what an experiment will probably say, but what it did say once clean identification is itself in doubt.\n",
    "\n",
    "## Authors\n",
    "\n",
    "- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026.\n",
    "\n",
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames\n",
    ":::\n",
    "\n",
    "## Watermark"
   ]
  },
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     "shell.execute_reply": "2026-06-01T17:16:23.604855Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Mon, 29 Jun 2026\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.13\n",
      "IPython version      : 9.14.0\n",
      "\n",
      "pytensor: 3.0.3\n",
      "xarray  : 2026.4.0\n",
      "\n",
      "arviz     : 1.1.0\n",
      "matplotlib: 3.10.9\n",
      "numpy     : 2.3.5\n",
      "pandas    : 2.3.3\n",
      "pymc      : 6.0.1\n",
      "scipy     : 1.17.1\n",
      "\n",
      "Watermark: 2.6.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pytensor,xarray"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbbeeb58",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
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