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    "(sensitivity_confounding)=\n",
    "# Sensitivity Analysis for Unmeasured Confounding\n",
    "\n",
    ":::{post} May 2026\n",
    ":tags: experimentation, sensitivity analysis, causal inference, confounding, robustness\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:* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis (this notebook):* 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",
    "All applied inference is argument. Against every experiment you can set the contention that the working conditions were imperfect. Some aspect of the evaluation was flawed. Maybe treatment assignment introduced a subtle kind of bias, or the subjects didn't comply fully with the design. Against every experiment you can contrast the scientific ideal of perfect randomisation and clear adherence. Holding an experiment against that ideal is due diligence. Sensitivity analysis does it systematically, by varying how far the working conditions fall short of perfect randomisation.\n",
    "\n",
    "## The randomisation gap\n",
    "\n",
    "Randomisation is an assumption you maintain by design, not a fact you assert by intention. The checkout experiment ran, the headline effect on revenue-per-visitor looks positive, and somewhere in the diagnostic notes there is a line about compliance being 73%: users on slow connections were silently routed back to the old flow by a CDN edge case, and the routing was not random in the way it touched the population. The intent-to-treat estimate now depends on a counterfactual the experiment did not produce: what those users would have done under the new flow. Without further assumptions, the data cannot say what the treatment effect would have been if randomisation had held.\n",
    "\n",
    "This notebook develops the Bayesian response to this situation. Where Rosenbaum's $\\Gamma$ {cite:p}`rosenbaum2002observational` and the E-value {cite:p}`vanderweele2017sensitivity` give point summaries of how strong an unmeasured confounder would need to be to nullify the result, the Bayesian framing makes the same unmeasured confounder a *parameter* in the model, with a prior over its plausible strength and a posterior shaped by both the data and the analyst's commitments {cite:p}`imbens2003sensitivity`, {cite:p}`cinellihazlett2020omitted`. We develop the machinery on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the second of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The clean primary analysis of a well-run experiment, the posterior on the effect with the decision rule applied, appears as the demonstration step in {ref}`assurance_planning`; this notebook takes up the interpretation once that clean identification is itself in question.\n",
    "\n",
    ":::{admonition} Where this lands in regulatory practice\n",
    ":class: note\n",
    "\n",
    "The sensitivity construction here follows the regulatory recommendation directly. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials describes sensitivity analysis as varying the prior over a critical assumption, and notes that \"some approaches can build uncertainty about specific assumptions into the prior itself\" {cite:p}`fda2026bayesian`, which is the move made below. The guidance goes further and sanctions modelling a discrepancy between data sources with \"an assumed bias parameter in the model\", the exact object this notebook places a prior on and sweeps. The clinical-trial setting differs from a product quasi-experiment; the bias parameter is the same.\n",
    ":::"
   ]
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   "id": "3abbded2",
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    "execution": {
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     "iopub.status.busy": "2026-06-02T17:35:59.159124Z",
     "iopub.status.idle": "2026-06-02T17:36:01.747061Z",
     "shell.execute_reply": "2026-06-02T17:36:01.746567Z"
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   "source": [
    "import warnings\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)"
   ]
  },
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   "execution_count": 2,
   "id": "f669edc2",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-06-02T17:36:02.092571Z"
    }
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   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "az.style.use(\"arviz-variat\")\n",
    "rng = np.random.default_rng(7)\n",
    "RANDOM_SEED = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31dda6b3",
   "metadata": {},
   "source": [
    "## What the data can and cannot say\n",
    "\n",
    "The structural picture is small and the notation traditional. Let $T$ be the observed treatment indicator (which flow the visitor actually saw), let $Y$ be the outcome (revenue), and let $U$ be an unmeasured user characteristic: connection quality, engagement disposition, whatever drives the differential compliance. Under randomisation $U$ is independent of $T$ by construction; under compliance failure $U$ is associated with $T$ and unobservable."
   ]
  },
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   "id": "dc1a9456",
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     "shell.execute_reply": "2026-06-02T17:36:02.928074Z"
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    "tags": [
     "hide-input"
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      "text/plain": [
       "<Figure size 3000x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 723,
       "width": 3023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 3.5))\n",
    "ax.set_xlim(0, 10)\n",
    "ax.set_ylim(0, 5)\n",
    "ax.axis(\"off\")\n",
    "\n",
    "nodes = {\"T\": (2, 1.5), \"Y\": (8, 1.5), \"U\": (5, 4)}\n",
    "for name, (x, y) in nodes.items():\n",
    "    ax.scatter(x, y, s=2200, facecolor=\"white\", edgecolor=\"black\", zorder=3)\n",
    "    ax.text(x, y, name, ha=\"center\", va=\"center\", fontsize=16, zorder=4)\n",
    "\n",
    "\n",
    "def arrow(a, b, **kw):\n",
    "    (x0, y0), (x1, y1) = nodes[a], nodes[b]\n",
    "    ax.annotate(\n",
    "        \"\",\n",
    "        xy=(x1, y1),\n",
    "        xytext=(x0, y0),\n",
    "        arrowprops=dict(arrowstyle=\"->\", lw=2, shrinkA=22, shrinkB=22, **kw),\n",
    "    )\n",
    "\n",
    "\n",
    "arrow(\"T\", \"Y\")\n",
    "arrow(\"U\", \"T\", color=\"firebrick\")\n",
    "arrow(\"U\", \"Y\", color=\"firebrick\")\n",
    "\n",
    "ax.text(5, 1.8, r\"$\\tau$ (causal effect)\", ha=\"center\", fontsize=11)\n",
    "ax.text(3.2, 3.3, r\"$\\lambda_T$\", color=\"firebrick\", fontsize=12)\n",
    "ax.text(6.8, 3.3, r\"$\\lambda_Y$\", color=\"firebrick\", fontsize=12)\n",
    "ax.set_title(\"The identification gap: $U$ unobserved\", fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8f31fe6",
   "metadata": {},
   "source": [
    "What we want is $\\tau$, the causal effect of $T$ on $Y$. What the data identify is $\\tau$ *plus* the contribution of any path that flows through $U$: the product of the two red edges, collected into a single bias term $\\beta = \\lambda_T \\cdot \\lambda_Y / \\mathrm{var}(T)$ at the scale of the observed difference in means {cite:p}`hernan2020whatif`, {cite:p}`cunningham2021causal`. The naïve estimator returns $\\tau + \\beta$. The data are silent on the decomposition; the prior is what sets it.\n",
    "\n",
    "## The bias parameter\n",
    "\n",
    "The Bayesian sensitivity analysis makes $\\beta$ a model parameter with a prior. The data inform the sum $\\tau + \\beta$ through the observed difference; the prior on $\\beta$ controls how much of that sum is attributed to the unmeasured confounder rather than to the treatment. Three prior commitments:\n",
    "\n",
    "- **Dismissive prior** ($\\beta \\sim \\mathcal{N}(0, 0.05)$): \"I am confident there is essentially no confounding.\"\n",
    "- **Moderate prior** ($\\beta \\sim \\mathcal{N}(0, 0.3)$): \"I will allow that confounding may have shifted the apparent effect by up to a few tenths of a revenue unit.\"\n",
    "- **Sceptical prior** ($\\beta \\sim \\mathcal{N}(0, 0.7)$): \"I will not commit to confounding being small; the data must speak loudly to be heard.\"\n",
    "\n",
    "Each is an auditable commitment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9d37c3cd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:02.930162Z",
     "iopub.status.busy": "2026-06-02T17:36:02.929961Z",
     "iopub.status.idle": "2026-06-02T17:36:02.933311Z",
     "shell.execute_reply": "2026-06-02T17:36:02.932936Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed difference d_hat = 0.793 (sampling SE = 0.089)\n",
      "True tau = 0.3, true bias = 0.5, true sum = 0.8\n"
     ]
    }
   ],
   "source": [
    "N = 4000\n",
    "TRUE_TAU = 0.30\n",
    "TRUE_BIAS = 0.50\n",
    "SIGMA_OBS = 4.0\n",
    "\n",
    "\n",
    "def simulate_quasi_experimental_gaussian(N, true_tau, true_bias, sigma_obs, rng):\n",
    "    baseline = 10.0\n",
    "    y_A = rng.normal(baseline, sigma_obs, size=N)\n",
    "    y_B = rng.normal(baseline + true_tau + true_bias, sigma_obs, size=N)\n",
    "    return y_A, y_B\n",
    "\n",
    "\n",
    "y_A_obs, y_B_obs = simulate_quasi_experimental_gaussian(N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, rng)\n",
    "d_hat = y_B_obs.mean() - y_A_obs.mean()\n",
    "sigma_d = np.sqrt(2 * SIGMA_OBS**2 / N)\n",
    "print(f\"Observed difference d_hat = {d_hat:.3f} (sampling SE = {sigma_d:.3f})\")\n",
    "print(f\"True tau = {TRUE_TAU}, true bias = {TRUE_BIAS}, true sum = {TRUE_TAU + TRUE_BIAS}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba7bfe6c",
   "metadata": {},
   "source": [
    "The observed difference recovers the *biased* effect, as it must. $\\tau$ is what we want; $\\beta$ is what we cannot observe. Before asking how a prior reshapes that sum, confirm the machinery is faithful: hand the model the belief an analyst would hold if they knew the confounder exactly, a prior on $\\beta$ centred at the true bias, and the treatment effect should return unbiased across repeated experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "39981d0f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:02.935072Z",
     "iopub.status.busy": "2026-06-02T17:36:02.934958Z",
     "iopub.status.idle": "2026-06-02T17:36:03.173574Z",
     "shell.execute_reply": "2026-06-02T17:36:03.173186Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 4000x800 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 823,
       "width": 4023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gaussian_sensitivity_posterior(\n",
    "    d_hat, sigma_d, tau_prior_sd, bias_prior_sd, tau_prior_mean=0.0, bias_prior_mean=0.0\n",
    "):\n",
    "    \"\"\"Closed-form posterior over (tau, beta) given the observed effect.\"\"\"\n",
    "    prior_precision = np.diag([1.0 / tau_prior_sd**2, 1.0 / bias_prior_sd**2])\n",
    "    F = np.array([[1.0, 1.0]])\n",
    "    data_precision = F.T @ F / sigma_d**2\n",
    "    post_precision = prior_precision + data_precision\n",
    "    post_cov = np.linalg.inv(post_precision)\n",
    "    prior_mean = np.array([tau_prior_mean, bias_prior_mean])\n",
    "    rhs = prior_precision @ prior_mean + F.flatten() * d_hat / sigma_d**2\n",
    "    post_mean = post_cov @ rhs\n",
    "    return post_mean, post_cov\n",
    "\n",
    "\n",
    "# Across many synthetic quasi-experiments, where does the posterior mean of tau land\n",
    "# when the analyst's prior on the bias is centred at the true confounding strength?\n",
    "recovery_rng = np.random.default_rng(RANDOM_SEED)\n",
    "n_recovery = 500\n",
    "tau_posterior_means = np.empty(n_recovery)\n",
    "for i in range(n_recovery):\n",
    "    y_A_i, y_B_i = simulate_quasi_experimental_gaussian(\n",
    "        N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, recovery_rng\n",
    "    )\n",
    "    d_hat_i = y_B_i.mean() - y_A_i.mean()\n",
    "    post_mean_i, _ = gaussian_sensitivity_posterior(\n",
    "        d_hat_i, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.1, bias_prior_mean=TRUE_BIAS\n",
    "    )\n",
    "    tau_posterior_means[i] = post_mean_i[0]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20, 4))\n",
    "ax.hist(tau_posterior_means, bins=30, color=\"C0\", alpha=0.7, edgecolor=\"white\")\n",
    "ax.axvline(TRUE_TAU, color=\"C2\", linestyle=\"--\", linewidth=2, label=f\"true \\u03c4 = {TRUE_TAU:.2f}\")\n",
    "ax.axvline(\n",
    "    tau_posterior_means.mean(),\n",
    "    color=\"C3\",\n",
    "    linewidth=2,\n",
    "    label=f\"mean estimate = {tau_posterior_means.mean():.3f}\",\n",
    ")\n",
    "ax.set_xlabel(r\"Posterior mean of $\\tau$ across simulated experiments\")\n",
    "ax.set_ylabel(\"Frequency\")\n",
    "ax.set_title(r\"Recovery of $\\tau$ when the bias prior is correctly centred\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "054df778",
   "metadata": {},
   "source": [
    "The sampling distribution of the posterior mean sits on the true $\\tau = 0.30$: with the confounder's strength correctly specified, the estimator is unbiased across repeated experiments. The recovery is real, but read what produced it. The data fixed the sum $\\tau + \\beta$ through the observed difference; the correctly-centred prior on $\\beta$ is what split that sum into its parts. A single difference in means cannot separate a treatment effect from a confound that imitates it. The data identify the two only in combination with a commitment about the confounder. The prior is the content of that decomposition, which is why an honest analysis varies it rather than fixing it. Recentre the prior on $\\beta$ at zero, where an analyst lands by default with no oracle for the confounder's size, and the estimate moves. The moderate prior below makes the shift concrete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7d543aca",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:03.174922Z",
     "iopub.status.busy": "2026-06-02T17:36:03.174827Z",
     "iopub.status.idle": "2026-06-02T17:36:05.724139Z",
     "shell.execute_reply": "2026-06-02T17:36:05.723669Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "NUTS[nutpie]: [tau, beta]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x535.887 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 559,
       "width": 2423
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gaussian_sensitivity_model(d_hat, sigma_d, tau_prior=(0.0, 1.0), bias_prior=(0.0, 0.3)):\n",
    "    with pm.Model() as model:\n",
    "        tau = pm.Normal(\"tau\", mu=tau_prior[0], sigma=tau_prior[1])\n",
    "        beta = pm.Normal(\"beta\", mu=bias_prior[0], sigma=bias_prior[1])\n",
    "        observed_effect = pm.Deterministic(\"observed_effect\", tau + beta)\n",
    "        pm.Normal(\"d_hat\", mu=observed_effect, sigma=sigma_d, observed=d_hat)\n",
    "    return model\n",
    "\n",
    "\n",
    "with gaussian_sensitivity_model(d_hat, sigma_d, bias_prior=(0.0, 0.3)):\n",
    "    idata_moderate = pm.sample(\n",
    "        draws=2000,\n",
    "        tune=2000,\n",
    "        chains=2,\n",
    "        target_accept=0.95,\n",
    "        random_seed=RANDOM_SEED,\n",
    "        progressbar=False,\n",
    "    )\n",
    "\n",
    "az.plot_dist(idata_moderate, var_names=[\"tau\", \"beta\"])\n",
    "axes = plt.gcf().axes\n",
    "for a in axes:\n",
    "    a.set_title(\"\")\n",
    "axes[0].axvline(TRUE_TAU, color=\"C2\", linestyle=\"--\", label=f\"true τ = {TRUE_TAU:.2f}\")\n",
    "axes[0].legend()\n",
    "axes[1].axvline(TRUE_BIAS, color=\"C2\", linestyle=\"--\", label=f\"true β = {TRUE_BIAS:.2f}\")\n",
    "axes[1].legend()\n",
    "plt.suptitle(r\"Posterior of $\\tau$ and $\\beta$ under a moderate bias prior\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74929da4",
   "metadata": {},
   "source": [
    "Under the moderate prior, centred at zero, the posterior of $\\tau$ is pulled well above the true 0.30 and the posterior of $\\beta$ settles near zero: with no prior reason to expect a confounder, the treatment absorbs the sum. The true $\\beta = 0.50$ falls in the prior's right tail. The data informed the sum; the prior shaped the split.\n",
    "\n",
    "### Tipping-point analysis under a Gaussian outcome\n",
    "\n",
    "The model with a flat prior on $\\tau$ and a Gaussian prior on $\\beta$ is fully conjugate; the posterior is a closed-form bivariate Normal that we can compute analytically. This lets us trace the tipping point: the bias prior strength at which the posterior probability of a positive treatment effect drops below the team's decision threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2f6ee70f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:05.725817Z",
     "iopub.status.busy": "2026-06-02T17:36:05.725672Z",
     "iopub.status.idle": "2026-06-02T17:36:05.746568Z",
     "shell.execute_reply": "2026-06-02T17:36:05.746120Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">MCMC</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Analytical</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>tau</th>\n",
       "      <td>0.72</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.722</td>\n",
       "      <td>0.299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>0.065</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.065</td>\n",
       "      <td>0.287</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       MCMC       Analytical       \n",
       "       mean    sd       mean     sd\n",
       "tau    0.72   0.3      0.722  0.299\n",
       "beta  0.065  0.29      0.065  0.287"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify the closed form agrees with MCMC under the moderate prior\n",
    "post_mean_anly, post_cov_anly = gaussian_sensitivity_posterior(\n",
    "    d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.3\n",
    ")\n",
    "mcmc_summary = az.summary(idata_moderate, var_names=[\"tau\", \"beta\"], kind=\"stats\")[[\"mean\", \"sd\"]]\n",
    "analytical_summary = pd.DataFrame(\n",
    "    {\"mean\": post_mean_anly, \"sd\": np.sqrt(np.diag(post_cov_anly))},\n",
    "    index=[\"tau\", \"beta\"],\n",
    ")\n",
    "pd.concat({\"MCMC\": mcmc_summary, \"Analytical\": analytical_summary}, axis=1).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d2acc0d",
   "metadata": {},
   "source": [
    "The two posteriors agree. The analytical form carries the sweep."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e9d91b3f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:05.747862Z",
     "iopub.status.busy": "2026-06-02T17:36:05.747780Z",
     "iopub.status.idle": "2026-06-02T17:36:06.105478Z",
     "shell.execute_reply": "2026-06-02T17:36:06.104918Z"
    }
   },
   "outputs": [
    {
     "data": {
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AQP5kxtylPs8/+eSTE5u2d+/ePX71q1/FH//4xxg+fHjOTdtT1l9//XSuTH0/INWc89hjj43OnTu3YMUAAPmRGbNbvnx53H777YnH9OrVK2688cYWNW1PaWhoiMsuuyz+/d//PfG45557Ll555ZUWzQEAUCw1NTUxcODA2G+//eKHP/xhet8slVt++ctfVuVFVwsDAEBT7MXK1AAA2ciMuVNfDgBUI7mxuNSXAwCVQGbMnfpyAKAayY3ZqTEHAEimxvz/UmNOpdG4HQBokdmzZ8dtt92WOWTU1qYfvJnUUDzJrrvuGqeeemriMVdccUWUg7Vr16Y365OcccYZscsuu7To/KmH4KceApb0AP1bb7015syZ06LzAwC0lMyYm9122y3+9Kc/pXP2gQcemHOz9qZsscUW6SyYrXn7s88+G5MmTcp7PgCAlpAbi+/CCy+MBQsW/MvP11tvvTjzzDNbYQUAAPmRGVvmnHPOSV+7TFL7hn/+85/TTagKZeONN44f//jH6b1JAIDWJDM2zyOPPBKLFi1KPOaSSy6JDTfcMK/70a5du/R3SHv37p143IQJE/KaBwAgX/369Yu99torzjrrrLjpppvimWeeif/+7/+OX/3qV3H88cfHjjvuGJ07d67KC60WBgCAptiLlakBALKRGXOjvhwAqFZyY/GpLwcAyp3M2DLqywGAaiM3No8acwCA/0uNeWZqzKlEGrcDAC2SeiDVqlWrMo4fdthhMXTo0Lyu7je+8Y30Q90zmTJlSjz66KNR6lJrTK01k0033TS+9rWv5TXHTjvtFAcffHDG8dS9uvnmm/OaAwAgVzJj87PcHXfcEddff33eGbopPXv2jBtuuCG6du2aeFyqaTwAQFuQG4vr73//e9x///1Njp199tnR0NBQ5BUAAORPZszd3XffHQ899FDG8b59+8bYsWNjwIABed0bAIBSITM2z5NPPpk4vv3228fuu+9ekHvSqVOnOPnkk/NaDwBAofXu3TtOP/30uO6669JZ5OGHH44rr7wyTjzxxBg2bFjW79lVE7UwAAA0xV6sTA0AkI3M2DzqywGAaic3Fpf6cgCgEsiMuVNfDgBUI7mxedSYAwDVTo1586kxpxJp3A4A5GzlypXxl7/8JeN4fX19nHbaaXlf2fbt28cZZ5yReMwtt9wSpS7bGr/zne9EXV1d3vN8+9vfTl+zTP785z+n7x0AQGuQGZvnyCOPjD/84Q+x7bbbFvV+bLjhhvHNb34z6wb44sWLi7oOAIDPkxuLK5Xvzj///CbHUs2X9t57b29KAKDkyYy5W7p0afzyl79M/Ez/mmuuiT59+uR1bwAASoXM2HxvvPFG4vjBBx8chXTggQcmfj/yrbfe8r1GAKBVbbLJJnHKKafEyJEjo2fPnq5+ArUwAAB8nr3Y3MjUAEA1khmbR305AFDt5MbiUl8OAFQCmTF36ssBgGokNzafGnMAoNqpMW8+9TBUIo3bAYCcPfLII7Fw4cKM4/vvv3/07t27IFd2zz33jH79+mUcnzRpUsyfPz9KVWptTzzxRMbxAQMGxL//+78XZK7UQ/X33XffjOOffPJJPPbYYwWZCwAgG5mxebp3795qb6ajjz461l133Yzjq1atiueff77V1gMAkCI3Ftdll10Ws2bN+pefd+rUKc4991xvQgCgLMiMubvxxhtjzpw5GcfPOOOMGDx4cF73BQCglMiMzffee+8ljg8fPjwKqaGhIbbZZpuM442NjfH+++8XdE4AAPKnFgYAgKbYi5WpAQCykRmbR305AFDt5MbiUl8OAFQCmTF36ssBgGokNzafGnMAAJpDjTmVSuN2ACBn9913X+L4mDFjCnZV27VrFwcddFDG8dWrV8cDDzwQper+++9PrzGTgw8+OGprCxfJRo8enTh+7733FmwuAIAkMmPpqa+vj5EjRyYe8+qrr7baegAAUuTG4nn++efj1ltvbXLs1FNPjX79+nkTAgBlQWbMzdKlS+OPf/xjxvGBAwfGsccem/d9AQAoJTJj8y1atCjx+5r9+/ePQttoo41avCYAANqGWhgAAJpiL1amBgDIRmYsPerLAYBSJDcWj/pyAKBSyIy5UV8OAFQrubH51JgDANAcasypVBq3AwA5WbNmTUyaNCnj+HrrrRdDhw4t6FXdb7/9Escfe+yxKFXZ1rbvvvsWdL6dd945evfunXE8de9S9xAAoJhkxtI1fPjwxPEZM2a02loAAOTG4lm5cmX85Cc/ibVr1/7L2ODBgzXqBADKhsyYu/Hjx8eCBQsyjp988snRvn37vO4LAEApkRlz09Se4ae6desWNTU1UWg9evRIHF+9enXB5wQAID9qYQAA+Dx7sTI1AEA2MmPpUl8OAJQSubF41JcDAJVCZsyd+nIAoBrJjblRYw4AQHOoMadSadwOAOTklVdeiUWLFmUcHzFiRMEf3LnppptG3759M44/88wzJfngzlWrVqXXlkm/fv1i4403LuictbW1seuuu2YcX7hwYUyePLmgcwIAfJ7MWLr69OmTOJ7U0AkAoNDkxuK55pprYtq0aU3uH1544YVRV1dXxNkBAApHZszd7bffnnGsd+/ese++++Z1TwAASo3MmJuuXbtmHCtG0/ZshfyfNowHAKB0qIUBAKAp9mJlagCAbGTG0qW+HAAoJXJj8agvBwAqhcyYO/XlAEA1khtzo8YcAIBs1JhTyTRuBwBy8vTTTyeO77LLLkW5oknnXbJkSUk2I0+taenSpRnHhw0bVpR5kxq3N+ceAgDkS2YsXb169UocX758eautBQBAbiyOKVOmxPXXX9/k2BFHHBHbbLONNx8AUDZkxtxMnTo1nQczOeCAA6K+vj7v+wIAUEpkxsJ9ZrxgwYKsTdZbInXeJD169Cj4nAAAtJxaGAAAmmIvVqYGAMhGZixd6ssBgFIiNxaH+nIAoJLIjLlRXw4AVCu5MTdqzAEAyEaNOZVM43YAICevvvpq4nixmv4MGTIkr3W1BdcKAKhWclDpWrFiReJ4hw4dWm0tAAByY+E1NjbGOeecE6tWrfqXsfXWWy/OPPNMbzwAoKzIjLmZOHFi4vg+++yT1/0AAChFMmNuttpqq4xja9asiZkzZ0ahTZ8+PeNYat+yZ8+eBZ8TAICWk7EBAJAT8yNTAwDVSg4qXerLAYBSIjcWnvpyAKDSyIy5UV8OAFQruTE3aswBAJCxqWYatwMAOXnttdcyjnXu3Dk22mijolzRrbfeOnH89ddfj3K6VilbbrllUebdeOONo1OnTmV1rQCAyiIzlq7Zs2cnjnft2rXV1gIAIDcW3h/+8Id46aWXmhw7++yzo6GhwRsPACgrMmNunnjiiYxjPXr0iCFDhuR9TwAASo3MmJuhQ4cmjk+aNCkKafHixfHyyy+3eD0AALQ+tTAAAOSaE9WXy9QAADJjaVNfDgCUEnuNhae+HACoNDJjbtSXAwDVSm7MjRpzAADyydgp+i1SzjRuBwCabenSpTFz5szEhuE1NTVFuaKbbLJJ4vibb74ZpWbKlCl5/U0tVVtbm74XmcyYMSOWLVtWlLkBAGTG0vbqq68mjg8YMKDV1gIAVDe5sfA++OCDuPzyy5sc23333WPvvfcuwqwAAMUjM+beEHPy5MkZx3faaaeifZ4PANBWZMbcjRo1KtZZZ52M43fffXcU0j333BOrV6/OOG7fEgCg9KiFAQDg8+zFytQAANnIjKVNfTkAUCrkxsJTXw4AVBqZMTfqywGAaiU35k6NOQAA2agxp5LVtfUCAIDykWravnbt2ozjAwcOLNrcDQ0N0atXr5g3b17GtZWa9957L+NY7969o3PnzkWbO9VwM1PRVOoevv/++7HpppsWbX4AoHrJjKXt0UcfTRzfYostWm0tAEB1kxsL77zzzkt/ifjzOnXqFOeee24RZgQAKC6ZMTf//Oc/ExtibrvtthnHPvroo3jkkUfiueeeS39hdtasWelC/TVr1qSbenbr1i369esXG2+8cWy33Xaxyy67RN++fXNcIQBA4cmMuevevXsceOCBcccddzQ5/sILL6Sz4e677573/UntV/7mN7/JOL7BBhuki/wBACgtamEAAPg8e7EyNQBANjJjaVNfDgCUCrmx8NSXAwCVRmbMjfpyAKBayY25U2MOAEA2asypZBq3AwDNlq05eupB7cXUv3//jI3b58+fH0uWLClqM/RcpB5iv2DBgja9VtnupcbtAEAxyIyl65133omXXnop43htbW0MHTq0VdcEAFQvubGw7r777njssceaHDv11FOLvh8JAFAMMmNu3nzzzcTxLbfc8l9+lmrU/rvf/S7+/ve/R2NjY8bPvlOv999/P5555pm4/fbb0z/fZptt4stf/nIcdNBBUV9fn+NqAQAKQ2ZsmdSe4QMPPBALFy5scvzss89O575s30NMksqX3/3ud2Pu3LkZj/n2t78d7dq1a/EcAAAUnloYAACaYi9WpgYAyEZmLF3qywGAUiI3Fpb6cgCgEsmMuVFfDgBUK7mxZdSYAwCQiRpzstW9UgAAdMdJREFUKl1tWy8AACgfH3zwQeL4uuuuW9T5e/XqlTj+4YcfRqlo62uV7fyph+oDAFRiDiqnzNjafv/738fatWszju+4447Ro0ePVl0TAFC95MbCmT9/flx66aVNjg0ePDiOPfbYAs4GANB6ZMbcTJ06NXF8k002+d//nj17dpxxxhlx1FFHxd/+9reMTduTvPzyy3HOOefEHnvsERMmTMj59wEACkFmbJk+ffqkm7Nn8tFHH8XXvva1eOONN1pciHXmmWems2Ymu+++exx88MEtOj8AAJWbsdXCAACUprbOieVUK9TW10qmBgCqNQeVU2ZsberLAYBSIjcWjvpyAKBSyYy5UV8OAFQrubFl1JgDAFCqGVs9DMWmcTsAkNMXNJP07t27qFcz2/mzra81ZVtLW/8fiY8//rio8wMA1UtmLE3Tpk2LcePGJR5zyCGHtNp6AADkxsK55JJLmtzvq62tjQsvvDDq6uq84QCAsiQz5ubtt9/OONahQ4dYb7310v/91FNPpRtkPvDAA1EIqSbw3/3ud+Ob3/xmfPLJJwU5JwBAc8mMLZfKhKeddlrG8XfffTe+/OUvx3/91381+7uZq1evjnvvvTd97vvvvz/jcVtuuWX84he/aNG6AQAoLrUwAAC0JCeqL5epAQBkxtKkvhwAKDVyY+GoLwcAKpXMmBv15QBAtZIbW06NOQAALcnY+i1S7jylHwBotmwPWe/SpUtRr2a285fSQ+CzraVr165teq0WLFhQ1PkBgOolM5aetWvXpht2ph6Sn8kGG2wQ++23X6uuCwCobnJjYTz22GMxYcKEJseOOOKI2GabbQo0EwBA65MZc2+gnrT/V1NTEw899FB8+9vfjlWrVkWh/f3vf4/DDjssfv/730e/fv0Kfn4AgKbIjPk59dRTo76+Pi6//PJYs2bNv4yvWLEirrrqqrjuuutixIgRMXTo0Bg8eHB069Yt/R3F5cuXx8KFC9NN3l944YX4xz/+EXPmzEmcM7Vnee211xb9O5QAALSMWhgAAFqSE9WXy9QAADJj6VFfDgCUIrmxMNSXAwCVTGbMjfpyAKBayY35UWMOAECuGVu/Rcqdxu0AQMHCcUNDQ1GvZrbzl1Iz8tTDSEv5WpVSk3sAoLLIjKXnT3/6Uzz55JOJx5xyyinRvn37VlsTAIDcmL+lS5fG+eef3+TYeuutF2eeeaY3GgBQ1mTG3B6uOW/evIzjPXv2jKeeeqpoTds/lWrYedRRR8Vtt90W66+/ftHmAQD4lMyYvxNPPDF22GGH+NGPfhTTp09v8phUA/e//e1v6VdL1dbWxnHHHZfet/TZNABA6VILAwBAU+zFytQAANnIjKVHfTkAUIrkxvypLwcAKp3M2HzqywGAaiY35k+NOQAAn6XGnEqncTsAkNMXNZN06tSpqFcz2/mXLVsWpWLJkiVteq06d+5cNtcKAKgsMmNpefPNN+PnP/954jFDhgyJQw89tNXWBACQIjfm71e/+lW8//77TY6dffbZ0dDQ4M0GAJQ1mTG3YrKkhuypsVSDzKRjBg4cGP/xH/8R22+/ffTq1Svd7H3RokUxd+7cmDp1arpJ5yuvvJIu4k/y4Ycfxje/+c30Az+L/bk4AIDMWBhf/OIXY+LEiTFhwoS48cYbY8qUKQV7c7Vr1y723nvvOOWUU2LQoEEFOy8AAMWhFgYAgKbYi5WpAQCykRlLi/pyAKBUyY35U18OAFQ6mbH51JcDANVMbiwMNeYAAHxKjTmVTuN2AKDZVq9enRws6oobLdq3b584nvSQ+dbmWgEA1UoOKh2LFy+O008/PZYvX56YsS+66KKoqalp1bUBAMiN+XnppZfilltuaXJs9913TzdCAgAodzJj8y1btixxPNVwPZNNNtkkzjnnnBg+fHjGY1IN3VPN2KdNmxYXX3xxTJo0KXG+119/PX7+85/H+eef34zVAwC0nMwYBW2wfvDBB6dfzz33XDrLTZ06tcXn69SpU7pZ+yGHHBI9e/Ys4EoBACgmGRsAADlRpgYAsLdY3tSXAwClzGfS+VFfDgBUA5mx+dSXAwDVTG4sHDXmAADI2FSD2rZeAABQPrI1Ri924/Zs5y+lxu1tfa1SG9zlcq0AgMrS1jmonDJjMTU2NsZZZ50V06dPTzzutNNOi8GDB7faugAAPiU35nftUo01U5mvqWZI5557rjcaAFARZMbmW7FiRYuu8Ve+8pW45557Epu2f9agQYPid7/7Xfz0pz+N2trkrx7edttt6YafAADFJDMW9gEFd911Vxx55JFx9NFH59W0PWXp0qVx+eWXx3e/+90YP3581XxWDwBQ7to6Y6uFAQAoTW2dE8upVqitr5VMDQBUaw4qp8xYTOrLAYBSJzfmd+3UlwMA1UBmbD715QBANZMbC0eNOQAApZCx1cNQbBq3AwA5bZrmE17zle382dbXmtasWZM47loBAJVKZiwNP//5z+ORRx5JPGbXXXeNb3zjG622JgCAz5IbW+7aa6+NKVOmNDl26qmnRr9+/bzZAICKIDM238qVK3O+vsccc0xccMEF0b59+5x/9/DDD4///M//TGzevnbt2rjssstyPjcAQC5kxsKYMGFC7LXXXvGDH/wgnn/++fSD3AtVkDVp0qT40Y9+FHvuuWfcdttt6ZwIAEDpUgsDAEBT7MXK1AAA2ciMpUF9OQBQ6uTGllNfDgBUC5mx+dSXAwDVTG4sDDXmAAB8So05lU7jdgCg2erq6hLHC/WwzpaG82zra03ZGrNn+1uq6VoBAJVFZmx7t9xyS/z+979PPGb99ddPN01KaqwEAFBMcmPLTJs2LV1Y35TBgwfHsccem9d9AQAoJTJj8+Xa/HLHHXeMH//4x5GPAw88MI477rjEY1544YV0408AgGKRGfOzcOHC+M53vhPf/e53Y+bMmVFMH3zwQZx33nnxta99LWbPnl3UuQAAaDm1MAAANMVerEwNAJCNzNj21JcDAOVAbmwZ9eUAQDWRGZtPfTkAUM3kxvyoMQcA4PPUmFPpdOwEAJqtffv2ieOrVq0q6tVcvXp1XutrTdnWku1vKXbj9lK6VgBAZZEZ29bEiRPjoosuSjymU6dO8V//9V/Rs2fPVlsXAMDnyY0tK5Y655xzYuXKlf8yVltbGxdeeGHWLxEDAJQTmbFw1+qzOnbsGJdeemnU1NREvr797W/HI488Em+//XbGY26//fYYOnRo3nMBADRFZmy5+fPnxzHHHBNTp07NeuzgwYNj+PDhseOOO8bAgQOje/fu0aVLl1i6dGl88sknMWvWrHj++efjmWeeiaeeeioaGxsznuuJJ56I0aNHx9ixY2PTTTf1xgYAKDFqYQAAaElOVF8uUwMAyIxtS305AFAu5MbcqS8HAKqNzFi4a/VZ6ssBgEojN7acGnMAAFqSsfVbpNx5cj8A0PzgkKXpT7HDcTk1bm/ra5XtIQeldK0AgMrS1jmonDJjoT322GPx/e9/P/Eh+Km//+qrr44hQ4a06toAAD5Pbszdn/70p3jhhReaHDviiCNim2228UYDACqKzNh8uex7HnzwwbHhhhtGIXTo0CFOOumk+MEPfpDxmIcffji9b5vtfgIAtITM2DKpZuvHHXdc1qbtO+20U5x88skxbNiwJse7deuWfg0YMCB97Le+9a14++2348Ybb4xx48alHxbalHnz5qXn/8Mf/hAbb7xxC/8KAAAqMWOrhQEAKE1tnRPLqVaora+VTA0AVGsOKqfMWGjqywGAciI35k59OQBQbWTG5lNfDgBUM7mxZdSYAwBQqhlbPQzFVlv0GQCAitGpU6fE8aVLlxZ1/iVLliSOd+zYMUpF586dE8ddKwCgUsmMbePZZ5+N0047LXFDuV27dvHrX/86dt1111ZdGwBAU+TG3MyaNSsuu+yyJsfWW2+9OPPMM73RAICKIzPm1kC9uQ4//PAopH333Te6d++ecXzRokXx4osvFnROAIBPyYwtc95558Wbb76ZWEh11llnxdixYzM2bc9kk002iYsvvjiuvfbaxJw4d+7cOP3002PlypU5nR8AgOJSCwMAQFPsxcrUAADZyIxtQ305AFBu5MbcqC8HAKqRzNh86ssBgGomN7aMGnMAADJRY06l07gdAGi2bt265dVYPV/Zzp/0kM/W1rVr15K+VtnuJQBAS8mMre/ll1+Ok046KZYvX57xmJqamrjkkkti1KhRrbo2AIBM5MbcnH/++Rn3/M4+++xoaGjwZgMAKo7MWLhr9akvfOELMXjw4Cik+vr62GuvvRKPeemllwo6JwDAp2TG3E2cODHuv//+xGN+9rOfxYknnpj+nLmlRo4cGX/605+iS5cuGY+ZMmVKXHnllS2eAwCAwlMLAwBAU+zFytQAANnIjK1PfTkAUI7kxtyoLwcAqpHMWLhr9Sn15QBAJZIbc6fGHACAJGrMqXQatwMABduAXrhwYVGvZrbzl1Iz8mxr+eSTT4o6/6JFi8qmyT0AUFlkxtb1xhtvxAknnJCxieenzj333Dj44INbbV0AANnIjbl9yfXvf/97k2O777577L333t5wAEBFkhmbr0OHDtGxY8esx2233XZRDNtuu23i+Ouvv16UeQEAZMbcNDY2xuWXX554zMknnxwHHHBAQd5cgwYNiiuuuCKxAfxNN90Uc+bMKch8AADkTy0MAAAtyYnqy2VqAACZsXWpLwcAypXc2HzqywGAaiUzNp/6cgCgmsmNuVFjDgBAvhlbv0XKncbtAECz9ezZM3H8o48+KurVzHb+bOtrTdnWMm/evKLOP3fu3MTxHj16FHV+AKB6yYytZ9q0aXH88cdn3aT+/ve/H0ceeWSrrQsAoDnkxuZZsGBBXHzxxU2OderUKc4991xvOACgYsmMuWnOZ8DZGqy3VLbzzpw5syjzAgDIjLl5+OGH491338043rdv3/jWt75V0DfW8OHDY6+99so4vmrVqrjlllsKOicAAC2nFgYAgJbkRPXlMjUAgMzYetSXAwDlTG5sHvXlAEA1kxlzo74cAKhWcmNu1JgDAJBvxtZvkXKncTsA0Gyph3KWcmH9BhtsEKWi1K9Vv379ijo/AFC9Sj0HlVJmzEfqYfrHHntszJ8/P/G4008/Pb7+9a+32roAAJpLbmyeX/ziFxkz7qmnnmqfDwCoaDJjbtZff/2sx/Tv37/F9yOf886aNaso8wIAyIy5ueeeexLHTzrppKivry/4Gyv1uXWSO++8s+BzAgBQmRlbLQwAQNso9ZxYSrVCpX6tZGoAoFpzUCllxnyoLwcAyp3c2DzqywGAaiYz5kZ9OQBQreTG3KgxBwCg3DO2ehjyVZf3GQCAqpHtYeszZ84s6vxJ5+/Zs2d07tw5SkVDQ0N07949FixYUHLXqpgP5AcAkBmL77333ks3bZ87d27icSeeeGKccsop3pQAQEmSG5tn8uTJGa/fHnvsUbB9xoULFyaOf/zxx4lzdezYMXr16lWQtQAAfEpmzM2GG24YL7zwQuIxXbp0KcobbJ111kk3+Fy5cmWT44sXLy7KvAAAMmNunn/++YxjNTU1MWrUqKK8qQYNGhSbbrppvPXWW02Oz549O2bMmBEDBgwoyvwAADSfWhgAAJpiL1amBgDIRmYsPvXlAEAlkBubR305AFDNZMbcqC8HAKqV3JgbNeYAAGSjxpxKp3E7AJDTBnTq4Zxr165tcvzdd98t2tVMPch93rx5iV8SKDWpNWVq3J5qsrl06dLo1KlTUeZOPcQ0k9Q97NevX1HmBQCQGYvrww8/TDdtT/2b5JhjjomzzjrLGxIAKFlyY35STdT33HPPaC0///nP069M/uM//iN+85vftNp6AIDqIDPmpjlNLrt27dri+9Gcc3/00UdNji1fvrxo8wIA1U1mzO07hZnyWsoWW2wRvXr1imLZddddMzZuT3nhhRc0bgcAKBFqYQAA+Dx7sTI1AEA2MmNxqS8HACqF3Jgf9eUAQDWQGXOjvhwAqFZyY/OpMQcAoLnUmFPJatt6AQBA+Ug1GU9tQmfyzjvvZGzqnq+33347cXyzzTaLUpNtTdOmTSvKvI2Njel7kfSFio4dOxZlbgAAmbF4Zs+enW7a/v777yce95WvfCXOPvtsb0YAoKTJjQAAyIyFtemmm2Y9plif52c7d01NTdHmBQCqm33G3D5vTrLJJpvkfT/yOX/qIfMAAJQGtTAAAHyevViZGgAgG5mxeNSXAwCVRG4EAEBmLCz15QBAtbLX2HxqzAEAaC415lQyjdsBgJxsueWWGceWLFkS06dPL8oVffXVVxPHt9hiiyg1W221VeL4a6+9VpR5U03bly5dWlbXCgCoLDJj4c2bNy+OO+64ePfddxOPGz16dPz0pz8twgoAAApPbgQAQGYsnK233jrrMQsXLizam27RokUZxzp06FC0eQEA7DM2z4IFCxLHe/ToUdQ3U8+ePfNaHwAArUctDAAATbEXK1MDAGQjMxae+nIAoBLJjQAAyIyFo74cAKhm9hqbR405AADNpcacSqZxOwBQ0A/jX3nllaJc0Zdffjmv0N4Wsq2pWNcq23lL8VoBAJVFZiysjz/+ON20/e233048br/99otLLrkkampqCrwCAIDikBsBAJAZC6d///5Zm20mNVfPx7Jly2LlypUZx7t161aUeQEAUuwzNs+SJUsSxzt37lzUN1RDQ0Pi+OLFi4s6PwAAzacWBgCAptiLlakBALKRGQtLfTkAUKnkRgAAZMbCUV8OAFQze43No8YcAIDmUmNOJdO4HQDIyU477ZQ4/tRTTxXlij799NOJDwzNtjHeFlJrSnqYabGu1ZNPPpk4vvPOOxdlXgCAT8mMhbNw4cL42te+FlOmTEk8btSoUfHzn/88amtt9wEA5UNuBABAZmzdjP3ee+8V5U2X7bzrr79+UeYFAEixz9g8HTp0yPrZdDF98sknea0PAIDWoxYGAICm2IuVqQEAspEZC0d9OQBQyeRGAABkxtbN2OrLAYBKZa+xedSYAwDQXGrMqWQ6OQEAORkyZEh06dIl4/jjjz8ea9euLehVnTZtWrz//vuJm+J1dXVRalJr2nHHHRO/tDB9+vSCztnY2BiTJk3KON61a9eSbHIPAFQWmbEwFi9eHCeccEK89tpriceNHDkyfvWrX5VkJgYASCI3AgCQjcyYmxEjRiSOv/TSS0V502U778CBA4syLwBAiszYPEnf+0z5+OOPi/qGynb+zp07F3V+AACaTy0MAABNsRcrUwMAZCMzFob6cgCg0smNAADIjIWlvhwAqFb2GptHjTkAAM2lxpxKppsTAJCTdu3axfDhw+OBBx5ocnz27Nnx/PPPxw477FCwKztx4sTE8d122y1KVWptjzzySOLfdvLJJxdsvmeffTbmzp2bcTx171L3EACgmGTG/C1btixOPPHErA2PUvnuqquuivr6+gLMCgDQuuTG7O6+++5WuBORzpT/9V//lXH80ksvjUMOOaRV1gIA8FkyY+6fT9fU1MTatWtLqnH71ltvXZR5AQBSZMbm2WCDDRLH33jjjaK+oV5//fW81gcAQOtSCwMAwOfZi5WpAQCykRnzp74cAKgGcmN26ssBgGonM+ZGfTkAUK3kxuZRYw4AQC7UmFOpatt6AQBA+dl///0Tx++8886CzdXY2Jj45dG6urrYe++9o1Tts88+6TVmkvrbMj00vyXGjx+f170DACgUmbHlVqxYEd/61rfi+eefTzxup512iquvvjo6dOiQx2wAAG1LbgQAQGYsnPXXXz923HHHjONvvfVW1oaZLdnPfPDBBxOPGTp0aEHnBAD4PPuM2fXv3z/xu4zvvPNOfPjhh0V7cz3xxBOJ4xtttFHR5gYAIHdqYQAAaIq9WJkaACAbmbHl1JcDANVEbgQAQGYsHPXlAEA1s9eYnRpzAAByocacSqVxOwCQs5EjR0bXrl0zjk+YMCHmzZtXkCubesD7e++9l3F8xIgR0bNnzyhVqbXtuuuuGcenT58eDz/8cEHmmjNnTtx3330Zx7t16xa77bZbQeYCAMhGZmyZlStXxmmnnRZPPvlk4nHbb799/Pa3v42OHTt6MwIAZU1uBABAZiys0aNHJ47feuutBZ1v4sSJsWDBgozj/fr1i8GDBxd0TgCAz7PPmF2HDh1i8803Tzwm9d3PYnj++efj/fffzzheU1MTQ4YMKcrcAAC0jFoYAACaYi9WpgYAyEZmbBn15QBAtZEbAQCQGQtLfTkAUK3sNWanxhwAgFyoMadSadwOAOSsvr4+DjvssIzjK1asiKuuuirvK7t69eq44oorEo856qijotR99atfTRy//PLLY82aNXnPc+WVV8aqVasyjn/5y19O3zsAgNYgM7Ys/5511lnx6KOPJh639dZbx/XXXx+dO3du8f0BACgVciMAADJjYe27777Rq1evjOP33HNPzJgxoyBzpb4bcO211yYes//++xdkLgCAJPYZm2fYsGGJ4zfeeGMsXry44G+21Hckk2y11VbRpUuXgs8LAEB+1MIAAPB59mJlagCAbGTG3KkvBwCqkdwIAIDMWFjqywGAamWvsXnUmAMAkAs15lQijdsBgBY59thjo3379hnH77jjjnjxxRfzuro33HBDTJs2LeP4ZpttFrvttltec/zwhz+MzTffPOMrNZ6vkSNHpteayZQpU+J3v/tdXnM899xzMW7cuIzjqXt1zDHH5DUHAECuZMbma2xsTGfP//7v/048bvDgwens6KH1AEAlkRsBAJAZC/f59DrrrBPHHXdcxvFly5bFj3/841i7dm1BGnC+8847GcfbtWsXRxxxRN7zAAA0h33G7Pbee+/E8QULFsTPfvazgr7h/vznP8czzzyTeMxee+1V0DkBAKqBWhgAANqKvdjmU18OAFQrmbH51JcDANVMbgQAQGZUXw4AYK+xdWqF1JgDAFQONebQMhq3AwAt0qdPnzj88MMzjq9ZsybOPPPMmDNnTovO/+STT8ZVV12VeMwZZ5wR5eL0009PHL/iiiuyPpw0k9mzZ8dZZ52VLsbKJPUw/PXWW69F5wcAaCmZsXlSDZLOPffcmDBhQuJxX/jCF+L3v/99dOvWzZsSAKgociMAADJjYR155JGJnw8/++yzcemll+Y1xz333BM33XRT4jFjxoyJDTbYIK95AACayz5jdkOGDEm/sjVav/766wvyxkt9D/SnP/1p4jEdOnRI50YAAEqTWhgAAD7PXqxMDQCQjczYPOrLAYBqJzcCACAzFpb6cgCgWtlrzE6NOQAAuVJjTqXRuB0AyCsc9+jRI+P4Bx98EMcff3z631w88cQTcfLJJ8fq1aszHrPrrrvGHnvsEeVi1KhR6TVnsmrVqvjmN78ZTz31VE7nnTlzZhx33HExa9asjMf07NkzTjvttJzOCwBQKDJjdpdcckn64fdJNtpoo3TT9lS2AwCoRHIjAAAyY+E0NDTEj370o8Rjbr755jjvvPPSn1Xn6vbbb48f/OAH0djYmPGYLl26+JwaAGh19hmzS31PMZtf/vKX6ay4cuXKFt+LsWPHxje+8Y2sefPLX/5y9OrVq8XzAABQXGphAABoir1YmRoAIBuZMTv15QAAciMAANnZa2w+9eUAQDWTG7NTYw4AQC7UmFNpNG4HAFqsa9euce655yYe89Zbb8Xo0aPjzjvvTHxoe8rixYvjsssuixNOOCGWLl2a8bjOnTvH+eefH+Um9SDTTp06ZRxfsmRJfO1rX4tf//rX6f9OkrqW48aNizFjxsTbb7+deOxPfvKT9L0CAGgLMmOyK664Iv3A+iQ9evRIF9+vWLEiZs6cWfTX6tWrC/oeAABoDrkRAACZsbD23Xff2HPPPROPue222+Kggw6KJ554olnnnDZtWnz9619Pf08g2+f/qWPWW2+9nNYMAJAv+4zZ7bHHHrHbbrtlPe7TrDh+/Piszdc/67HHHoujjz46Lr744qy/l2rYnnoQAgBAa0t9Ry7X79V99NFHiedcuHBhzudM/U45UAsDAMDn2YuVqQEAspEZk6kvBwCQGwEAaB57jblRXw4AVCu5MTs15gAAasxzpcacSlLX1gsAAMpb6sP4J598Mu64446MxyxYsCB++MMfxtVXXx377bdfbLfddtG3b99YZ5110s3aU43Hn3766XjggQdi0aJFWee84IILYuDAgVFuNtpoo/Tav/vd72Y8Zs2aNfHb3/42br311th7771jp512ik022SQaGhrSzew/+OCDePHFF+O+++6L999/P+ucX/nKV9L3CACgLcmMmd19991Zr9/HH38cRx55ZLSWv/3tb9G/f/9Wmw8A4FNyIwAA2ciMubn00ktjypQpMX369MRm7Mcff3z68+z/+I//iO233z7WXXfd6N69e/rz/FRDqtQ5UvuGL7/8cqxduzbrvEcccUQceOC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      "text/plain": [
       "<Figure size 4000x800 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 823,
       "width": 4023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "bias_sd_grid = np.linspace(0.001, 1.0, 40)\n",
    "sweep_records = []\n",
    "for bias_sd in bias_sd_grid:\n",
    "    pm_a, pc_a = gaussian_sensitivity_posterior(\n",
    "        d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=bias_sd\n",
    "    )\n",
    "    tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0])\n",
    "    prob_positive = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd)\n",
    "    sweep_records.append(\n",
    "        {\"bias_sd\": bias_sd, \"tau_mean\": tau_mean, \"tau_sd\": tau_sd, \"prob_positive\": prob_positive}\n",
    "    )\n",
    "sweep_df = pd.DataFrame(sweep_records)\n",
    "\n",
    "decision_threshold = 0.95\n",
    "above_threshold = sweep_df[sweep_df[\"prob_positive\"] >= decision_threshold]\n",
    "tipping_point = above_threshold[\"bias_sd\"].max() if len(above_threshold) else np.nan\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 4))\n",
    "axes[0].plot(\n",
    "    sweep_df[\"bias_sd\"],\n",
    "    sweep_df[\"tau_mean\"],\n",
    "    linewidth=2,\n",
    "    color=\"C0\",\n",
    "    label=r\"Posterior mean of $\\tau$\",\n",
    ")\n",
    "axes[0].fill_between(\n",
    "    sweep_df[\"bias_sd\"],\n",
    "    sweep_df[\"tau_mean\"] - sweep_df[\"tau_sd\"],\n",
    "    sweep_df[\"tau_mean\"] + sweep_df[\"tau_sd\"],\n",
    "    alpha=0.25,\n",
    "    color=\"C0\",\n",
    "    label=r\"$\\pm 1$ SD\",\n",
    ")\n",
    "axes[0].axhline(0.0, color=\"black\", linestyle=\":\")\n",
    "axes[0].set_xlabel(r\"Prior SD on bias $\\beta$\")\n",
    "axes[0].set_ylabel(r\"Posterior of $\\tau$\")\n",
    "axes[0].set_title(\"Posterior shifts as the bias prior loosens\")\n",
    "axes[0].legend()\n",
    "\n",
    "axes[1].plot(sweep_df[\"bias_sd\"], sweep_df[\"prob_positive\"], linewidth=2, color=\"C3\")\n",
    "axes[1].axhline(\n",
    "    decision_threshold,\n",
    "    color=\"black\",\n",
    "    linestyle=\"--\",\n",
    "    label=f\"Decision threshold = {decision_threshold}\",\n",
    ")\n",
    "if not np.isnan(tipping_point):\n",
    "    axes[1].axvline(\n",
    "        tipping_point,\n",
    "        color=\"C3\",\n",
    "        linestyle=\":\",\n",
    "        alpha=0.7,\n",
    "        label=f\"Tipping point ≈ {tipping_point:.2f}\",\n",
    "    )\n",
    "axes[1].set_xlabel(r\"Prior SD on bias $\\beta$\")\n",
    "axes[1].set_ylabel(r\"$P(\\tau > 0 \\mid d_{\\text{obs}})$\")\n",
    "axes[1].set_title(\"Tipping point in the decision rule\")\n",
    "axes[1].legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e15e75ee",
   "metadata": {},
   "source": [
    "Read the left panel from left to right: as the analyst loosens their prior on the bias, the posterior mean of $\\tau$ drifts downward and the posterior interval widens. Read the right panel: there is a bias prior strength at which the posterior probability of a positive effect falls below the conventional decision threshold. The tipping point is a price tag on the claim rather than a refutation of the experiment. To assert a positive effect requires a stated belief that the bias prior is *tighter* than the tipping point. The honest version of the conversation with stakeholders runs through this number. The posterior is what makes that conversation possible: the same inference machinery that reads the experiment's results in a clean world is what traces the contour of its fragility here. The question has shifted from what the treatment did to which commitments about the unmeasured bias are needed to believe it did anything, and a posterior answers the new question as readily as the old.\n",
    "\n",
    "The same machinery runs on the log-odds scale. Before mapping the full topology of the bias-prior space, we confirm that the one-dimensional fragility picture is not an artefact of the Gaussian likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22d603ff",
   "metadata": {},
   "source": [
    "## The same machinery on a binary outcome\n",
    "\n",
    "The conversion-rate version of the experiment uses the same structural model on the log-odds scale. The bias parameter now lives on the logit, but the framing is identical: the observed log-odds difference is the sum of a treatment effect and an unmeasured-confounder contribution, and a prior over the latter is the only thing that separates them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "97c262c4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:06.107055Z",
     "iopub.status.busy": "2026-06-02T17:36:06.106914Z",
     "iopub.status.idle": "2026-06-02T17:36:06.110905Z",
     "shell.execute_reply": "2026-06-02T17:36:06.110266Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed conversions: A = 834/8000, B = 1165/8000\n",
      "True p_A = 0.1000, p_B (with bias) = 0.1484\n"
     ]
    }
   ],
   "source": [
    "def simulate_quasi_experimental_bernoulli(N, baseline_rate, true_tau_logit, true_bias_logit, rng):\n",
    "    from scipy.special import expit\n",
    "\n",
    "    p_A = expit(np.log(baseline_rate / (1 - baseline_rate)))\n",
    "    p_B = expit(np.log(baseline_rate / (1 - baseline_rate)) + true_tau_logit + true_bias_logit)\n",
    "    n_A = rng.binomial(N, p_A)\n",
    "    n_B = rng.binomial(N, p_B)\n",
    "    return n_A, n_B, p_A, p_B\n",
    "\n",
    "\n",
    "BASELINE_RATE_B = 0.10\n",
    "TRUE_TAU_LOGIT = 0.15\n",
    "TRUE_BIAS_LOGIT = 0.30\n",
    "\n",
    "n_A_obs, n_B_obs, p_A_true, p_B_true = simulate_quasi_experimental_bernoulli(\n",
    "    N=8000,\n",
    "    baseline_rate=BASELINE_RATE_B,\n",
    "    true_tau_logit=TRUE_TAU_LOGIT,\n",
    "    true_bias_logit=TRUE_BIAS_LOGIT,\n",
    "    rng=rng,\n",
    ")\n",
    "print(f\"Observed conversions: A = {n_A_obs}/8000, B = {n_B_obs}/8000\")\n",
    "print(f\"True p_A = {p_A_true:.4f}, p_B (with bias) = {p_B_true:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e0f3171d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:06.112390Z",
     "iopub.status.busy": "2026-06-02T17:36:06.112290Z",
     "iopub.status.idle": "2026-06-02T17:36:10.955670Z",
     "shell.execute_reply": "2026-06-02T17:36:10.954860Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n",
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n",
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n",
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n",
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n",
      "NUTS[nutpie]: [logit_p_A, tau, beta]\n"
     ]
    },
    {
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       "    .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>bias_sd</th>\n",
       "      <th>tau_mean</th>\n",
       "      <th>tau_sd</th>\n",
       "      <th>prob_positive</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.369</td>\n",
       "      <td>0.070</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.358</td>\n",
       "      <td>0.146</td>\n",
       "      <td>0.998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.324</td>\n",
       "      <td>0.193</td>\n",
       "      <td>0.955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0.273</td>\n",
       "      <td>0.267</td>\n",
       "      <td>0.835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.191</td>\n",
       "      <td>0.342</td>\n",
       "      <td>0.716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.80</td>\n",
       "      <td>0.110</td>\n",
       "      <td>0.401</td>\n",
       "      <td>0.600</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bias_sd  tau_mean  tau_sd  prob_positive\n",
       "0     0.05     0.369   0.070          1.000\n",
       "1     0.15     0.358   0.146          0.998\n",
       "2     0.20     0.324   0.193          0.955\n",
       "3     0.30     0.273   0.267          0.835\n",
       "4     0.50     0.191   0.342          0.716\n",
       "5     0.80     0.110   0.401          0.600"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def bernoulli_sensitivity_model(\n",
    "    n_A, n_B, N, baseline_logit_prior=(-2.0, 0.5), tau_prior=(0.0, 0.5), bias_prior=(0.0, 0.3)\n",
    "):\n",
    "    with pm.Model() as model:\n",
    "        logit_p_A = pm.Normal(\n",
    "            \"logit_p_A\", mu=baseline_logit_prior[0], sigma=baseline_logit_prior[1]\n",
    "        )\n",
    "        tau = pm.Normal(\"tau\", mu=tau_prior[0], sigma=tau_prior[1])\n",
    "        beta = pm.Normal(\"beta\", mu=bias_prior[0], sigma=bias_prior[1])\n",
    "        logit_p_B = pm.Deterministic(\"logit_p_B\", logit_p_A + tau + beta)\n",
    "        p_A = pm.Deterministic(\"p_A\", pm.math.invlogit(logit_p_A))\n",
    "        p_B = pm.Deterministic(\"p_B\", pm.math.invlogit(logit_p_B))\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",
    "tipping_records_bern = []\n",
    "for bias_sd in [0.05, 0.15, 0.2, 0.30, 0.50, 0.80]:\n",
    "    with bernoulli_sensitivity_model(n_A_obs, n_B_obs, N=8000, bias_prior=(0.0, bias_sd)):\n",
    "        idata = 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",
    "        )\n",
    "    tau_samples = idata.posterior[\"tau\"].values.flatten()\n",
    "    tipping_records_bern.append(\n",
    "        {\n",
    "            \"bias_sd\": bias_sd,\n",
    "            \"tau_mean\": tau_samples.mean(),\n",
    "            \"tau_sd\": tau_samples.std(),\n",
    "            \"prob_positive\": float((tau_samples > 0).mean()),\n",
    "        }\n",
    "    )\n",
    "tipping_bern_df = pd.DataFrame(tipping_records_bern)\n",
    "# prob_positive decreases as the bias prior loosens; interpolate to the threshold crossing\n",
    "tip_bern = float(\n",
    "    np.interp(\n",
    "        decision_threshold,\n",
    "        tipping_bern_df[\"prob_positive\"].values[::-1],\n",
    "        tipping_bern_df[\"bias_sd\"].values[::-1],\n",
    "    )\n",
    ")\n",
    "tipping_bern_df.round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "69190ddc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:10.957347Z",
     "iopub.status.busy": "2026-06-02T17:36:10.957218Z",
     "iopub.status.idle": "2026-06-02T17:36:11.260109Z",
     "shell.execute_reply": "2026-06-02T17:36:11.259622Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 4000x800 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 823,
       "width": 4023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(20, 4))\n",
    "axes[0].errorbar(\n",
    "    tipping_bern_df[\"bias_sd\"],\n",
    "    tipping_bern_df[\"tau_mean\"],\n",
    "    yerr=tipping_bern_df[\"tau_sd\"],\n",
    "    marker=\"o\",\n",
    "    linewidth=2,\n",
    "    capsize=4,\n",
    ")\n",
    "axes[0].axhline(0.0, color=\"black\", linestyle=\":\")\n",
    "axes[0].set_xlabel(r\"Prior SD on bias $\\beta$ (log-odds)\")\n",
    "axes[0].set_ylabel(r\"Posterior of $\\tau$ (log-odds)\")\n",
    "axes[0].set_title(\"Bernoulli case: posterior of treatment effect\")\n",
    "\n",
    "axes[1].plot(\n",
    "    tipping_bern_df[\"bias_sd\"],\n",
    "    tipping_bern_df[\"prob_positive\"],\n",
    "    marker=\"o\",\n",
    "    linewidth=2,\n",
    "    color=\"C3\",\n",
    ")\n",
    "axes[1].axhline(\n",
    "    decision_threshold,\n",
    "    color=\"black\",\n",
    "    linestyle=\"--\",\n",
    "    label=f\"Decision threshold = {decision_threshold}\",\n",
    ")\n",
    "axes[1].axvline(\n",
    "    tip_bern,\n",
    "    color=\"C3\",\n",
    "    linestyle=\":\",\n",
    "    alpha=0.7,\n",
    "    label=f\"Tipping point ≈ {tip_bern:.2f}\",\n",
    ")\n",
    "axes[1].set_xlabel(r\"Prior SD on bias $\\beta$ (log-odds)\")\n",
    "axes[1].set_ylabel(r\"$P(\\tau > 0 \\mid \\text{data})$\")\n",
    "axes[1].set_title(\"Tipping point on the log-odds scale\")\n",
    "axes[1].legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a03b1409",
   "metadata": {},
   "source": [
    "The shape of the curve confirms what the Gaussian case showed: the decision rule loses confidence as the prior on bias widens, and the tipping point is identifiable on the log-odds scale just as it was on the revenue scale. The E-value of {cite:p}`vanderweele2017sensitivity` corresponds, roughly, to the bias magnitude at which a frequentist decision would tip; the Bayesian curve is the full posterior over that commitment. One dimension, two likelihoods, the same fragility picture. The complete audit needs both dimensions of the bias prior, the full region of commitments the conclusion can survive. That surface is below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad6b05cf",
   "metadata": {},
   "source": [
    "### The sensitivity surface\n",
    "\n",
    "Both the Gaussian and the binary sweep moved one dimension of the bias prior. The complete audit requires the other: a map of the full region of $(\\mu_\\beta, \\sigma_\\beta)$ commitments the experiment can survive. The sweep below opens the line into a surface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c46490fc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:11.261451Z",
     "iopub.status.busy": "2026-06-02T17:36:11.261355Z",
     "iopub.status.idle": "2026-06-02T17:36:12.083932Z",
     "shell.execute_reply": "2026-06-02T17:36:12.083206Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x1000 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1023,
       "width": 3016
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bias_mu_grid = np.linspace(-0.5, 0.5, 25)\n",
    "bias_sd_grid_2d = np.linspace(0.01, 1.0, 25)\n",
    "prob_grid = np.zeros((len(bias_sd_grid_2d), len(bias_mu_grid)))\n",
    "\n",
    "for i, b_sd in enumerate(bias_sd_grid_2d):\n",
    "    for j, b_mu in enumerate(bias_mu_grid):\n",
    "        pm_a, pc_a = gaussian_sensitivity_posterior(\n",
    "            d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=b_sd, bias_prior_mean=b_mu\n",
    "        )\n",
    "        tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0])\n",
    "        prob_grid[i, j] = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "im = ax.imshow(\n",
    "    prob_grid,\n",
    "    origin=\"lower\",\n",
    "    aspect=\"auto\",\n",
    "    extent=[bias_mu_grid.min(), bias_mu_grid.max(), bias_sd_grid_2d.min(), bias_sd_grid_2d.max()],\n",
    "    cmap=\"RdBu_r\",\n",
    "    vmin=0.0,\n",
    "    vmax=1.0,\n",
    ")\n",
    "contour = ax.contour(\n",
    "    bias_mu_grid,\n",
    "    bias_sd_grid_2d,\n",
    "    prob_grid,\n",
    "    levels=[0.5, decision_threshold],\n",
    "    colors=[\"white\", \"black\"],\n",
    "    linewidths=[1.2, 2.0],\n",
    ")\n",
    "ax.clabel(contour, fmt={0.5: \"P=0.5\", decision_threshold: f\"P={decision_threshold}\"})\n",
    "ax.set_xlabel(r\"Prior mean of bias $\\beta$\")\n",
    "ax.set_ylabel(r\"Prior SD of bias $\\beta$\")\n",
    "ax.set_title(r\"$P(\\tau > 0)$ under bias-prior commitments\")\n",
    "plt.colorbar(im, ax=ax, label=r\"$P(\\tau > 0 \\mid d_{\\text{obs}})$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13d4a25c",
   "metadata": {},
   "source": [
    "The decision threshold contour partitions the bias-prior plane into a region where the experiment is defensible and a region where it is not. The analyst who wants to claim a positive effect commits to a point inside the inner contour. The dissenter who wants to claim the effect is artefactual commits to a point outside it. The graph locates the disagreement rather than settling it. It shows which region of the bias-prior plane each party's commitments occupy, and whether that region sits inside or outside the contour of defensibility. The audit has a legible geometry."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bea675c",
   "metadata": {},
   "source": [
    "## Robustness as a posterior question\n",
    "\n",
    "A sensitivity analysis maps the randomisation gap rather than closing it. The sweep above does not prove the experiment robust; it produces an auditable exhibit of which bias commitments the experiment can survive and which it cannot. That exhibit is the deliverable.\n",
    "\n",
    "This changes what honest reporting looks like. The headline from a quasi-experiment becomes the *tipping point*, the prior on the bias at which the conclusion turns, and the sensitivity surface widens that point into a region: the full set of bias-prior commitments the experiment can survive, with its boundary drawn as a contour. Two analysts who hold the same data and reach opposite conclusions are reading the same difference in means through different priors on the confounder, and the surface shows precisely which commitment divides them.\n",
    "\n",
    "What a clean experiment reports as one posterior on the effect, a quasi-experiment reports as a posterior spread over the bias the data cannot rule out. Mapping that spread, and naming the commitment a positive conclusion requires, is what the quasi-experiment owes its readers. {ref}`meta_analysis_experiments` turns from a single threatened experiment to a whole series of them.\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "66eea177",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-02T17:36:12.085879Z",
     "iopub.status.busy": "2026-06-02T17:36:12.085748Z",
     "iopub.status.idle": "2026-06-02T17:36:12.100168Z",
     "shell.execute_reply": "2026-06-02T17:36:12.099634Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Fri, 12 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": "edf11e5a",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
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