{
"cells": [
{
"cell_type": "markdown",
"id": "58b4b1c0",
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"source": [
"(meta_analysis_experiments)=\n",
"# Multiple Experiments and Bayesian Meta-analysis\n",
"\n",
":::{post} May 2026\n",
":tags: experimentation, meta-analysis, hierarchical models, partial pooling, replication\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:* 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 (this notebook):* 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",
"## The replication-as-evidence problem\n",
"\n",
"Eight quarterly A/B tests of the same checkout-flow redesign, run across eight markets, return eight different point estimates. Two cross the conventional significance threshold; the other six do not. The product manager asks the natural question, \"did it work?\", and gets two incompatible defaults depending on which colleague answers: vote-counting (\"four out of eight worked, so it's a wash\"), or pool-everything (\"the combined estimate is positive, so it works\"). Both are mistakes. The vote-count discards the magnitude information in each estimate; the pool-everything pretends the markets are exchangeable in a way the evidence does not support. The honest answer requires a model that estimates between-market differences rather than assuming them away.\n",
"\n",
"Each experiment speaks about one market. The hierarchy is what lets us hear all of them at once.\n",
"\n",
"This notebook builds that model. The hierarchical Bayesian meta-analysis treats each experiment as a noisy estimate of its own market's true effect, and treats the per-market effects as draws from a population whose mean and variance are themselves the quantities of substantive interest {cite:p}`borenstein2009meta`, {cite:p}`higgins2009meta`. The structure is the one Rubin used for the 8-schools problem in 1981 {cite:p}`rubin1981estimation`, {cite:p}`gelman2013bayesian`, transposed to product experimentation. We develop it on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the third of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`sensitivity_confounding` for the interpretation counterpart. Readers wanting a deeper view of the partial-pooling vocabulary should also consult the existing PyMC notebooks on {ref}`multilevel_modeling` and {ref}`hierarchical_partial_pooling`, which we treat as predecessors rather than re-derive.\n",
"\n",
":::{admonition} Where this lands in regulatory practice\n",
":class: note\n",
"\n",
"The hierarchical model here is the borrowing mechanism a regulator now describes by name. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials presents subgroup analysis through a *one-way Bayesian hierarchical model* whose subgroup estimate is \"a weighted average of its raw estimated treatment effect ... and the overall estimated treatment effect\" {cite:p}`fda2026bayesian`, the shrinkage picture this notebook builds. The same guidance treats hierarchical models as the main way to borrow information across related trials by assuming the group parameters are drawn from a common distribution, which is the $\\theta_k \\sim \\mathcal{N}(\\mu, \\tau)$ structure below. Borrowing across studies, and the use of one trial's synthesis as the next trial's prior, is the regulatory form of the lifecycle loop these three notebooks trace.\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d5b9bd7c",
"metadata": {
"execution": {
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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",
"from scipy import stats\n",
"\n",
"warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
"warnings.filterwarnings(\"ignore\", category=UserWarning)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b8567665",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:28.477124Z",
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"source": [
"%config InlineBackend.figure_format = 'retina'\n",
"az.style.use(\"arviz-variat\")\n",
"rng = np.random.default_rng(11)\n",
"RANDOM_SEED = 11"
]
},
{
"cell_type": "markdown",
"id": "ebedae74",
"metadata": {},
"source": [
"## Heterogeneity is not new: groups within a single study\n",
"\n",
"The across-study problem looks novel, but its structure appears inside a single experiment whenever the treatment effect varies across user segments. It is worth meeting the problem on this familiar ground first, because the tool that solves it here is the tool we will carry across studies, and its classical name is the analysis of variance.\n",
"\n",
"Consider one market's experiment broken out across six user segments. The redesign helps some segments more than others, and the per-segment treatment effects are themselves draws from a population. We give the section its own random generator so the across-study results later in the notebook are unaffected."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "409b8357",
"metadata": {
"execution": {
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{
"data": {
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],
"text/plain": [
" segment d se\n",
"0 New / mobile 0.614 0.338\n",
"1 New / desktop 0.869 0.334\n",
"2 Returning / mobile 1.243 0.251\n",
"3 Returning / desktop -0.339 0.268\n",
"4 High-value -0.912 0.215\n",
"5 Reactivated 0.229 0.212"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def segment_effect_estimates(df):\n",
" recs = []\n",
" for name, g in df.groupby(\"segment\", sort=False):\n",
" t = g.loc[g.treatment == 1, \"revenue\"]\n",
" c = g.loc[g.treatment == 0, \"revenue\"]\n",
" recs.append(\n",
" {\n",
" \"segment\": name,\n",
" \"d\": t.mean() - c.mean(),\n",
" \"se\": np.sqrt(t.var(ddof=1) / len(t) + c.var(ddof=1) / len(c)),\n",
" }\n",
" )\n",
" return pd.DataFrame(recs)\n",
"\n",
"\n",
"seg_est = segment_effect_estimates(study_df)\n",
"seg_est.round(3)"
]
},
{
"cell_type": "markdown",
"id": "e1511edd",
"metadata": {},
"source": [
"The classical question \"does the effect differ across segments?\" is a test for the treatment-by-segment interaction, and the two-way analysis of variance answers it with an $F$-test. We compute it directly, as a comparison of nested least-squares fits, which keeps the dependency surface small and makes the variance decomposition explicit. The interaction row is the one to read."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "96f71013",
"metadata": {
"execution": {
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" sum_sq df F PR(>F)\n",
"C(segment) 402.260 5.0 5.057 0.00\n",
"C(treatment) 23.888 1.0 1.502 0.22\n",
"C(segment):C(treatment) 828.451 5.0 10.415 0.00\n",
"Residual 92081.361 5788.0 NaN NaN"
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],
"source": [
"def anova_two_way(df, outcome, factor, treatment):\n",
" \"\"\"Type-II two-way ANOVA via nested least-squares fits (treatment is binary).\"\"\"\n",
" y = df[outcome].to_numpy(dtype=float)\n",
" n = len(y)\n",
" ones = np.ones((n, 1))\n",
" A = pd.get_dummies(df[factor], drop_first=True).to_numpy(dtype=float) # factor dummies\n",
" B = pd.get_dummies(df[treatment], drop_first=True).to_numpy(dtype=float) # treatment dummy\n",
" AB = A * B # interaction columns\n",
"\n",
" def fit(*blocks):\n",
" X = np.hstack([ones, *blocks])\n",
" beta, *_ = np.linalg.lstsq(X, y, rcond=None)\n",
" resid = y - X @ beta\n",
" return float(resid @ resid), np.linalg.matrix_rank(X)\n",
"\n",
" rss_full, k_full = fit(A, B, AB)\n",
" rss_add, k_add = fit(A, B)\n",
" rss_A, k_A = fit(A)\n",
" rss_B, k_B = fit(B)\n",
" df_resid = n - k_full\n",
" mse = rss_full / df_resid\n",
"\n",
" terms = {\n",
" f\"C({factor})\": (rss_B - rss_add, k_add - k_B),\n",
" f\"C({treatment})\": (rss_A - rss_add, k_add - k_A),\n",
" f\"C({factor}):C({treatment})\": (rss_add - rss_full, k_full - k_add),\n",
" }\n",
" rows = [\n",
" {\n",
" \"sum_sq\": ss,\n",
" \"df\": float(dof),\n",
" \"F\": (ss / dof) / mse,\n",
" \"PR(>F)\": stats.f.sf((ss / dof) / mse, dof, df_resid),\n",
" }\n",
" for ss, dof in terms.values()\n",
" ]\n",
" rows.append({\"sum_sq\": rss_full, \"df\": float(df_resid), \"F\": np.nan, \"PR(>F)\": np.nan})\n",
" return pd.DataFrame(rows, index=list(terms) + [\"Residual\"])\n",
"\n",
"\n",
"anova_tbl = anova_two_way(study_df, \"revenue\", \"segment\", \"treatment\")\n",
"anova_tbl.round(3)"
]
},
{
"cell_type": "markdown",
"id": "398b3030",
"metadata": {},
"source": [
"The interaction $F$-test reports whether heterogeneity is detectable; it does not estimate how large it is.\n",
"\n",
":::{admonition} Three numbers for heterogeneity\n",
":class: note\n",
"\n",
"Given per-group effect estimates $\\hat d_k$ with standard errors $s_k$ and inverse-variance weights $w_k = 1/s_k^2$:\n",
"\n",
"- **Cochran's $Q$** measures how far the estimates spread beyond what sampling noise alone would produce. It is $Q = \\sum_k w_k (\\hat d_k - \\bar d)^2$, where $\\bar d$ is the precision-weighted mean, and it is simply the inverse-variance-weighted version of the between-groups sum of squares from ANOVA. If every group shared one true effect, $Q$ would follow a $\\chi^2$ distribution with $K-1$ degrees of freedom, so a $Q$ much larger than $K-1$ is evidence of real heterogeneity.\n",
"- **$I^2 = \\max\\!\\big(0,\\, (Q - (K-1))/Q\\big)$** rescales $Q$ onto the unit interval: the share of the total variation in the estimates due to genuine between-group differences rather than sampling error. $I^2 = 0$ means the spread is all noise; $I^2 = 0.9$ means most of it is real.\n",
"- **The DerSimonian–Laird estimator** is the classical, non-Bayesian way to turn $Q$ into a point estimate of the between-group variance $\\tau^2$. It is a method-of-moments calculation, and once $\\hat\\tau^2$ is in hand the random-effects pooled mean re-weights each group by $1/(s_k^2 + \\hat\\tau^2)$ instead of $1/s_k^2$, so noisy groups count for less and no single precise group dominates.\n",
"\n",
"See {cite:p}`borenstein2009meta` for the full treatment and {cite:p}`higgins2009meta` for the random-effects model these statistics serve.\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b06c639a",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:28.825435Z",
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"shell.execute_reply": "2026-06-01T17:59:28.828657Z"
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cochran's Q = 53.38 (df = 5, p = 0.000)\n",
"I² = 0.91 DerSimonian–Laird between-segment SD τ = 0.807\n"
]
}
],
"source": [
"d = seg_est[\"d\"].values\n",
"s = seg_est[\"se\"].values\n",
"w = 1.0 / s**2\n",
"d_fixed = np.sum(w * d) / np.sum(w)\n",
"se_fixed = np.sqrt(1.0 / np.sum(w))\n",
"df_q = len(d) - 1\n",
"Q = np.sum(w * (d - d_fixed) ** 2)\n",
"p_Q = stats.chi2.sf(Q, df_q)\n",
"I2 = max(0.0, (Q - df_q) / Q)\n",
"C_dl = np.sum(w) - np.sum(w**2) / np.sum(w)\n",
"tau2_DL = max(0.0, (Q - df_q) / C_dl)\n",
"w_re = 1.0 / (s**2 + tau2_DL)\n",
"mu_DL = np.sum(w_re * d) / np.sum(w_re)\n",
"se_DL = np.sqrt(1.0 / np.sum(w_re))\n",
"\n",
"print(f\"Cochran's Q = {Q:.2f} (df = {df_q}, p = {p_Q:.3f})\")\n",
"print(f\"I² = {I2:.2f} DerSimonian–Laird between-segment SD τ = {np.sqrt(tau2_DL):.3f}\")"
]
},
{
"cell_type": "markdown",
"id": "04a75e3b",
"metadata": {},
"source": [
"The hierarchical Bayesian model is the same random-effects analysis of variance, with one difference that matters when the number of groups is small: it returns a posterior over $\\tau$ rather than a single number. With only six segments $\\tau$ is weakly identified, and the DerSimonian–Laird point estimate can collapse toward zero even when real heterogeneity is present; the posterior shows that uncertainty honestly instead of hiding it in a point."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "378cc883",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:28.830087Z",
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},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"NUTS[nutpie]: [mu, tau, offset]\n"
]
}
],
"source": [
"coords_seg = {\"segment\": SEG_NAMES}\n",
"with pm.Model(coords=coords_seg) as segment_model:\n",
" mu = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n",
" tau = pm.HalfNormal(\"tau\", sigma=1.0)\n",
" offset = pm.Normal(\"offset\", mu=0.0, sigma=1.0, dims=\"segment\")\n",
" theta = pm.Deterministic(\"theta\", mu + tau * offset, dims=\"segment\")\n",
" pm.Normal(\"d_obs\", mu=theta, sigma=s, observed=d, dims=\"segment\")\n",
" idata_seg = 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",
" )"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "500ed2c0",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:31.103366Z",
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{
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"metadata": {
"image/png": {
"height": 559,
"width": 1732
}
},
"output_type": "display_data"
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],
"source": [
"pc = az.plot_dist(\n",
" idata_seg,\n",
" var_names=[\"tau\"],\n",
" visuals={\n",
" \"title\": {\"text\": r\"Posterior of between-segment SD $\\tau$ (one study, six segments)\"}\n",
" },\n",
")\n",
"az.add_lines(\n",
" pc,\n",
" values=np.sqrt(tau2_DL),\n",
" visuals={\"ref_line\": {\"color\": \"C1\", \"label\": f\"DerSimonian–Laird τ = {np.sqrt(tau2_DL):.2f}\"}},\n",
")\n",
"pc.get_viz(\"plot\").legend();"
]
},
{
"cell_type": "markdown",
"id": "2e5f189d",
"metadata": {},
"source": [
"Three estimators, three commitments about how much the segments share. The fixed-effect ANOVA assumes one common effect and pools completely; the random-effects ANOVA admits between-segment variance and estimates it by moments; the hierarchical model carries that variance as a posterior. The grouping factor was the segment. Replace it with \"study\" and the model is untouched: meta-analysis is the random-effects analysis of variance with studies as the groups, and the index $k$ ranges over experiments rather than segments. The rest of this notebook makes exactly that substitution. Making that substitution is mechanical. What it reveals is substantive: once studies replace segments, τ becomes the quantity the replication programme was designed to estimate.\n",
"\n",
"## The hierarchical re-framing\n",
"\n",
"The model is the one we just fit, with markets in place of segments. Let $\\theta_k$ be the true treatment effect in market $k$, and let $\\hat d_k$ be the observed estimate from market $k$'s experiment with standard error $s_k$. The single-experiment view treats each $\\hat d_k$ as the answer to its own question; vote-counting and pool-everything are degenerate cases of that view. The hierarchical view writes:\n",
"\n",
"$$\n",
"\\theta_k \\sim \\mathcal{N}(\\mu, \\tau), \\qquad \\hat d_k \\mid \\theta_k \\sim \\mathcal{N}(\\theta_k, s_k),\n",
"$$\n",
"\n",
"where $\\mu$ is the population mean effect across markets and $\\tau$ is the between-market standard deviation. $\\mu$ tells the team what to expect on average; $\\tau$ tells them how variable that expectation is across markets. Neither quantity is recoverable from any single experiment. Both are recoverable from the joint."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "b2a086f6",
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Market G
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" market N_per_arm true_theta d_hat se z_score\n",
"0 Market A 200 0.220 0.483 0.423 1.143\n",
"1 Market B 250 1.002 0.998 0.359 2.782\n",
"2 Market C 300 1.098 1.383 0.330 4.189\n",
"3 Market D 350 0.559 0.493 0.296 1.663\n",
"4 Market E 400 0.607 0.438 0.277 1.581\n",
"5 Market F 500 0.155 0.101 0.255 0.395\n",
"6 Market G 700 -0.057 0.072 0.212 0.338\n",
"7 Market H 1200 -0.050 -0.001 0.163 -0.004"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"K = 8\n",
"TRUE_MU = 0.4\n",
"TRUE_TAU = 0.5\n",
"SIGMA_OBS = 4.0\n",
"MARKET_NAMES = [f\"Market {chr(65 + i)}\" for i in range(K)]\n",
"# Per-market sample sizes vary; smaller markets have noisier estimates, which\n",
"# is the regime where partial pooling does substantively visible work.\n",
"N_PER_MARKET = np.array([200, 250, 300, 350, 400, 500, 700, 1200])\n",
"meta_rng = np.random.default_rng(20)\n",
"\n",
"\n",
"def simulate_meta_dataset_gaussian(K, N_per_market, true_mu, true_tau, sigma_obs, rng):\n",
" theta = rng.normal(true_mu, true_tau, size=K)\n",
" d_hat = np.zeros(K)\n",
" s = np.zeros(K)\n",
" for k in range(K):\n",
" N_k = int(N_per_market[k])\n",
" y_A = rng.normal(10.0, sigma_obs, size=N_k)\n",
" y_B = rng.normal(10.0 + theta[k], sigma_obs, size=N_k)\n",
" d_hat[k] = y_B.mean() - y_A.mean()\n",
" s[k] = np.sqrt(y_A.var(ddof=1) / N_k + y_B.var(ddof=1) / N_k)\n",
" return theta, d_hat, s\n",
"\n",
"\n",
"true_theta, d_hat_obs, se_obs = simulate_meta_dataset_gaussian(\n",
" K, N_PER_MARKET, TRUE_MU, TRUE_TAU, SIGMA_OBS, meta_rng\n",
")\n",
"markets_df = pd.DataFrame(\n",
" {\n",
" \"market\": MARKET_NAMES,\n",
" \"N_per_arm\": N_PER_MARKET,\n",
" \"true_theta\": true_theta,\n",
" \"d_hat\": d_hat_obs,\n",
" \"se\": se_obs,\n",
" \"z_score\": d_hat_obs / se_obs,\n",
" }\n",
")\n",
"markets_df.round(3)"
]
},
{
"cell_type": "markdown",
"id": "958dfc38",
"metadata": {},
"source": [
"The per-market `z_score` column is what a frequentist replication exercise would consult: anything above 1.96 in absolute value counts as \"significant\", anything below does not. The columns disagree about how many markets \"worked\"; the underlying true effects disagree less. This is the gap the hierarchical model closes. The quantity no single experiment can recover is τ.\n",
"\n",
"## No pooling, complete pooling, partial pooling\n",
"\n",
"Three estimators reflect three commitments about how much the markets share. *No pooling* fits each market in isolation; the per-market estimate is $\\hat d_k$. *Complete pooling* fits a single mean across all markets, treating them as draws from one distribution with no between-market variance. *Partial pooling* fits the hierarchical model above and lets the data weigh how exchangeable the markets are. The PyMC code below makes all three explicit so the shrinkage that distinguishes them becomes visible."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "ea8e78de",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:32.166252Z",
"iopub.status.busy": "2026-06-01T17:59:32.166169Z",
"iopub.status.idle": "2026-06-01T17:59:33.447380Z",
"shell.execute_reply": "2026-06-01T17:59:33.446901Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"NUTS[nutpie]: [mu]\n",
"NUTS[nutpie]: [mu, tau, theta_offset]\n"
]
}
],
"source": [
"coords = {\"market\": MARKET_NAMES}\n",
"\n",
"with pm.Model(coords=coords) as complete_model:\n",
" mu_complete = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n",
" pm.Normal(\"d_hat\", mu=mu_complete, sigma=se_obs, observed=d_hat_obs, dims=\"market\")\n",
"\n",
"with complete_model:\n",
" idata_complete = 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",
"\n",
"with pm.Model(coords=coords) as partial_model:\n",
" mu = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n",
" tau = pm.HalfNormal(\"tau\", sigma=1.0)\n",
" theta_offset = pm.Normal(\"theta_offset\", mu=0.0, sigma=1.0, dims=\"market\")\n",
" theta = pm.Deterministic(\"theta\", mu + tau * theta_offset, dims=\"market\")\n",
" pm.Normal(\"d_hat\", mu=theta, sigma=se_obs, observed=d_hat_obs, dims=\"market\")\n",
"\n",
"with partial_model:\n",
" idata_partial = 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",
" )"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "35d9a55e",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:33.448789Z",
"iopub.status.busy": "2026-06-01T17:59:33.448713Z",
"iopub.status.idle": "2026-06-01T17:59:33.646494Z",
"shell.execute_reply": "2026-06-01T17:59:33.646063Z"
}
},
"outputs": [
{
"data": {
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"text/plain": [
"
"
]
},
"metadata": {
"image/png": {
"height": 1066,
"width": 3967
}
},
"output_type": "display_data"
}
],
"source": [
"no_pool_mean = d_hat_obs\n",
"no_pool_se = se_obs\n",
"complete_pool_mean = idata_complete.posterior[\"mu\"].mean().item()\n",
"complete_pool_se = idata_complete.posterior[\"mu\"].std().item()\n",
"partial_pool_summary = az.summary(idata_partial, var_names=[\"theta\"], kind=\"stats\")\n",
"partial_pool_mean = partial_pool_summary[\"mean\"].values.astype(float)\n",
"partial_pool_sd = partial_pool_summary[\"sd\"].values.astype(float)\n",
"\n",
"forest = pd.DataFrame(\n",
" {\n",
" \"market\": MARKET_NAMES,\n",
" \"no_pool_mean\": no_pool_mean,\n",
" \"no_pool_lo\": no_pool_mean - 1.96 * no_pool_se,\n",
" \"no_pool_hi\": no_pool_mean + 1.96 * no_pool_se,\n",
" \"partial_mean\": partial_pool_mean,\n",
" \"partial_lo\": partial_pool_mean - 1.96 * partial_pool_sd,\n",
" \"partial_hi\": partial_pool_mean + 1.96 * partial_pool_sd,\n",
" }\n",
").round(3)\n",
"\n",
"fig, ax = plt.subplots(figsize=(20, 5.5))\n",
"y_pos = np.arange(K)\n",
"ax.errorbar(\n",
" forest[\"no_pool_mean\"],\n",
" y_pos - 0.18,\n",
" xerr=[\n",
" forest[\"no_pool_mean\"] - forest[\"no_pool_lo\"],\n",
" forest[\"no_pool_hi\"] - forest[\"no_pool_mean\"],\n",
" ],\n",
" fmt=\"o\",\n",
" color=\"C0\",\n",
" label=\"No pooling\",\n",
" capsize=3,\n",
")\n",
"ax.errorbar(\n",
" forest[\"partial_mean\"],\n",
" y_pos + 0.18,\n",
" xerr=[\n",
" forest[\"partial_mean\"] - forest[\"partial_lo\"],\n",
" forest[\"partial_hi\"] - forest[\"partial_mean\"],\n",
" ],\n",
" fmt=\"s\",\n",
" color=\"C3\",\n",
" label=\"Partial pooling\",\n",
" capsize=3,\n",
")\n",
"ax.axvline(\n",
" complete_pool_mean,\n",
" color=\"black\",\n",
" linestyle=\"--\",\n",
" alpha=0.7,\n",
" label=f\"Complete pooling (mean = {complete_pool_mean:.3f})\",\n",
")\n",
"ax.axvline(0.0, color=\"grey\", linestyle=\":\", alpha=0.5)\n",
"ax.set_yticks(y_pos)\n",
"ax.set_yticklabels(MARKET_NAMES)\n",
"ax.set_xlabel(\"Estimated treatment effect\")\n",
"ax.set_title(\"Forest plot: three pooling strategies on eight markets\")\n",
"ax.legend(loc=\"upper right\", bbox_to_anchor=(1.0, 1.0), framealpha=0.95)\n",
"plt.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "33737f97",
"metadata": {},
"source": [
"The partial-pooling estimates are pulled toward the population mean: the canonical *shrinkage* picture {cite:p}`gelman2006multilevel`, {cite:p}`gelman2020regression`. The pull is strongest for the markets whose individual estimates are noisiest (widest no-pooling intervals) or most extreme; it is weakest for markets whose estimates are tight and central. This is the data-driven version of \"borrowing strength\" that vote-counting cannot do and complete-pooling does only by force."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "261a8315",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:33.647890Z",
"iopub.status.busy": "2026-06-01T17:59:33.647802Z",
"iopub.status.idle": "2026-06-01T17:59:33.932721Z",
"shell.execute_reply": "2026-06-01T17:59:33.932284Z"
}
},
"outputs": [
{
"data": {
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"text/plain": [
"
"
]
},
"metadata": {
"image/png": {
"height": 1023,
"width": 4023
}
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(20, 5))\n",
"for k in range(K):\n",
" ax.plot([0, 1], [no_pool_mean[k], partial_pool_mean[k]], color=\"grey\", alpha=0.5, zorder=1)\n",
" ax.scatter(0, no_pool_mean[k], color=\"C0\", zorder=3, s=55)\n",
" ax.scatter(1, partial_pool_mean[k], color=\"C3\", zorder=3, s=55)\n",
" ax.text(1.04, partial_pool_mean[k], MARKET_NAMES[k], ha=\"left\", va=\"center\", fontsize=9)\n",
"ax.axhline(\n",
" complete_pool_mean,\n",
" color=\"black\",\n",
" linestyle=\"--\",\n",
" alpha=0.7,\n",
" label=f\"Complete-pooling mean = {complete_pool_mean:.3f}\",\n",
")\n",
"ax.set_xticks([0, 1])\n",
"ax.set_xticklabels([\"No pooling\", \"Partial pooling\"])\n",
"ax.set_xlim(-0.15, 1.25)\n",
"ax.set_ylabel(\"Estimated treatment effect\")\n",
"ax.set_title(\"Shrinkage: per-market estimates pulled toward the population mean\")\n",
"ax.legend(loc=\"lower right\");"
]
},
{
"cell_type": "markdown",
"id": "30196761",
"metadata": {},
"source": [
"### The substance lives in $\\tau$\n",
"\n",
"The hierarchical model returns two population-level quantities, and the conventional reporting habit of leading with $\\mu$ obscures the more important one. The posterior of $\\tau$, the between-market standard deviation of true effects, is what tells the team how transportable any single result is to a new context. A small $\\tau$ means the markets are nearly exchangeable, and the experiment generalises cleanly; a large $\\tau$ means the markets are heterogeneous, and the next market is a meaningfully new experiment. Reporting only $\\mu$ collapses this into a point and hides the variability that the next stakeholder will live with."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "74a6c277",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-01T17:59:33.934141Z",
"iopub.status.busy": "2026-06-01T17:59:33.934048Z",
"iopub.status.idle": "2026-06-01T17:59:34.138886Z",
"shell.execute_reply": "2026-06-01T17:59:34.138478Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"metadata": {
"image/png": {
"height": 559,
"width": 1223
}
},
"output_type": "display_data"
}
],
"source": [
"pc_mu = az.plot_dist(\n",
" idata_partial_bern,\n",
" var_names=[\"mu\"],\n",
" visuals={\"title\": {\"text\": r\"Population log-odds effect $\\mu$\"}},\n",
")\n",
"az.add_lines(\n",
" pc_mu,\n",
" values=TRUE_MU_LOGIT,\n",
" visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_MU_LOGIT:.2f}\"}},\n",
")\n",
"pc_mu.get_viz(\"plot\").legend()\n",
"\n",
"pc_tau = az.plot_dist(\n",
" idata_partial_bern,\n",
" var_names=[\"tau\"],\n",
" visuals={\"title\": {\"text\": r\"Between-market SD $\\tau$ (log-odds)\"}},\n",
")\n",
"az.add_lines(\n",
" pc_tau,\n",
" values=TRUE_TAU_LOGIT,\n",
" visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_TAU_LOGIT:.2f}\"}},\n",
")\n",
"pc_tau.get_viz(\"plot\").legend();"
]
},
{
"cell_type": "markdown",
"id": "355a8d07",
"metadata": {},
"source": [
"The Bernoulli picture is the Gaussian picture on a different link. The population mean log-odds effect is recovered; the between-market variance is recovered; the per-market shrinkage works as before. The log-odds parameterisation carries a structural advantage the probability scale does not: a given value of τ means the same degree of between-market variability in the treatment effect regardless of what the baseline conversion rate happens to be. On the probability scale, a τ of 0.05 is meaningful heterogeneity at a 5\\% baseline and negligible noise at a 50\\% baseline; on the logit, τ is scale-invariant in the way the analysis needs it to be."
]
},
{
"cell_type": "markdown",
"id": "d4c871ab",
"metadata": {},
"source": [
"## How much to borrow\n",
"\n",
"With $\\tau$ estimated on both scales, borrowing across markets raises a question the hierarchical model answers quietly: how far should one market's estimate move toward the others. The shrinkage already shown is that answer in action. Each market's pull toward the population mean is a weight set by its own precision against the between-market variance $\\tau$ the data infer."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "4c87404e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
market
\n",
"
se
\n",
"
weight_on_population_mean
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0
\n",
"
Market A
\n",
"
0.423
\n",
"
0.466
\n",
"
\n",
"
\n",
"
1
\n",
"
Market B
\n",
"
0.359
\n",
"
0.385
\n",
"
\n",
"
\n",
"
2
\n",
"
Market C
\n",
"
0.330
\n",
"
0.347
\n",
"
\n",
"
\n",
"
3
\n",
"
Market D
\n",
"
0.296
\n",
"
0.300
\n",
"
\n",
"
\n",
"
4
\n",
"
Market E
\n",
"
0.277
\n",
"
0.272
\n",
"
\n",
"
\n",
"
5
\n",
"
Market F
\n",
"
0.255
\n",
"
0.241
\n",
"
\n",
"
\n",
"
6
\n",
"
Market G
\n",
"
0.212
\n",
"
0.180
\n",
"
\n",
"
\n",
"
7
\n",
"
Market H
\n",
"
0.163
\n",
"
0.115
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" market se weight_on_population_mean\n",
"0 Market A 0.423 0.466\n",
"1 Market B 0.359 0.385\n",
"2 Market C 0.330 0.347\n",
"3 Market D 0.296 0.300\n",
"4 Market E 0.277 0.272\n",
"5 Market F 0.255 0.241\n",
"6 Market G 0.212 0.180\n",
"7 Market H 0.163 0.115"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tau_post_mean = float(idata_partial.posterior[\"tau\"].mean())\n",
"shrinkage_weight = se_obs**2 / (se_obs**2 + tau_post_mean**2)\n",
"borrow_df = pd.DataFrame(\n",
" {\n",
" \"market\": MARKET_NAMES,\n",
" \"se\": se_obs,\n",
" \"weight_on_population_mean\": shrinkage_weight,\n",
" }\n",
").round(3)\n",
"borrow_df"
]
},
{
"cell_type": "markdown",
"id": "5511e1fd",
"metadata": {},
"source": [
"Noisy markets carry the largest weight on the population mean, so they borrow the most; precise markets keep their own estimate. The between-market variance sets the scale, and the data set $\\tau$, so the borrowing rate adapts to the evidence. This is the dynamic borrowing the FDA guidance describes, where the amount borrowed responds to the similarity among the sources {cite:p}`fda2026bayesian`.\n",
"\n",
"Borrowing earns its keep through precision: a prior built from real past experiments sharpens the next posterior and lowers the sample size needed to reach a given assurance, so the eight markets already run are information the ninth should use. The open question is how much of it to grant, and a *power prior* makes that dial explicit {cite:p}`ibrahim2000power`. Raise the pooled likelihood from the past markets to a discount $\\alpha$ in the unit interval and use the result as the prior for the new market. With $n_0$ past subjects it contributes about $\\alpha\\, n_0$ observations' worth of information, so $\\alpha$ is the fraction of the historical sample size carried forward, the prior effective sample size {ref}`assurance_planning` planned around. At $\\alpha = 1$ the past markets count in full, as if pooled; as $\\alpha$ falls toward zero the prior widens and the borrowing fades. Fixing $\\alpha$ in advance is what makes the power prior the static counterpart to the hierarchical model's data-driven $\\tau$.\n",
"\n",
"The word *power* here means raising the likelihood to an exponent, a separate idea from the statistical power and assurance of {ref}`assurance_planning`. The two meet only through effective sample size: $\\alpha$ sets how many past observations the prior is worth, and that count is the quantity the planning notebook traded against sample size."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "5915e805",
"metadata": {},
"outputs": [
{
"data": {
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" alpha prior_mean prior_sd\n",
"0 0.10 0.308 0.286\n",
"1 0.25 0.308 0.181\n",
"2 0.50 0.308 0.128\n",
"3 0.75 0.308 0.105\n",
"4 1.00 0.308 0.091"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w_pool = 1.0 / se_obs**2\n",
"pooled_mean = float(np.sum(w_pool * d_hat_obs) / np.sum(w_pool))\n",
"pooled_var = float(1.0 / np.sum(w_pool))\n",
"\n",
"alpha_grid = np.array([0.1, 0.25, 0.5, 0.75, 1.0])\n",
"power_prior_df = pd.DataFrame(\n",
" {\"alpha\": alpha_grid, \"prior_mean\": pooled_mean, \"prior_sd\": np.sqrt(pooled_var / alpha_grid)}\n",
").round(3)\n",
"power_prior_df"
]
},
{
"cell_type": "markdown",
"id": "bb991411",
"metadata": {},
"source": [
"The power prior must be measured against the belief the hierarchical model already holds about a market it has not seen. That belief is the model's *predictive distribution*, and it comes in two forms. The true-effect predictive gives the unknown effect of a new market drawn from the same population,\n",
"\n",
"$$\\theta_{\\text{new}} \\mid \\text{data} \\sim \\mathcal{N}\\!\\left(\\mu_{\\text{post}},\\ \\sqrt{\\tau_{\\text{post}}^2 + \\sigma_{\\mu,\\text{post}}^2}\\right),$$\n",
"\n",
"and the observation predictive layers experimental noise on top,\n",
"\n",
"$$\\hat d_{\\text{new}} \\mid \\text{data} \\sim \\theta_{\\text{new}} + \\mathcal{N}(0, s_{\\text{new}}).$$\n",
"\n",
"We draw both now. The first sets the width the power prior is chasing; the second is the yardstick for the conflict check below. The power prior borrows the precision of the pooled mean and treats every market as one draw from a single shared effect, while the hierarchical predictive folds the between-market variation back in through $\\tau$. The figure sets the two side by side."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "91ce8350",
"metadata": {},
"outputs": [],
"source": [
"mu_samples = idata_partial.posterior[\"mu\"].values.flatten()\n",
"tau_samples = idata_partial.posterior[\"tau\"].values.flatten()\n",
"rng_pp = np.random.default_rng(RANDOM_SEED + 1)\n",
"theta_new_samples = rng_pp.normal(mu_samples, tau_samples)\n",
"s_new = np.median(se_obs)\n",
"d_hat_new_samples = theta_new_samples + rng_pp.normal(0.0, s_new, size=len(theta_new_samples))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "de589904",
"metadata": {},
"outputs": [
{
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321L/fOdB6MVYxGMyzPi5w4wrPCpFMPqg0td7FO/Spm0sLEa+sNht2mqr2X3nhwpuX/7//ZuIufl2AHwZEt8Nhk/jA/fOr5sedIxq9l6lUinG5kzlgQceGHpMr8XFxSLUvRPs3pnebukEwK+srIz8MwKjk37WU3n11VdHts1qtTpQ0HsnHD7VndI735lOYwwLhAcAGI6/5gEAAADYlQHp+4ant/Kovu6Rgbe39GM/Ha3PP10MyLDn0nEP+lDMMA8ajcowAc9TYzzeYR5g22lwexp0Z2qifICt/YBUN0g9fe06geqd9sk0324/eXyoXda+6h07O2ZGptlsjjxYvTNdhCUCcdQD13cStJ7ajh8/LnAdAOjKm+n6ys3Il2+tq2+u1imgvbXkrCXVmYjJM8XgMCmcPabO9tTnIurHPXQOAACMVH7jVjRTSPvjn4/mZ78QMb86IMRuys6cjMqbXx/Vt7w+Ko8+FFmjEY987nObrlOvG0ATerXyPH7zlVvxwadeiQ+9cD2WRzE4TES8++Kp+K7X3hfvuHDSdQgAAAAAgE1cnJmMv/CWh+JPvfH++IWnXomf+fyL8fzc8M/Cpau8//HFG0U5Pz0R73/ofLzvofPxwLFpXwcYMMQ9vu4rI78zF83f+2w0P/GZaH36iYjlXRpIfGExWr/zeFGS7OK5IsC9mkLcH3t4uGAAAADgyCrCxqcvRjZ9se/yvNWIWL4R+eKr7WD3spRh7yng/UYZfn6otVbfTYwnNw5Aqx0rA90nUqD7qcgmTrbrU+2Q95MR9RORZZW9PXwAAAD2vaxei6jXIjs+u6PtFON7pjF2e8Les3OnB99QoxGRbSMFfDcMM37uGIPmhzveMY57NDHc/eTWJz4T+fV0bWQI1cqakPfVUPfJ/oHvvX2mJqP6+tcMt1/2VApGnp6eLsrFi/2vNW7X0tLSQGHvGy1bWFgY2ecDdn/88/TznMoopUD4jULdtxv+vtF8bdAMBgCAA8b/7QAAAAAcYcVDSI3mmoD1ImR9uSdsvae+J4h9g/6xssELSMdnY/rvfP+wBxvjkD5TNjsz0DrjHAiieJhsQAfueKenovLIA+VDSOtD1jvh60XYeppPDye121P4epqeqBsc/QD8bkoPFo06WD3VabsA66UHIrcKVt8qfF3gOgAw0N89rZWI5VvtAPZOfTPyFMK+0p5fuhXRnHdiO7JaOdDL5Jl2OPuZNdMxcSay2pTzBQAA7Kp8aSlaTzxThrV/+onIX7q6Z2c8e/ByEdReffPrI7t8cc09z6laLd7ylrfs2bHAQfbC3GL8wtNX418//Uq8ND+aQWwmKll804Pn4ztfe1+85sRgz5gAAAAAABx1M7Vq/BeP3Rff/uil+NUXrsc/+dyL8TvX7uxom1cXluN//fTzRfnScyfiWx6+EL/vypmYrlVHdtxw2KUQhdo731aUfGUlWp99Mpqf/Gw0P/mZiFs7+xndTP7yq9FM5UMfSaMNR+XRB6PyxseKweuL+6QVgYAAAMDwskotYup8ZFPn+/9NkrciVu62w9xvtMPcU7j7jdVw95XRBq3sW427Rcnnni1m+4/8lEVMnFgX7n6yZ76so35MwDsAAAADK96hTGPIpvFlTx4f+gzW3/91Ufvm3xexvFKEjBfj4PaEwa+ZX1wq3iMt6xQa31m+Oj9IsHoxLu6Aiv2PyTDjE+eL4wuaH3Y85eJrOaxmK2J+MfL5xdXtbXfdiXpM/8//z4F32fjQR6J17cY9wfBrwuMn6muC4ouxl91f3xcmJyfj/PnzRdmJlZWVuHPnzkBh7/1KGpsZOLiB8J2f5d34XbWTMPiN+qXxniv+PQIA9gHB7QAAAAAHJWA9haGn4PTiQZ8yRD0q1ag8cN/A21v8//z9yK+lALDliFYr9sywD6aMMVi8eChqUOnBrnEZ5hzv1vGmgWyKAPV2wHoRoN4OWC8efpuI6qMPDbzZbGY6Jv+7P70rh8z2NRqNmJ+f74ajp9I7P8yy3rD19CAAwGZqtdqa0PTt1qkIXAcAdkveavQPZF++taaOxpwvwnr1k+0g9k44+9nIJk+3g9nPGpwFAAAYX1D7F56N1uefitbnnorWMy/s3T32ei0qr3tNVN/8uqJkJ0/szX7hEFpsNuNDz1+PDz51NX7z6ugGzT09WY8/8ujF+LZHLsWZqfrItgsAAAAAcBRVsyy+5srZonzq+p34p597MX75+WvR3Pbo1v399qu3i/I/fbwav//+s0WI+5vPpLCwbFSHDodeVq9H9U2vK0r+X7wv8mdfLALcm5/4TOTPv7R7O242i8D4VBppfmYqKo89HNXHHo7Kax+O7L4LBpoHAABGKssq7SDyExHHH+nbJ2+tlO8KLl6PWG6HubdD3TvT0VwN7jrc8vZ7lOm5vKc3CSnrnNfeQPeT7aD39vzkqYjarIB3AAAAdkURYJ3Gwk1j457c2bby9I5pJ9S9W7fD3RfXzmfnzwy+gzEGoQ81/vMYg+aHHq86jek9Dul7cAjN3/m9aH3+6cFXrNeKYPdssgx1L6fboe69Ae/rlq2Gwtej8sgDkdXE2+0H9Xo9zpw5U5SdSOM99wuA36r0BsR31i/GzAcOhaWlpaJcv3595NvuDXQfNBh+ZmamO9+Z7q2FwgMA2+UvWwAAAIARylPQcHpoZmk1YD1PD2P0Ti+tbNxWBLKvTq+GtK+k9PZ79pc9cF9Mff+fHfxAF5YiFsbwgk/6bK3WwAMhFA9rjEnxENSAiqDycdnp8aaHatKDZEW4enpQpv1gWeoz2dPefuCsd7r4OvWu68GasUoPwnQC0YcNWN+s7/K4HjQDDkXY+iBB6xvVk+nfJQOlAQB7pBxM5XbkK7fbAey9wey3Il8qA9qjcdfXpJ/qZDuI/Uw7lP1MZBMplP1sZFNnysFVKsLNAACA8Uv3h1tfeGY8Qe3JsZmovvn1Ram8/jVjvVcOB10a8OHTN+fig0+9Ev/22Vfj7kpzZNt+zYnp+K7XXo4/8MC5mKwO9gwMAAAAAABbe9OZ4/HD7zweL80vxf/5xEvx80++vOPrvPONZvzLp14pyiPHp4sA92988FycHee7gHAApXd5sgcvR+XBy1H/5t8Xres3o/XJzxZB7q3PPRnR3MX7q/OL0frdTxelIMgdAAAYg+I9uKnzkU2d37BP3pi/J8w9X7rRrq+V7yLmo3umbf9rrb6XWca995dV7w10L+bX1gLeAQAAGKdiTOXpqaJku7D9ypteGxMnv7Md/r5c1mmM6nZIfDndrlPI+9JqgHysNHa072IM4j0Yt3lUhnkHtxg7fIfnaVjDvjM89DlOn3OlEflcz7YG3MTU3/0raRDRgdZpfOTj0Xrm+TIcfk0Q/LoQ+c6yToh8vTbwmOUMrlqtxqlTp4qy03d40zjVnSD3Tpj7+unttqVxtIHDqTOe/W6YmpraMNh9q7btrJN+ZwIAh4PgdgAAAODIScHhawLSU90OW89mp6Py4JXBttdsxuJf/58i0rZ2c0CBfoZ9cGKcg7unEPoU7H1QjneYczzEg0ZDS+emE56eHjSZmR54E9n998XU//uvFg+zZG4E7plWq1U8YDKKEPV+yxYXF/fuwwCHWnpIJIWljyJwXdg6ALCf5HkrYuVuxMrtyJdvlQHsRTB7T718O2LlVkQaKIX+slrE5Ol2EPupyCbPlsHsPSHtUZ0uBuoEAADYl0HtTz67GtT+9PN7G9Se/qy6dL4Man/L66Py0BWDCsAO3VxaiV965tX44NOvxOdvjfaazrsuniwC29954aRrHQAAAAAAe+DSzGR871seij/1hvvjF55+JX7mcy/GC/NLO97uk3cW4u994un48U8+E++571R8y0MX4t2XTket4jk3GFTlzKmofPU7ovbV74h8YTFan34imp/4TDR/73MR8wu7e0LvCXKfjspjD0X1sYej8tqHI7vvgvuvAADAWGS1mYjaTGSz92/8buPy7XaI+43IF6+vCXXPl28UyweP0jrgUph9J+x+009fiZg4EVE/0Q55PxFZvVOfaIe8p+UnI6pTnvcDAADgwN2DjVSGUISSp3GfF9th7inUfU24e2/oe1l3g+AXlyM7c3LwnY4xuH2o8arHebxp3OhhHLBz3PrME9H8z58Ybn/dMPeegPeirnfD33uni3qy3g1/rzzyQGTTU8Ptm4Gk8cQ6Icf33XffjkPg0zjag4a9b9TWaDR8NeGISL87Url27dqubD+Noz2KAPiN1qnVRMgCwF7xry4AAACwL+Xp5mZ60KM3XL09nwLS86WViJWV8uGObtvy2uXFsnZb7/TKxjdOK1/8hpj8nu8c6FiLoOtxhLYn6fMMIT1UMLbXctLXadDg9mEfLBmF9PDQgIqHNvouyCKm0kMdk2sD11NdzE9GNtV+8KPd3hvKXixLfVJ7mq7XRzJoRPE9PF3d8XYOk2az2Q1V36x0QtK3W3oD1hcWdnnQEeBI64St7zRoPdVTU15EBQAOjvQAfjQXykFLUuD6cjuUfaW3boexL99Jr3mM+5D3t+p0GcaeQtknTkc2meoUzr4a1B61YwYuAQAADoz9ENQe01NRef1rovqGR6OSypADaACrmnkeH3n5ZnzwqVfiP75wIxrpGtGITFSy+MYHz8d3PnZfPHpyxmkHAAAAABiD2Xo1/svH7os/8uil+I8vXI9/8rkX43evpWcAd359+UMv3CjK2al6vO/B8/H+hy/EQ8enR3LccNSkwc+rb3tTUfJWK/JnXojm458vBmVvPfVcRGuX32yeXxDkDgAAHAhZVinf20vv520gbzXK9yGXUoj7jciXbrbrGz31zTLs/MhJwffpfNyMfK5s2fAvzspE/4D3NN8JeS/qE5FV6nv4GQAAAGD0uuMLT09FtkcnODt7Kmrf8FXtoPjltaHx68LiNxsTfKh9H7Dg9qGOt/1u9FhUq+X31ICKseKH1RmPvnd7A6w++Vf+m8iuXBpol82PfSqav/t4Mc53NzR+olO3pyfrq6HxvW2ddYY4T6wNgZ+eni7KxYsXdzwG3dLS0kBh75stX065A8CRlX6fpHL9+vVd2f7ExMSOAuBT3Snpd2jvfKetMoIMCwA4DAS3AwAAAMMFYLWD1deEqfeZzi6dj+qjDw20/dar12Pph/7eeL4yw97YTzfOFxZjrxVh9MMY8kGNUUgPe2R79GDJjlWrkTcGfzmp8tjDMfEX/+Q9oexRrwkyG8Hvn/TAwrDB6dsNXvdQBDCOoPUUkt4px44dWzM/aJuwdQDgsMlbK33C2PsHs0fqy9bqx8sQ9k4gexHGfqpdt4Paa1POJAAAcKDlt+5E66lni7D25heeLYIB9jyoPcui8tCVqLzxsTKo/cHLXsCHEWjleRHK88vPX4tffu5aXF0c7TWh05O1+COvuRTf9ppLcWbKYKwAAAAAAPtBNcvi9105W5RPXr8T//RzL8Z/eP5aNEeQBX1tcSU+8NkXivKmM8fi666cja+9cjbum50cxaHDkZNVKpE9fH9UHr4/4pu+JvIUqv65J6P5+BPR+vTnI79+a/cPol+Q+2seiMoj7ZLu3ab3wwEAAPahrFKLmDwT2eSZDfvkeSti5W43yD1fvhGxdLNdp/mbEUvXI1pHOFwoffalVyNferWY3fQyUm0mon4ysokT/cPeizoFvh+LLBN0AgAAAEnl4vmovP/rtnUy8mazCE4vA93LMPdOqHu+2A5779SdIPhO/06dxj1vr1uM9bxXY3mPwrDja48ruP2gHW+SQtUH1Hr2xWj+1id3tt9qpX+w+7q2Yjqd13qq61F50+uicm7j638MFwKfxuNN5fz58zs+hZ0Q+O0EwKf67t27xXSn7pQ0n0qR7QDQlnIQUrl58+aunZP0+3B9oPtOy/qQ+MnJSdkbAOx7gtsBAADgCEgPE+SvpJcHViJWVsoHDYo6Ba+nBw7KkPWybbnoU/RdE8a+tm9s8wZf9b3vHDi4vbiRPC7DPjyRjnkMwe1DP4gwxuD2oc7xdo63khUPzJQh6WUpvpc6wenp4YSe6WyqDFPv1N1lU6vbyGrDXT7Ljs9G9fhsHDWNRiMWFhaKstPg9M1Ka6+DFAC2EbTeL0Rd0DoAwMaKh8ebC+3A9dsRK3ciX7lTBq+n6d62NN2cdzq3LSsD2SdPleHrKZS9qHvnT0VWETgGAAAcLmnAhvyFV4qQ9k7Jr+/eC4qbyU6fjMobH43q6x+NyutfE9nM9FiOAw6bZp7Hx1+9XQS1/8oL1+PVEYe1J192/kR8y8MX4muunImpanXk2wcAAAAAYDTefOZ4/J13Ho+X55fig0+/Er/w1NV4cX5pJNv+1PW7Rfl7n3g6vuj0bBHgnsLi7z82NZLtw1GU7plWv+SLipKeI86vXovW409E89Ofj9bnnirfXd+LIPdPfrYohRQuf/+l1SD3VE6f3P3jAAAAGJEiPDyFjKdQ8WMPbf4uZzfYvQx0T0HvZeD7zaKOxpyvS2M+UskXXizP3cZnvgh2j4njkaW6nurj7XD3cr5sa39tvMsJAAAA5V/U6X29menxvnNbq0X1S9+0Ngy+py7KbgUrDzEeeHFtZ0xB6EXw+AELbi/GFB9QMSb/TjVb5dj0C4vda0rb+S6aOHs6YsDg9uYnPhMr/+ZX+gbDF231ddOdMdonOnVZiumib7382aSvFEacyrlz53Z8htKY6mls9d5Q951Mp2KcdmAri4uLRbl+/fqunawsy0YeDt8vJL6e/t0CgCEJbgcAAIA9VtzsbjTWhqUXoejtUPXlRretd3kRor60EtW3flFUX/fIQPtsPfN8LP8vH4ixGOZF+XTDd0yKhySGvCm/S49UbK7ZKgafH/Tm9jAPEYzzHFff9LrITp5YDVTvDWfvhLLXqsXNGXrOdZ7H8vJycUO+N1B9lNO9bSujeNAEYIxB64O0pQen/LsDALBW3moUYetl4PrtInA9753vBrKX05E3ncKB/8d2OmLiZGQTKYT9VGQTJyMmT0c2cbpdp/YTkWVehAAAAA6/fG4+Wk89V4a0p/qp5/ZmMP9+6rWovPbhqL7hsSKwPbtwzn0EGJFGK4+PtcPa/8ML1+PG0uh/zi9OT8T7H74Q73/ofFyeFboDAAAAAHCQXJyZjO954wPxp95wf/z21dvxwadeif/w/LVYao3mjc/fuzFXlP/lk8/E60+lEPczRZD7g8fHOIg4HHDpnax0T7Vy4VzU3vvOyFca5X3fT38+mo8/EfnzL+3NgbRakT/zQjRT+dBHymM7dWJNkHsKdjdAOQAAcJAV42LUZoqSzV7ZsF/eXIooAt3LIPdusPvyrYjlW0XYe1ruvdDibEWs3CrKtoK4qlOrQe6pnuiEu6eg93Y9UdbF1ymrjPabAAAAAOiqnD0dE3/iOzYfO36lUYa5L/eEui+mayf3Br0XdaffYrtuz6/2W4po5cONB56OZbeC5HdpjPhinP1xGeaYxxg0P8zx5rfvRP7ci6MdC79aWRsC3wl0b093QuCrX/bFUX39awY73larDLY3dnxUKpVifONULl26tOMvW/p9lcKYRxEC35k2vjww7O+jubm5ouymWq22ZdD76dOn4+1vf3t8xVd8RbzlLW/Z1eMB4GAR3A4AAABDaL34SjQf/3yfcPV1050w9pX2dGd+B3c1s3OnBw5uz8YYhF48ODCodEN2XIa9sT/OY04392cGHORju98TWbtvT1h6t26337OsX/+JtWHrg6rcd6Eoh0Gr1eoGnW8UgD7K6eKBH4ADKN3o7gSmdx4sWl9mZ2fvCVQXtA4AMDrF35TNhSJovQxcv9MOYk+h7D1h7KktLW/OO/3DSgNvdAPZ1wWzF3W7vTrpHAMAAEdSeik7v3otWl94thyw/8lnI3/51bEeU3b5YlTf+GhUUlj7ax6MrO71DBiVRqsV//mV2/HLz1+LX3nhetxaboz85NYrWbz38pn4locvxJdfOBnVNDgtAAAAAAAHViXL4ssunCzKX15+JP7dc68WIe4pdH1UPnNzrig/+aln47ETM/G1958tgtwfOTEzsn3AUZTutaZ351Op/8HfH/ntu9H8zBPRevyJoo47uzuga6/85u1ofuxTRSnUa1F58PJqmPvDD0R2fHbPjgcAAGCvFO8uTl+MbPri5u+cNubKgPciyL0T6L4a7N4Jehfw3qO5WJR88Wp5Hjf9SlTaoe6rAe+r4e6dwPeeEPjqGMeWAwAAgEMoS+8ZTrRDq2M094bLayrNNCj14Cs3m1F57cPdoPhueHwKiR9me4MYJmh+7EHoQ4wRP8ag+SIYfUDF13/UUrD6wmJReq9drb+OVXnwSsSAwe2tJ56J5R/76fTDtfqz1Q6G7063g+GL89EJi+/Xt6gn+m+jWK8WWaUSR+n31fT0dFEuXBjN2P1LS0sjC4FPJW0PYFQajUbcvn27KJv5qZ/6qaL+1m/91vixH/uxuP/++30RABDcDgAAwMGQN5vd0PPeAPTudE9gehmW3thw+frp+nd9S1Rf/+hAx9N69oVo/Pz/FWORjv0AhYoXX4MBFTc3a9XygYI9NuyN5xRKPrZ47HSOBwxur77tTWUQek/A+tpQ9nTDeqK8SX0EBqZeWVkZOBh92EB1N4uBw2h9oPpmYevb6ZNC26vV6rg/FgDAoZPnrXJQjJW77QD2dt242w5g763LUHaDY+xQZWJt8Pr6QPbJkxH1U5HVpkbzRQYAADgEigEIbt4uns1oPbNaYn5h7EHtaXCD6mMPR+WxhyKbFcABo7TcbMVHX7lVhLX/6gvX4/bK7jw39PpTs/EtD52Pb3jwXJwc4zNVAAAAAADsnuMTtfi211wqyudvzcUHn7oa/+aZq3FruTGyfXz+9nx8/vfm4x/83rPxyPHpboj7oydmjsQ7mbCbshPHovblXxLx5V9S3D/OX3k1Wp97Klqffyqan3tqT4Pc05gFaRDxVLrHd/5MEeaePXA5Kg9dicr9lyKbnNy7YwIAABiT4ppH/VhRstn7t36XdenmPYHuq/OpTsEauxwwduC0IlZuFSWfL1s2HdesOtUT5N7+2tSO9QS+d6aPRdSOR1QnXbsCAACAsVxTqQ237vRUTH7vn+i7LG80yrH224HuKTA9X1pZDXdPY5ants6yYjz+fv1SW8920tj+Q4aKF8eVtjEOQ4Z2DzN+/lENmh/qeDt5Cmn8gKX291/P4pGP6Z9+1trB79WvfHvU/8B7B/7+bX3mC8U2ylD42trpTrD8IQ2In5ycLMq5c+dGNu5/J8h9bm6umN5pSeP8A2zHz//8z8d/+A//IT784Q/HG97wBicN4Igb7q9yAAAAjrxikOwUqp1ueq00VoPQVxqR3Xdh4JuqjY9+PJof/njPdjoB7O355i4+XD+/OPAqWbpRNi7ppvagxjnI8LA3cicmIhoLB+t4tyOF0BYB6elmawruqpdh6RM9Yek9bWuW91sntR2bHfhwq699OCKVffi7ZXFxsQg436gexbLekm60Npu7M9g3wH5TqVQGDlHfqt/09HSxXQAA9l7eTC85lMHrq0Hsd/u0lXUx0MXoH1M/mir1tQHsawLZVwPa06AXBmAFAADYXH777tqQ9mdfiLh9d+ynTVA77L6lZis+8vLNMqz9xRtxd5fC2k/Uq/GND56P9z98oQhuBwAAAADg6Hjs5Gz8d18yG3/hLQ8W16I/+NQr8eGXbo40EuzJOwvxjx5/rigPHpuKr71ytghyf91JIe6wU+k53Ozi+ahcPB/xni8ff5B7usd99Xo0r16P+K1Ptg8yymN88HJUHrgcWaqvXBp6EHsAAICDLssqRVh4ERgeD2we8J7efe0GuXfqW+2g996Ad+/G9tVcLEq+eHX1vG76xamtBrx3vkbtoPduWy3VnbbZyLLqDr4bAAAAgN2S1WoRtVpkM9Mj3W7eapVjtKd6CJVHHoi4O98Ngu8NkS/Cu3fLdseHX29cQfNJGmP+AB1vdhCC5lcaZWbG/EL5PTeg/NbdWP6pn9m6Y7WyGuLeG+iesiva8wNPnzgWlQujCUzfL+r1epw+fbooo5KyBFKmwE7C39eHyKdg+daQv/OA/e3WrVvxbd/2bfHRj360GEsfgKNLcDsAAMAhHtQ6n5tfDVUvbhZ1wtDb06nuhKS324r+ncD09vLVZWn91X4b3eSc/Cv/TWRXLg12vDduFS9Hj0NxfgY1xhelhznebNibxqMwxM3JJAWSFzc391q6mZ/nAwdq1b7mXZG//c1rA9dTPbkuhD0Ftx8A6RwsLS1tGoQ+yiD1Tp32CcDqwyXpZu7s7OzIwtanpoRGAgDsV8UAE4351aD1RhnA3gliL+p1bdEa4wP/h1LWHkjiRGQTJ8oA9nq7TvP1k+1g9hMRVYOpAgAADCM9y9Ib0J4/80LkN9NgiuMnqB325nmUZ+8uxm+8fDN+46Wb8duv3i7C23dDevLnHRdOxrc8fCG++vKZmEyDIAAAAAAAcGTVK5UyUP3K2XhlYSl+8elXixD35+YWR7qfZ+4uxk9/5vminJ+eiHddPBnvvng6vvzCyTgxYbgvOIxB7ikRL3/pajRT+ejvlG2VLLJLF8ow93bJ7rtYDtYNAADAasB78S7nicjiwc3fv03h7Su3y0D3Tr18O/KVtXU0xzBm2UGSp3EFbxalM4LglnFptdk1oe5F2Hsn/L0b+t5pOx5RmRh4/DYAAABg/8gqlYipyaHXn/ye7+zbnu7vR6OdeZDGrO8Gu5eh7vnyasB7MV3UK/37tcPgO+Hw0WiWY8APodjHAQpCH+fxxkE73hSKPqjt5j+kd6MXlorSe31ty2ttm6h88Rs2/PnZzNI/+meRpXeoixD4lItQW51eEyq/wXRRd9ap7ftre9VqtRhrO5VR5zHsJAy+X5G3APvD448/Hj/xEz8RP/ADPzDuQwFgjDzBDQAAsIvyVqu8ybLcCU/vnb43SL0bst5u6/Srf+e3DBz2vPLz/zaa//kTu/bZNt95Y29uYI3KMDfuxnm8wwShTx6soPltneN0764bkF6PaIejF9OpTvPpc3faJlNd9i+mJ3vD1dvT7XoY1Tc+Frsh3bBbXl7elZD0rZYBsD0zMzPdcPV+9TBtqUykf6MAADiQ8lajHbI+F3m7TvP5ujoac+0Q9jQ9HxG7E1J15FWnNwhhXxvOXgwSkQ12HRYAAIAtQtqfe6kb0F7U127um1O2Jqj90QcjOzY77kOCQ2lupRn/+eqt+PBLN4vA9hfnl3Z1f/fNTBZh7e976Hxcmhl+cBAAAAAAAA6vC9OT8SfecCW++/WX4+Ov3okPPv1K/N/PXYvFNKDuCF1dWI4PPnW1KJWIeNOZY/GuS6fi3RdPxRtOH4vqPh/kFg6CfRnknrTyyF94OZqpfPhjZVu1Ut6nTkHuD6RyXxHuLswdAABgGwHvk6eKstXVlLy51A52vx2xfCvylbLuF/ZehJiztUZ6J3ou8oWXV8/zZv0r9TLsvZbC3tfWUZ9th7132o+V7bXp8usMAAAAHFpFGHQnTHp2ZqTbzpvNMhR+CNXHHorWsZnVIPg0nv7SymqQfKp3ksa9mWHGHT5gwe3bDkLfN8c7vmuGwzw/knJQWr/z+AgPIiValqHuWTvIfaOw9+zMqah/8+8b/Jjn5iMqlXI/teq+CIpPxzA1NVWUc+fOjWy7KysrMTc3t2XAe+rT6deZXj/fOy0/Agb3cz/3c4LbAY44we0AAMCRUdw4Szc8ms2hbso1PvSRaL386tqA9bS9dDOtN4i9E8Kebl6N6AX9+rd9Y8R09cAEiw8T1F3cgBmTfIgbjUUQ+LgMc6NxHOe3kpWh6UPuu/4d7yt+XouQ9bSNyfYNuU64eq22JzfUWq1WLC0tFTeieku/tkHbN+rbKZ0A9TRIAAA7U61WBwpW327Aegptr6SHPQAAOJSKv8mbC6sB62lwgZW7kbfr3vbu8hTIngZ2YHdltXtD2OsnIyZORFaEsPfU1SFeTgAAAGCgZ3Lyq9ej9fxLkT//crReeLmYjlt39s9ZrFbLwe8feaAshyyoPT1f8KlPfWrTPm9605tienp6z46Jo6uV5/G5W/Px4ZdvFmHtv3PtTjR3+dmXSzMT8bVXzhYlhd5U9sFL+gAAAAAA7H/pHdW3nT9RlL/81kfi11+6Eb/83PX4tZdujDzEPW3tE9fvFuWnfu+5ODlRi3dcOBnvvnQq3nnhVJyb9qwj7GqQ++efjtZTz0XryWcjf+XaeE52sxX5sy9GM5X4rbKtko73XFQuX4rsysWoXLkUlSsXI44f2xcDUwMAABw0WXUyono+sqnz23h/eL4Mck8h7iu3eup1Ae8r6ZloY4BtWyuNwXizKJ2ztvXZy8qw906we+/0mpD32W4d9WORpZB4AAAA4MjLqtXiXfJh1P/g79/6OlIKhd8w2L09ndqKZWX7hst7p4cI6i7WH5NhchmKc3aQjneIvIqRGSbLYZi8is2kC3lFzkoj8li4Z1Gv7MqloYLbl/7nn4r82o32RtqfO4W412tlOHw7ML47nbIoJmoD9yvbe/vVIzu+t+NL1Ov1OHXqVFFGqdlsbhjwvlng+3aWNdLvOziEPvzhDxfjshhzBeDoEtwOAACMTX77bp/A80Z5A6o3GD1Nt29KpWVr+/Ws11mn0TvfDlFPba32Jf3jszH9d75/4ONtfvz3ovXE0zEW6XMMOm7yMDfcRnm8g0o3M8ZlmBtLYwxuz5eGCJpPgbLpe6L3a1OtFMHq6bMUNxCLuh2Kvn46haWnm0rt+SKQvTPdE6xe1u31qtUdvRBeff1ripvSy8vLq2Hmd27F0qs7D0YfpH1l1DceAdhUunG5ncD0QQPWJ9K/XQYqAQA4sooH31vL7WD1+TJ4vTG/JoR9NYw9XbdsB7CnPnlz3Id/dFTSNajj7RD2VI5HVj/eDmHvCWhPgezVaf+PDwAAMAb5/EK0nn858hdeKuoU0p6/+Mpwz4rsphPHVkPaU7n/vvLl2kMqvQD74osvbtrn9a9//Z4dD0fPzaWV+Mgrt4qg9hTYfn2I55sGdXlmMr7u/jKs/Y2nZ10rAgAAAABgR2Zq1fj6+88VZaHRjN94+Wb88nPXihD3+cZoQ9yTW8uN+HfPXStK8tqTM/Hui6fiXZdOxRefPR719F4wMNog96/8sqItvzPXDXEvyjPPj++edyuP/MWr0XzxasRvfWK1/dhMN8Q9u9yuL56LLA1ADQAAwI4VY9Ck8O8UBD5z36Z98/SecXr/ePlW5Cu3e+oU7n6nCHYv58vpiNFfSzr8UgBa+x3veLm3dRvvJbcD3dsh72vD3ss6ajORFV/vmXK64u9rAAAAYIDrSEXwcz2y2Zmxn7bKW94Q2amT3WD4Imi8Ewa/Piw+TY/yeYj9ECy+2zkSB+14xxg0X2RUDKHIkunOtD9D+3P0Xg/c8trgoCbqMf0//z8HXq3xKx+O1ivXBguPr/VZlqZH9ExgtVqNEydOFGXUUibIqMPgO9PFeKAwRvVh/h0D4NBwh5ixeeaZZ+JDH/pQfPKTn4wnnngiXnrppeJ/kFNI3szMTBGo9MADD8Sjjz4aX/qlXxpf9VVfFadPn/YVAwAYkbzV2jDgfLtB6J1+2ZlTUf+Grxr4GBb/7k9E3J3f+69p+jzDGOPgzenrMGj8dRGgPS7D3KhxvPdKN506Yenp+68dll65dH6oL8vkX/tz5Q2aTlh7tbpp/1arVfyN1ls64ebF9J3buxqY3mkDYH9JAegpCD1dw+uEo6+f32zZZvOpTjf+AQBgI3mrEdFciFiZWw1fb6yfToHscxHN+XYAe9ke+T4LkDsS0gsHaYCDE+0A9hTEnoLX23WnrR3UnlUnx33AAAAA9DxblL96PfIUzv78S2VAewpsv3Fr/52jNND+lYtrgtrT80zFi/DArmi0WvGp63eLkPZUHr8xN/oX4Pu4f3aqHdZ+Jl5/Slg7AAAAAAC7Y7pWja+9kq5Hn43FZjM+8vKt+OXnr8WvvnAj5hrNXdnn527NF+UDn30hZmqVePv5k0WQ+zsvnoors5PufcEIZcdno/qW1xclyZvNyNN98U6Q+5PPRn7j9njP+d35aH3mC0XpqlbKEPoU4t4Oda9cvhjZ8WPjPFIAAIBDL8uqERMni7LV08l5nsZ3TO8534l8+XbEymq4ezFdtKWg93I+msZY25FWCiW7XpTOc6zbep41vc/cDnIvA93LkhXB7u32IvS9N/B9NqI67TodAAAAMFa1t78lIpVB8khSrkgn2D1li3QC31fWhryvbVs3vbwS2cz0gQoWHy5ofnxjFRb5EQMqsmLGZdjclmFzYsZ0vM1PfiZan31yNMdQrZSh7ikjpB0AvzbgvZzvLKt/6zcM/HOX30ljcTZWt1+rpqT3bV/XTGPPpzLqnMgU2r6wsDBw4Pv8/Hy3rTPdr60xru8rDozJycmopZ8LAI4s/wqwp5aXl+MXfuEX4gMf+EA8/vjjG/a7c+dOUV588cX46Ec/Gv/0n/7TIrDpPe95T3z3d393fOVXfuWeHjcAwG4ob1Q0yovDnRD09KJ2qqcno3LuzGDbW16JlX/6r4oLoWXIerqh0dluOd+dXk7hRqN7KTx76MpQwe0pWHwvBmu9R/r8Byy4fbgg9PEGzccBCpof5sZSNjkRcTKFStXLGxzp+DvT7cD1Tad7+7enW7VqLOetWEqB6a1m8TdUb1D6mvLzP983TH2jMkwfNxkADqZ082+YAPXt9nVzEQCAUTw4WYSv9watt4PXy6D13ra1yw1AsA9UJsqQ9YkUul6Gr3dC2Dttq6HsxyLLKuM+YgAAADZRDED/6o3IX74arZeuRv5Su3751bG+WLyp6amekPb7o/LQlcgmJ8d9VHCozTea8clrd+Ljqbx6Oz55/W4sNVt7su+Hj08XQe1fe//ZeOzEjAEvAQAAAADYU1PVarz38pmiLDdb8dFXyhD3//jC9bizsjsh7vONVvzqizeKkpyfqseXnDsRbz17vKgfOzkTlW0OpApsLUuDEz94JSoPXol477uKttaNW2uD3J97KSKNETJOzVbkL7wczRdejvjN311tPz4blYvnIrt0PiqXznfrOJ6e5fa7AgAAYC8V79TWj5Xv187ct2X/vLm8Nsi9mL4dsdyuO/Np+fKd9BfrnnyOQ6+5VJaewPdk63Exs3WB7zMR9XWB790g+HXT1Yld/UgAAAAA/WSVSkqrLco4niCovuNLirEAOuHvRV7K0r0B8d3lqa29LJaX17RHGr9wAEUmxICK/Y3LMDkdB+14k3GNYTFsYPMoz3F6Nz9dE15avudaZL/v7vof/PqBd7Hyi78czV/7rbWN6Ye/G+TeDolP8+221RD59nQKe1/ft7tsXd+e5ZX7LkQ21X/cj/QMUxrfPpXz58/HqKVMl82C3bcKft9q+coQ2TvsL+9///vHfQgAjJngdvbMhz70ofjhH/7heOaZZ4Zav9lsFttI5Z3vfGf8rb/1t+LRRx8d+XECAHTk8wvR+tyTawPVuwHr68LW22HpRWh6Jzi90ewJTb932WYvZVa//Itj4r/6tsG+GFkWzd/6xHi+gMNe4B5XsHgacLrVKm8WDaC4MDwuw5zjMQahD3W8EyM4v9VKGYZeb4ekr5teH67eqlZjKYuYv3guGi+/PHjA+ck8lpbuxNKcoHQAtq9SqawJRB82QH2jdScmvKQDAMAeBK+3VtpB6vPtYPUyiD1vpulyvmwv+xTL2n2KYmCA/aOSrqEdj6gdi6wTtt6t2wHsEymMvR3KXhWEBwAAcBClZ5fyq9dXg9k79SvXimdp9q00QP79l6LywOWoPHBfEdaeXTg78HM/wGBuLK3E776agtpvF0Htn7k5F83BxjPYkRTQ/vvuPxNfe+VsvObEzN7tGAAAAAAANjFRrcR77jtdlJVWK/5zEeJ+PX7lhetxe3n3BpS9urgS//65a0VJjtWr8cVnj8db22Hubzx9rDg2YHQqp08WJb70zcV8vrwcrWdeKEr+zPNl/eqN/XHK78xF685cxOefjjV3/2emVoPcL/YEup86IdAdAABgnyjCvKtnI5s6u2XfPG+V72j3hLnny+1Q96Ltblk3yjpW5rzPPXJ5RDq/jbsDBr633+cuAt5TiHtZR226DH1vz2e16XbQ+3TRVgbCp+npyCqiBAAAAICDJz2vEKmMYuzDNCbCRkHvS72B7+V0dt+FwXc0znDmYXJFxni8RfbHMF/HMQW3D3O8SZE3NC7DZOOkHKT10gXM9Dnan2U7ofHDmPhLfyqqr3lwoHUav/WJaP7qb7YD4Kv3hsVvFDLf7VeuU63X4kQqafnJ0xFnz68Nlq9Vd/S8VApu3yzYfadh8Sl4nt313/63/61TDHDEudvKrkv/0/g//o//Y/yTf/JPRrbNj3zkI/Gt3/qt8YM/+IPx7d/+7SPbLgCw+4qLoZ2g862Cz4v5jULR28vWh6h3AtN7+qVS+5p3R+297xzsWK/fjOV/9LMxFsNcgE0XBcclnedhpIuU45K+fyYqByYIvbjZM6BsFEHow+o53vRzn/4uSBd8U9h5b907vfDSK7FwrBJLeStWIi/rPI+lViuW03SrFUutRiw3W7HcbMRyqxlLjUYsF2WlqJd6trll6PrSUjSG/d4F4NCanJwsws/Xl04o+k5L2k69XjeoBQAAY5d3gteLQPUUrt4OXu+GsM8Vbd3w9RTE3hPKHrnrKvtWeiG/fjyy+rEijL073VOvCWkXxA4AAHCopMHiU0D7mnD2VK5ei2jtYeryMCqVyC5fiMqDKaT9clGnF6KLFyKBXZOe73pxfik+noLaX70dv3PtTjx1Z2HPz/jrTs7E195/tghrf+j49J7vHwAAAAAABlGvVOLdl04X5a+87ZH47au3uyHuN5Z2d0DcuyvN+PWXbhYlmaxk8UVnjrWD3E/Em88ei2PDDNoKbCibmIjqYw8XpSOfm4/Wcy+uBro/+0Lk12/tn7M4vxitLzwb8YVn1wa6T050Q9x76+z0ycgqA47BAQAAwJ7JskrxXnDxbnDct82g9/TO+Gqoe6zcjby3boe8l8vvRrSW9uSzHEnp3f7lW0UZOPQ9qUyWIe612TLgfU3Yexn+3hv8Xoa+d0Lhp8vvHwAAAIADqghc7oQ3x3QMH7+8ueq73hbVL/viMmejCIBPmTc9AfFpfpDpImi+seF0pOyeHeSKHLxQ8QN2vOM+5mHG2Rjj90QRpD6g9KxV6wvPxJ7oDYSvVaP+h74hqm970/ZWrdfj5MmTcXylGa3PP9v+fTQTceZEZBfK8PhuQHy7XjPfCZmvVvs+n5Uyc9aHvG8V9r6wsFBMb7ekvKCj6k//6T8dX/u1XzvuwwBgzLxdwa5K/3P2Z//sny2C1kcthTH+9b/+1+PJJ5+Mv/yX//LItw8Ah0XeSg9Mroajd4PQdzhfe9fbovLglYGOpfnx34vlfzyeIPT0wuPAxvgychE8P9QNg2r5tdprw16AHecL3+nC4MSAQezjHAR6i3PcbDbvCUWfe/mlmL9+NZZSyHmzuVpS4HnksZLFap23YjnyWG7lsRwpID2FppeB6UvNZhma3t1OWS8VYenNdmj6SiylcPZ2Wfon/8uaYwGAnUr/rzNsePp215ueno5qteqLBQDAvpe3Gu2g9YWI5mLkRd0OXk91c7G9bGHtsk7oegpgTy93s/9l6UHLdsB6p66V9Zq2dhh71Gcjy/xdAwAAcNilZ4vyazcjf+VatK5eK0LZU1h7ms9v3o4DIcvKAeBTSHu7ZJcvRlYf8HkeYGCtPI8nby8UIe0fv3a7CGx/ZWHvn/E6Xq/GOy6cinddOhXvungyLkxP7vkxAAAAAADAKNQqlXjHxVNF+YG3PRKfuTkXH375ZvzGSzfjk9fvRHPb6UvDWWrl8bFX7xQl4vlIw3q+9tRsfMnZ42WY+7njcXZqYncPAo6gbHYmqq9/tCgd+Z270Xp2Ncy99ewLEbfSz+Y+srQc+dPPR/Pp59e2p4GBz52O7MLZqFw4G9n5slQunIk4cbwc0wQAAIADFvQ+W757PL29dfLm8row93bd6IS9r10WjblBosfZidZSxHIqN4cLfq9O9QS8l2HuUU0B72W9Oj+1GvbebU9tU8LfAQAAgEOvCFSeSKUeMRu7FhCf5Cm0PeXKdMLeB81NScc7PRXVt7+5DHAvwuBXIu+Ewq+bjmZrtB9gmHEhxhk0P2zOzLjCriuVyIYYK3+YnKOxnuO9PN7iZ6ERsVBeV82bg+c65c+/FCv//N/s7DiqlW6oe6qzdj1RlGqcWR/8XoS+T0f1y98a1S9+w2DHm34PvHS12FbKHlpYWYmFleWYX16O+aXFol5cXBwoAH6r0koZafvIt3/7t8ff//t/37NvAAhuZ/ekcMY//+f//K6Etvf6qZ/6qZiYmIjv+77v29X9AMC2L26miys9YefFhaltzFff8vripbxBND7ysWj86m9uGrQerd15kLHyyAMDB7eni3tjM8xF2HGGdA8bvp4umo0huD1dcBtGusg3tkdtt3kRNl3YW0lh5MvLcXdxPhbm7kSj1eoGoHfC0FdaZem0r/QsT6HnnT5r12uUIepFWxmSvpznZZ36pLD0zrb+/f9ZBKuvD2fvTO+3C5AAHC0p8LwTfN47PWzQer/A9XT9x6AOAAAcimvIreVu6HreE7Behq73CVzv9l0Nai+2wcFTqUfUZouA9ay+ti4GPSjqThD7sYgU0F6d9LcQAADAEZW3WpHfuFWGsV+9vhrQnuav39y158J2RRblYO4PXikD2lNQ+5VLkU0Kh4C9uCb5/NxSPH7jbnz65lx8ul3fXdn75wzT4ARfdPpYEdT+7oun4o2nj0WtItwBAAAAAIDDpZJlxTXwVP7kG+6PO8uN+M9XbxUh7inM/eWF3X8OOL11nsLjU/nZJ14q2u6bmYw3np6NN5w+Fm84lerZODnEYL/A5rLjx6L6Ra8tSkd+63a0nnmxCHFvPfN8Eeged+f336lsNiN/+dWi3DN6xUS9HeJ+tgh2z86ficr59vSAY+UAAACwf2XViYjqmYjJM9sKpcrzVhneXoS6l+HuKfg9X5lbU6c+Zdh7OS3sfQzSGAWpxPXhgt/Td0QR/l4Gua+GuvcJf++GxLeXdcPfpyOrjHGMVwAAAIB9pBhrPWXLpDKkyn0XYuK7/8i2+hYh1e2A9yJbZqPpdtj7PdPF/Op05fKFgxOCXuTiDPesXD6usPlhvy/GdbzD5juN8XiLQPQBFXlgO9VsRTSXI5ba21y/jw1Wy06dGDy4/dUbsfQ//YPu/GS7nOrtVK2uDYov6npE/WzE2YuRXaz2DZpf279sy6uVWMnzmG82YmFmKpYunS3C3BcWFkYaDp+2t5Uv/dIvjf/hf/gf4pu+6ZuM5wpAwV1Kds0P//APx6/92q9t2e/KlSvxvve9L972trfF5cuXi1CvO3fuxBNPPBEf/ehH45d+6Zfi7t27m27jx3/8x+PRRx8ttgMAO9H4zd+J1pPPbhiCfk8oep8g9mFV/vKfGfhltPzOXOTphbxxGOaz7uCi704VX6c9uFA2MsNeICwuRravsO3T400DwXaC0O8sL8Xi3N21oefrgs87oef9gs8brXvD07tB6d3p3uWt7nzj1/91GZC+vNw9nvUltTeG+N4BgHGrVqvd8PR+geobTQ/StzM9OSlEEACAw694aTw93FYEqS+WAetFkPri2vnmUjt0fbFP4Ho7dD3f+0AkdkF6Wbw3eL022w5bny2D19fVxfJqekwRAAAA1j7TlF+/Ffm1G93Sunq9G9aeBkU/cCYnonLlYmSXLxV15XKavhDZpL+Ld1OtVov77rtvyz4cbunZvBdSSPvNu/HpGymkfS4+ffNu3BlDSHvHmcl6vPvSqXjXxVPxjgsn49SkABgAAAAAAI6W4xO1+H1XzhYlXct/8s5CfLgd4v6xV2/Hcmv70Ug78eL8UlF++fnr3bbLRZj7sSLEPdWvPzUbJybcU4JRy06eiOpbUnl9MZ9+F8TtO9F6/uWi5C+8VNavvBqxR78TBpYG537+pWg+/9K9y2amyyD3FOJ+7kxkZ09Hdu50VM6eijh+LLJKZRxHDAAAwB7IskpE/XhRstj8Wea17+0vRKzMRZ5C3deHvPe0F3U7GD5ay7v+edj0K9ceL6EMxBku/D0NvDvRDnlfG/5ehrxPdQPeozrZXl62FdPFsnap1IXtAAAAAAwgS+HMqUxNRjauMzczHRPf+91ltk03EL5nOuXC9FuW2jsh8kWf3vV65tMzOYclCH1iyHfyD1wQ+gELmj9wx7uNcSbSuDapLC0PFCS/kfSk2LGIOPm2N8XEV71roHXzVisW//LfaYfJd4Lh7w2Ob2VZLEY7IL7VLOrFZjPmGitx7qvfFY9++duL/AwA6OUtCXbFL/7iL8Y/+2f/bNM+p06dih/4gR+IP/yH/3BU+jxY/+Y3vzn+0B/6Q/HX/tpfi5/8yZ+Mf/yP/3G0Wq0Nt/c3/sbfKNZ56KGHRvIZADiaWp99Mpof+fhY9l2Ewg8oG+dAqsNcEEoXMg7U8e7voPn0/0YpWLwTOp7qO/N3Y+XWzW7geRGI3mx1A86Ltp4A85WetrS80bPO+uDzou4suyc8vRWNX/uFe0LP+4Wh75sg9BeeHvcRAHDEpIDz3Q5R70zX6wY6BwCAYjCzVgpSXywC1osA9SJgvR223g5dXxPG3ugJX+/pWxQOp6wW0Q5fXxOyvqY+VvTJ2nXRngYSAAAAgG28FBZ37kbr2s3IX10NZ8/TfKpv3R78LbV9pBhsPYWzX7lUBrSnwPYzpwy6PgbpPvGXfdmXjWPXjPH6ZwpXebwIaL8bn75Z1rfHGNKeVLMsvuTc8SKo/d0XT8VjJ2eiko3t9X0AAAAAANhXsiyL15yYKcoffd3lWGw047dfvR2/0Q5yf+bu3j6z/ML8UlH+7+evdduuzLbD3E+thrmn8HlgtL8LIoW5p/JFr+22pwGn85eutgPdX4o81S+8FDG/z99nmF+I/Onno/n08/cuq9fK5wjS8wVny7rSDnYv2qenxnHEAAAAjFHxjnat/b52XNj2enkrhS+VQe75mnpt2HvR3jN9oB/YP4xay2VZubWzAKAsBY1NtkPeU7D7VDsEvmwr5tslK9p75rt92/MV47UBAAAA7IWsXo/qax/ZxbFHW2XAe6MT6F6GuqfpbHJiqO1WXvNgxOLSmsD4NWHxuxSUPnQW1TizgIYIbj+UQei7ZZi8r7Ge3yGPN53jxtZB8umps35Pnk1cuhJVoe0A9OGNCEbu9u3b8UM/9EOb9nnNa14TP/VTPxX333//lts7duxYfP/3f3+8+93vju/93u+N+fn5vv3m5ubib//tv10EvAPA0ASh7+4FoXGe33UXLNOF097A8/UB6MX0/Hzceen5Ipi8E3ReBpi3Nm3rhJx32jph592Q9H7z69sqWTR+6kf6HldnPgW37yvPPzXuIwCAgVQqlV0LTl8/PTU1VewPAADYWJ632qHpSxGtFJa+1BOevtQz3w5j713eDmhfDWPvhK17kfpoyMqXo9ML+rWZ1Zf1108XoeszZUB7Z1llohz4DgAAAIZ9eTMNQH79VuTXb0ZrfTD79Zu79qLlnpqoR3Y5BbRfjMrlS2VY+30XDKAOe2S52Ypn7i7EF24vxOdupYD2uSKo/fby/vj9ct/MZBHS/q5Lp+Lt50/EsWFeqgYAAAAAgCNoqlaNr7h0uijJC3OLRYB7CnL/z1dvx/wYBvl8fm6pKP/+udUw9/tnJ+MN7TD3R0+WwfMXpz2DC7sxOHX2wOWoPHB57XMJN29H64WeMPdUX72eFu7/L0IarPrlV4vS1+z0aph7O9i9KGdORnbqZGQTgtMAAAAoFeHak6eLkg00fsFCRGM+8iLIfb4d7N4OdU/t7boMfy+XF/Np/AL2rzyF96SvVzlW/c5D4HuC3GudkPfJiEoKep9cna/2m+/0bbdX6sYvAAAAANhjxXiS1WrEdBkWParRJSf/mz+26fLi2Z70nF8n1D0FT68Jj18NeO+d706v69cJnM+OzQx1vMX+x2WYPKpxjsdywILmsyHObz7OoPmhzm9zPIHxABwJRkNi5P7e3/t7cePGjQ2X33ffffHTP/3TcfHixYG2+573vCd+/Md/PL7ne74nms3+/4P0a7/2a/Hv//2/j6//+q8f+LgBYOx/QO/jIPR0sa9RBIy3opG3YqXZjPyVlyN77rlukHij0dhyevmlV2Lhs58oAsqL7bTDyps90532Rm+fIgC93H+zG3S+GpDe2E6o+v+axcqf/xPdAPSN/n9iX3l53AcAAHsnBZyncPPeul/bIH22Wn9iwsAgAAAwrOIBwdZyO2R9KaKxGHk7PL0TrL4ast6ZX1obsr5uebE9jrbKRDtovSdcvT67Jmh97XQ7jL06HVlWGffRAwAAcAjlKyuR37gd+Y1bkd9M4ey3yulivmwvXpo8LOq1yC6ei8ql85FdOt+uL0R27nRkFX97w25Lz0I+c3cxnrydQtrn22Uhnr27EM19lLnwmhPT8dazJ+Kt547Hl5w7EZdmJsd9SAAAAAAAcChcnp2Kb3vNpaI0Wnl87tZcfPzVO/HxV2/H71y7HTeWxjPo53NzS0XpDXOfqVWLewYpxD3Vj5yYiUdPzMS5KaFEMPJBpU+fjGoqb3pdtz1fXo78xavRevlq5C9djdZLZZ1fuzFgMtmYzS1EPrcQzWde6L98diay0yfLIPdUnzpR1JU0ffpkxIljnmcAAABgQ8X758W76bORTZ0f6EzlrUb/oPc1AfCrQe+9fYpQcQ5YCPzdsuw0BL5QaYe6rwt6T8HuKRS+Mrka9t6uy/lOW3u+t39FlAQAAADAvn22JwVUt0OqRxUYP6yJ/+rbIl9YLAPGUyh6o1mGubcD4btB8Y110336dqf79m3ce+FsmLwvQejbd8DO71B5aiMIbh8m4B6Ao8G/EIzUyy+/HD/zMz+z4fJKpRI/8iM/MnBoe8dXfMVXxF/4C38hfvRHf3TDPmmZ4HYAxvEHdL9w8850o2e6016Elfe057/8f0frs5/aMgB9TRD6sy/E0u8+3hNefm+4eSfUvNEz3WnvBJz3tvdbt5lCmNb7h77PAOAwSoHmowxH3876AtQBAGB35HmrHa6+3A5LXyrD03sD15vL7bZyOtVlwPrafnlatqZfClk/SKN5sWeq0+1g9RS+PtOdL6Zr0xHVmdXA9TVB7DORVeq+UAAAAOyZvNmMuH038lt3igD2VieQvafE3fnD+RWZqPcEs6/W2ZlTBjSHPZCeyXz+7mIRzP5EO6T9ydvz8fSdxWj0e15zjKpZFm84PRtvPXs83nruRHzJ2eNxctJ1PAAAAAAA2G21ShZvPH2sKN/12vuK8SyevbtYhLh//FoZ5v783NLYvhDzjWZ88vrdovQ6Xq8WIe4pzD0Fuadg90dOTMeZSYHuMErZxERkD12JykNX1rTnyyuRv/JqN8i9G+j+6vWI1v66F7ktc/ORp/Lci/2XVyrdMPfsdKfuCXk/dSJiZrocJBsAAAAGUARlT5woyiB/VabreMWYDCu9ge49Qe/N+XZ7qhfK6ebqdDmOAwdbK6K5UJYNRuUY+CpNVo2oTJTB7u26CITvtqX5iTLsvQh/T9MpNH51edm2br1UspprJwAAAACHROW+C3uyn/I6aGtNyHtWHTxYvPKGxyJmZ9YGy/eEw28WLB9pzJidqA8TLH70gtCHlQ0RNF98fccRcA/AkSC4nZH66Z/+6SJEdiPf8R3fEW9/+9t3tI8/82f+TPyrf/Wv4sknn+y7/LOf/Wx86EMfive+97072g8AR8eNGzfigx/8YPz2b/92PP6rvx6LL1+9J9x8NRR9bQB6b3vfcPNB/Mv/fVQfCQA4BCYnJ0cWoL7dcPUUoF6pVMb90QEA4OiFq3cD0dvh6p3A9HZ4+vpg9TKAfXW6E7Ced/p02ryUyzCKoPWegPU0nULVq2W4ehnC3g5nL/qsBrVHdSqyzN+VAAAAjFfxgt/8QuQ3b5eh7N2ydj7u3B1itKsDZnoyKpcurIazXzxXBrSnAcoNSg67bm6lGc/NLcZzdxfj2bsL8eTthXiiCGhfiOV9GoowXa3EW84ejy85dzzeevZEvPnMsZjycioAAAAAAIxdur/34PHpovzBRy4WbVcXlssg93aY+xO35sd+C/TOSjN+99qdovQ6OVErgtxTiPsjx6fj/mNTRblvZjJq3muFkckm6pHdf19U7r9vTXsaxDi/em01yD2Fur98NfJXrkU0Wwf3K9BqRX79ZlE2VKtGdvJ4ZCdPFHUU08fLYPcTnenjkU1M7OWRAwAAcEgVz+lXp8oSZwcKfU/yVgocWmgHvbfD3IvA94V22HsZ8l6Gva8LgU9trY3HhucAy5trwuCLpvVdht541j/cvRsE369tMrKe0PiivWhb2ycFxHt3BQAAAOCwXgetlmVqcuDroB21d741IpUh5Ck4PgWTN/qEvLfD5Ivlneme5alvduLYEAdcizg2093ujsPjdzuQ/CgGzRsbA4ANCG5nZJaXl+Of//N/vuHyFP72vd/7vTveT71ej7/4F/9i/KW/9Jc27PN//B//h+B2ALbUarXiAx/4QPzAD/xAXL161RkDALpqtVoRaN4pnRD19WW32gWoAwDAPglUTy+lFqHo7RD01koZqr6+rTtdzqdl3X49bSlovQxh7wlmz8f4IBOHUKUdul6Gr2fdEPbpdgh7GcS+GsLe256C16cFrwMAALBvFS/NpUD223cjvzNX1rfbIewppD1N32zP7+XLbeNWrUZ27nRkF85G5fzZos7On4nKhbMRaYBxAe2wq+6uNOLZIpi9DGhPQe2d6etL+3/gw1MTtW5I+1vPnYjXnZoRjgIAAAAAAAfE+emJ+P0PnCtKcme5UQSmf/xaCnO/E4/fuBsrrXFHuZduLTfit1+9XZRe1SwrwtsfaAe53z9b1mn+8uxk1IW6w0hk9Vpkly9G5fLFNe15sxn5q9cjf+V6tK5eK8Ld86tp/lrkN9f+vB5YjWbk124WZVPTk91w9/Uljh+L7PhsMWBzNjm5V0cOAADAEZRVahGV4xH140OFHeVpbIt24PtquHsKfZ9bDXcvwt7bIeBFCHxZl8Hgi7vwqdjf8vLrnkr78fd+V5WHvtK8Lsw9K6bbpT1dhMBX6t35TsmKthQAX+/2L/uu65/VvDsDAAAAcMRk6dnCiVTq5fwe7LP+dV9ZlI48z3vC48s6XzPds6w3TL5dl/Pb6188wzSgYv1xqQ4RND+KsYKGCYwH4EjwLwQj8yu/8itx+/bGD9q///3vj/Pnz49kX9/wDd8QV65cieeff77v8l/7tV+L69evx5kzZ0ayPwAOp7/1t/5W/PAP//C4DwMAWCcNGj89Pb2rYemb9U0lBbcDAAD7T/FQUgo67w1KXxOSvtK/rad/GbLe7tdtWztf9Beozl4rXgztCVxfE7qe6qmeMPYyZD1qU2vC2YuXT4WxAQAAcNDC2BcW22HsKYj9bkQKZW9PFwHtnfa7cxH7JFRgz2VZZGdPRdYOZq+cP9Odzk6fLF8oBHbNreWVMpS9HdD+7Fw7pP3uYtxcHuPLqgOarlbidadm4w2nZ+ONp4/FG08di4eOT7mmCAAAAAAAh8TxiVp85X2ni5IsNVvx6Rt349M354oQ90/fmIun7iwMH7CzC5p5Hs+ley9zixEvr12W7oJempnsBrl3Qt1TuTI7FZNV90lhp7JqNbKL5yMuno/1Q+Xmy8tliPvV69FKQe7tYPfW1evFsx2HzsJS5AtXI3/p6ub9JuqRtYPcIwW5d0LdU33iWETPdDY5sVdHDwAAAIUi6DoFFU2cGC74PW+VAd7tIPduwHvvdHfZYk/4ewqEX52PaPmKUGotlSXulN9j/b7vdnyusnvD3NPYG8V0O/S927Z2vgyD72nrrl8vQ+LXhMmnNmNUAgAAANC+KpXGfq3XyrJ6pWrfqH7xG6Ly//reoYLiV/t35tf1751f6dM/Xace1AiC5rPaEIHxABwJ7vAwMv/6X//rTZd/+7d/+8j2Va1W4w/9oT8UP/ETP9F3eaPRiF/6pV+KP/pH/+jI9gnA4fIv/sW/ENoOAH1MTEx0w8t7S2+oeW/bbgSrp9B0IXMAAHAQAtSb7aDzRk8Q+krkxXRqawek5yk4fSXyVLfuLWX/fu1rg9i729tXw8RBMVJZGZpenWyHrE+VIeu9geu9gexF6PpUe1lPOLsXNAEAADhMQexz85HfnS/C1lNdlrmIdnsnkL0YyDutQ0QlK0PYz56OrB3MXumEs6fQ9ppH/2E3NFp5vLq4HC/NL8XL80vx0sJyWRfzy/HSwlLcXWkeuJM/1QlpP1WGtKew9oeOT0c1vfwLAAAAAAAcCSnY/EvOnShKx3yjGZ+9OVeEuD9+swxzf3qfhbl3pDvJL8wvFeWjr9xasyzd8Tg7VY+LM5NxaXoyLs1MFCHvxXzRNhEnJryvDDuRTUxEduVSxJVL94a6p2dDUoh7Eeh+PfJXrkXr1euRX7sRkZ4XOcyWV4rPWXzWraSQ93a4exybiezYbGTHZiJmV6eL+c70hKB3AAAAxivLKuV4CKkMGTJUjEeSxgfpBLz3hL2XIe99wt+LtsXIm535pTJAfl9euWT/yVcD4nuynXYlJD6NL9INei+D4ouA9858TykD4dslS33b9fplG63T2572CwAAAACDXMqanIzswuSBOWdpzJ36H/vWiGZvMHxPWHxzXTh8Md8bJt+MqA8RGA/AkWD0Nkai2WzGr/3ar224/MKFC/H2t799pGf7fe9734bB7cl//I//UXA7ABv6m3/zbzo7AOzroPTNAtMH7bPd5elYBKYDAMBBC09v9ASn94Set8PSi9D0bqh6oyckfW3ger5mG+1l+UrkKTC92EZvOHt72guOHGjpheGegPWinuq2FQHrnbYiZL0dvl4s6/Rt98kM6AcAAMAhvv60uBT5/ELE/ELkc6nMr4avpyD2Tij7XBnQnpZFy8BYG0qDbJ89HZUUzn7udGRnTpV1mj91IrKqgZRg1O6uNIoQ9pfm24HsC0tr5q8uLBehHwc9dOX1QtoBAAAAAIBtmKlV463nThSlY26lGZ+9VYa5f/rG3fj0zf0b5t6Rju3VxZWifCru9u0zVa2UYe7TvaHuE3GxCHqfjAvTEzFRrez5scNhkE1PRfbglag8eOWeZfnSUuTXbpbh5q/eiNb1m0WdX09h5zeL4PMjI4W8p8/+6jZC3pN6rQh0L54vaYe7l4Hv7aD32RT6Ph3ZzHRks9MRqTbYMAAAAPtMMZZhdbIscWqo8Pckz1vtAPgyzL0MdW+XIgB+qR3yXrblRRj8ap/V/u0geBiFvAyIKr63Ok0bdR3lGS8C42vtAPiJYpyT1aD3FBpfznemVwPge5Zl9ch61l0Nm+9sq3d+dT2h8QAAAADshfR8VO2db3WyAdgVgtsZiU984hNx586dDZe/5z3vGXn432OPPRaXL1+OF154oe/yj370o9FoNKJW820OwFqf/OQn41Of+pTTAnBE1ev1kQWe73QbKSi9UvFCPwAAHLyg9HaQeW9oep5C0dvzvUHn7T75mvbOup31+rS3p+9Zr2ebRQ1HSaX9cm4RnD4ZWc90EaheWQ1eXw1Yn74neL0oxcuBo71/CQAAAPtV3mrdG8Ceptt1b3tZz3fbhLAPaKIe2dlTZRB7CmjvDWZP7ZNp4DFgx7/X8jzurjTj1cXluFYEciwXoRzXirpsSyWFss81mofqhM/WqvHoyZkiqP2Np2fjDaeOxUPHp6NWcb0TAAAAAAAY8v5DvRpvO3eiKGvC3G/Oxadv3o3Hb8wV08/cXYxmeq/igFhstuKpOwtF2ciZyXqcm6rH2amJODedpifK6anOdLlsUsA7bFt6NiK7fDEilX7vZt2ZK0LdWynYvRPw3ik3bqdOR/dsrzQiv3Er4sat7Qd7pbD3FOieQtxnpleD3XunOyHvPe1R914NAAAA+1uWVVbHh9hBAHw3BL4b9L4UeSfwvdEJee8JfW+0Q99bS+221H91uqiN98K4AuNjKaJnuKE9CY1PP31F8HsKcm+XbnD86nT0mS6W37NufTVcvk97sWzNdlbbi/5Z1XgxAAAAAADAQCRaMxIf+chHNl3+rne9a1fOdNruv/gX/6Lvsrm5uSKY961vfeuu7BuAg+s3f/M3x30IAEcmHD0Fk6fSmd6qHlXfzvT60HRB6QAAsP8VL7t1QsnTS0PdMPNmT5D56vya6WJZM/LeYPN1y4oQ9X4B6u2A9NXw9T4B7V6cg+1LL7v1hqqvD1lPdRHEPrXx8k5bCmSvTpQv1gIAAMBRDl5fWIxYWFxbz5d132WdenFp1CPuHE1plK/jxyI7fTIqp09GduZkZKdOFvNlORFxbNbgP7ADS81W3FxaiZvLjXYIezuMfaE3mH0lri8ux1LrcP9im6lV4pHjM/Gak9PxmlSfmIlHTkzHhel0rVRIOwAAAAAAsAdh7udPFKVjpdWKZ+8uxhduz8cTt+bjC7cX4snb8/HcXAp0P5hfketLK0WJW/Ob9jter94T6F7U02VbCoA/NVmPExO1qLqXAxsq7nWeOBbZiWNReeSBe5bnzWbkN28X4eUpxL2s2+VmWcfCkjO8Puz95u2IdN4GOTPVSsT0VGTTU926mJ5Z23ZPn5lyWvA7AAAAB0kxVkVtuizt10N2ohybJgVolwHv64Pdi+D33raiT2/b4r1h8F78Yd/KI1rLEbEc0bxnyVZr7oKsJyS+Nxi+N0h+XWB8v+VZde12ikD4fsuqq4HxxTb7LetMp20YGwcAAAAAAPYbwe2MxKc+9alNl3/xF3/xrpzpt7zlLRsGt3eOS3A7AOtVq1UnBTgUv8v2Mgh90NB0gwMDAMD+kOfp9ZVWT8h5sx1e3q57ShmI3uzTZ5uB6EWo+vqQ9JWe8PXe4PXmBuHsDS+SwZ5KL6NNFKHoZYj6ZGQ90+WyyciK+XI6LStD1Xv6rQ9eT33SS2YAAABwxHUD11Nw+jbqNW1L7ToNNp2mD+gg9wfK5EQZxt4NYu8JZk/tJ49HVnPNA7arledxZ6URt5YacaMdxn6zt26331peiRtLjaKeb7SO3AmerKaA9ukimP01Jzr1TFycmYiKUA8AAAAAAGAfqVcq3XsZX3//avtysxVP312IL7TD3FOwe6qfn1s8NLe676w0487KQjx1Z2HTfinwKYW3n56sx8l19anJWhHufmqiU9fj9GQtpmrGQIHuz1C1GtnZ0xGpbCBfWGwHufcEu19fDXZPge+Rntlhc81WxN35yO/Ol+d10POVgt+npiKbmoyYmhy6jom68UkAAAA4cIrxNFKpzZbzoxgfKI3R01oNcy+D3lNZ7gmHL6fLMPjldp9OW0+/FLJd9E/vI6WxfOAwaf+8xMo+CZJfJwW794a6d4Lg221rwuHXBMuX82W4fHXAgPkyNL53PlvT1pnu6StoHgAAAACAI8TIcYzE7/3e7224bHZ2Nh5++OFdOdNvfvObN13++OOP78p+ATjYTp48Oe5DAPaxWq3WDR9PpV6vr5nfrH3QvinofNjQ9BTcDgAA7FbQed4OGW/1BJmvn16dzzvTfcLQVwPOU7/eQPSNQ9Lzjba1pm2zfuu2DRxwWTcMvROWvjY4vbdttV8Ztr42YD1rB7F3Q9krEwY3AgAAgHRFsNGIWF6JWFqOfHk5Ymkl8qXliOXldr2yZrqzrOi/tHbZ6jaWI1YMbrQvVLKI48ciO3WiDF8/cTyyU8d7ptvtM9PjPlLYl5aarbiz3ChC2FMgxe3O9HIjbhd1sztfBLUXwexlEHvzsCRxjMBMrRoPHJsqQtof6Qlpvzw7KaAdAAAAAAA40CaqlXjtydmi9FpsNIug8xTi/uTt+Xji9nw8c3cxXphbimbx/s7hkz5Vul+WynZNVitFgPvJiTLk/Xi9Fsfq1SIA/nh7/sREtV2X88fr1Tg2UYtqttNIKDh4sumposTli32X5ym0/c7dyG/difzmnbK+dbtdr5aYX9jzYz90we9z85HPDRn83pF+j03UIyYnIpuciJhIdb2oi7bOsvZ8EfTer9+6ZcV0pTLKTwwAAAC7Jkt/H6exQVKpHy/bRrTtYnyi3nD3FArf6hcCvzq9pk8Kh7+nrd0vFWDdD11nDLANfia3+pnd8/OZrQt37wl472krw+J7+6wPhW8Hz/dtvzc8PusXKH/P9is9AfSVNe1rp1fni9+nAAAAAACwjuB2dmx+fj6ee+65DZc/8sgju3aj4jWvec2myz/zmc/syn4BONh+/+///XH8+PG4c+fOuA8FjlwQ+m6GoG+372bbSKXixTsAALg3yLwI/857wso3DjFP092A8i363RN83nd5a5P+m2+3M51v2q/PvgEGUQSg11frIjS9DEUvSrVc1g1N79YpbH11ek0Ae2/AevFSkpeCAAAAOMLXJ5vNMgB9ZSXyor53OtXlfApRX+kGp+ftIPXe6W6oem8AexpImINpdjqyk+3g9TVltS2OzxqImUNvcXExPve5z93TvtxqxVKjVdSnH3goVir1mGs0Y26lWdTznemVRjGfQtjLMPbVcPal1uEMzdgNKSAjhbPfn8rsVDxwbLqYTm2nJlzrBQAAAAAAjpapWjXecPpYUXo1Wnm8PL8Uz84txnN3F+PZu2X93NxiPD+3GCtH7P7UUrMVL80vF2VQs7V2wHu92g15Pz5RjdlaLWbr1Zippenq6nS9nD/WM183vgKHTBHWXTw3ciLiwY37pWeJ8ts9Qe4bBbynZ47YPen5sM7zXZ2mUW27XmsHvKdw9zLkfU3oe2e6Nxw+TddrkdXLev101OuR1dJ229N+hwIAALDPFaHHtemImF5tG9G2izGgilD31RD4IgC+HfTeCYsv21bD4vOiTmWlZ/3lyDtt3eXLxoKCXZfGlWtENBtb9dru1sYs6xPwvlGdgt43DoHvN51ts99q/8qAwfPb2W7POpEZlwoAAAAAYBsEt7NjKbS9GBhzAw899NCuneVjx47F2bNn49q1axseGwCsNzMzE3/8j//x+Mmf/EknhwMjhYl3wsY7AeOjmN+szygC0wWhAwCwn5TXMdvh490Q8tTWW/dOpxDvnrDyYp1OaHi7dNfZrG39up0g9K3Wba45lm6A+nb3253vWbfzWXuDzLfa1j54FB5gYFltTWj6anB6b8j6RBmc3jNfrpP69rQVfdpt7enVsPZ6+cILAAAAHGLF9cVGM6KRBuBIdTPyom6025uRt8PTywD1lf7h6o1G5Ms9Qetp/eWe6b7baLSvk3KkzExFdvxYWU7MRnSmUwD7iU77sYhjM+VAyHAIpHCKxWYzFhqtWGg0Y7HZKkLVF9N8uz0tn091oxkLzbX9Fu7ejYknPhkreV5sq1N6f4N+7onbsVSfGuOnPBxSAHsRzJ4C2WfbIe3tcPaTaQB3AAAAAAAANlWrZHHl2FRR4uLaZc08j1fml4sQ9xTo/uzdhdVQ97uLsXTEQt23MtdoFuXFHWxjopKtCXWfadfTabpWjalqpZierlViqpraKjGV5tvtaflMz/KyrggKYd9LYd3ZuTMRqWwiX1qK/PbdyO/MRdy5250u63I+0vydu+WzTuwfnWfR5ua7TSP/V6RaiSiC3OuRpWD3WjvQvSfofbMg+C0D4mvVdqlFVl2dLuqK37UAAACMVzHeSnWqLJ22Ee8jT+NkNdsB792y0g6D3zr4vW8YfLF+73x7G8bZgsMTRJ/K9noPuvV9qBNW3w50j95w983bVoPi29so+m1ve1mfEPnou72t1u3so7PPYddt77/7GdJ0vzbXVQEAAADgKDJSHTu2VTj6lStXdvUs33///RsGt1+/fj3m5uZidnZ2V48BgIPn7/7dvxv/6T/9p/jEJz4x7kNhD2RZNrKg83HNp+B2AAAOYjB4Z74dvt2vrXgKtxMWvn5Z7/zqdtfspzeEvBvK3dr+8mJ76wLMt1ynt23tusW2tr2drcPT8w32c29bv+302R8AY5B1Q857SxmO3i5Zn2XdUPXJdlsniD3Nl8uy9UHqnZB1YeoAAADsc3mrFdFsRbTS4DFpuqzL9rVtqe72T21puk94etGvM98JWO8JW+83X4Spd/uXy4r53qD2tF/YiTRocApZL8psZLMz5Xw7gL0TyF4EtKflafBhGJN0b2q5lcdKqxVLzVastPJYbrZiubU6neq0bKndZ6uSwtU36p+WpSD2tM+dmFxZjNcuGQB+VMHsF2cm49LMRFycTvVkXJyZiCsppH12Ko5P+B0FAAAAAACwW6pZFvfNThblyy+cXLOsledxdWG5CHR/aX4pXlpYipfnl4vpl4v55eIeHINJ9yqXlxtxc3m09xtTsHsKeE8h7pO9pbJufosy1e5fq2QxUa1EvZIVZaLSbqu029rLalkmNJ6RyiYnIzs/GXH+7Kb9indhF5fKUPcU4t4JeL/Tru/ORczNR343lbmI+QWvvB4GxTN9yxFLy2veYN6Tt5lTEl4R5l5r19XIalvMd/p3AuGr1Y0D4tt9y22051NQfRoDKa1XTLfb0rKivVKu32nr7Z+CkQAAAGDQP3+z9t+lMXXPn8WjVI5z1lwb5J4C3tfNdwPhu8HvPW3FdCqNnmWN1fD49cu2GSwNsL2w+iF+9+3g1B7sER2znqD5noD34hrm2pD31bZ10+11sr7Lt7F+n77ZFoHz/Y91k231W97ddtYzv355u16/Tnu6HNttXd9tbbPfsWywfrEf15QBAAAAGB0jRrFjL7zwwqbLz507t6tn+ezZzR9mf/HFF+Oxxx7b1WMA4OA5ceJE/OIv/mJ80zd9U3zyk58c9+HsK9VqtRsaXqvVhpoedr1hprcTfJ4+EwBwuHVDrLsB10XruiDsdtua+fYgHPes397GltstklX676/vcfXb7mbHscX+NvuMG+2vmO1zzBvtrxssvr7fuvaNttHZV5/g8rxvOHm/APN7g8u3v047+HvN59o4EH31HG+yj42O5YA/QgrAEQ9Pz7YIVt9Oe59tlNs2sAoAAMBRVg5a0i4pcLyoN27L17el6W4p5/M+bb3z3ZDzvFPna+aLfRSh6T2lp0/eu05vn7RuJzi9N1i9lULUNwhi36C/S8ocaNOT7fD12TKMfbYMZO8bzp7aJycMknDEpMCEVJrpV2mqW3k08jwaqW6Honfm0/JuW0+/lfZ0sW47NL27jZ51erdd9mlvZ90+y/lyO6sB7ClMPY+VIpi93F5axuGVghouTk+0g9kni+kymH0yLhUh7RNFeAQAAAAAAAD7TyXLivs6qfSTnge5tdxoB7kvF8HuRcB7z/y1xZU9P+6jaqHZKso4TKQA90qlqMug97Xh7vXustX5enWDQPieeqJabjeFw6c+1VRnWVSL6Sjm0/RqW7vPBtNFrnF7G6k9fY+nwsFUBIhMT0U2PRVxYfNx8ZLiGbe5hciLMPe5iBTo3p5O4e7FfJqeW52ORnNPPgsHRHrEJX1P9HxfrH/qZV89BVPJegLeV0PdNwx6XxcIX7StW7fYZgr0SfNZVi7vtKc6/VwWy1bbst7lffrcs43t7Gddn+L3Qb/lPfsstgEAAMC+UYbl1iIqKbZjZrV9F/dZjAXYDYtfWVNWQ+C30Z4P2F9oPHDk9YwlusOLqKO8BruvrufuC1uFw/fObyMMvtOvpy3rCbvvDY0feJvd+3vt677r11sTRJ/69/l83enYoL0zvdm6vX3WHUvP9rPic/TbTqo2Wm+APlseY/Q5N5v3WXtON/t86/r0HsuaY+s9zz1tvftv16tfOwAAAOAgE9zOjl2/fn3T5efPn9/Vs7zV9rc6PgCOrvvvvz8+9rGPxU//9E/Hj/7oj8ZnPvOZWFlZGXm4+ajDylN9b/vG++q/vX7bqEctvaCy7ZtAA97K7YZ47mQ7+YCbSDfAlyNv7PE+B1uhT9dBb5MPsM/dPO6i+wjO7X45Vxs2j2ifIzlX/ba1+Wt0ZXDtRtvsDffdYv8bbifvM7lF3zXNG/Tte77W9b1nf8N8tt7j32jZZse91f769N3Ouex2HcF5H9W53LDvZt8vm22jt603fLpnnX6ff0249Pr1+rXnG5zPTp91/e7ZZ7/29esOcLyDfI71+1yz7kbnLu//WbuL9sHn6Ps9tM3vgTUB5gAA+1SWBgeptYPRa6svaVVqPUHna9tT36w7XevpU9bZPe1peqK9LNXC0wEOq9W/8ek5KU4G2/nhcZbY/vdJ7zXL9dcv+y3r/f5a/73Wb9mQ2893efsH7vg7gaqd4O+kaGuvl6+d7v4b2g0Qv7fPmm319ot10+1959vc9z3b3KB/3u8zrT/ee7bd+f+DdX22FY6+SZ/e9nVta0LV16zfDlBf097pt/ZLD+wjU5MRM9M9ZSpidibymanIp8u2NF3W0xHT5XyeBqDt+fXc/XVW/kYr695fZYvLa3/tb9a/3bZZ/zV3EfO1bev/SUm/t7bbPwWNF7/C2vtf39b5Vb2+rXO8rfb+Om1lvb22tM1i2z3LNjqO8tds+Rk2a2t1QtPbIeppPoWXd6bvWdadXg1cv2e9aC/rbieFod8b1A7jcHKiFuem6nF2aiLOTtXjXFFPxIUiqH0i7puZjNOTdUEHAAAAAAAAh1QaK+PUZL0obzjdv89ysxWvLCyXYe4LS3F1YSWuLS4Xge6vFvVyvLq4EotjChxnNJZbeSy3mjF/AE9oihjoDX3vDYIv6nUB8SnoPc0XGcHFfLsuMpJXlxV1rO2zflnvfKVPW++yyrpt9fZNc8XxpA/U7lsOZVP2L+IOusez2r8bmdBzrMU56S7r6bdu/fRfpae93H/Z3tlWp7132/fup/dYyuPt6AzHU26pJ7Jh3TA93eXd/uuWd445TdfqESdPRnbq5NbbyPPIVhoR8wuRLSyU9fxit87mF9Ysi7RsLtXzkQl8Zz8oHoi6ZxCoDR8xPfRPIBW/aPqEyHdK8UupLGV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"text/plain": [
"
"
]
},
"metadata": {
"image/png": {
"height": 923,
"width": 4023
}
},
"output_type": "display_data"
}
],
"source": [
"theta_new_mean = float(theta_new_samples.mean())\n",
"theta_new_sd = float(theta_new_samples.std())\n",
"alpha_match = (\n",
" pooled_var / theta_new_sd**2\n",
") # discount at which the power prior reaches the tau-driven width\n",
"xx = np.linspace(pooled_mean - 1.2, pooled_mean + 1.2, 400)\n",
"\n",
"fig, ax = plt.subplots(figsize=(20, 4.5))\n",
"for a in [1.0, 0.5, 0.1]:\n",
" sd_a = np.sqrt(pooled_var / a)\n",
" ax.plot(xx, stats.norm.pdf(xx, pooled_mean, sd_a), label=rf\"Power prior, $\\alpha$ = {a}\")\n",
"ax.plot(\n",
" xx,\n",
" stats.norm.pdf(xx, pooled_mean, np.sqrt(pooled_var / alpha_match)),\n",
" color=\"C1\",\n",
" linestyle=\"--\",\n",
" label=rf\"Power prior matching $\\tau$ ($\\alpha \\approx$ {alpha_match:.2f})\",\n",
")\n",
"ax.plot(\n",
" xx,\n",
" stats.norm.pdf(xx, theta_new_mean, theta_new_sd),\n",
" color=\"black\",\n",
" linewidth=2.5,\n",
" label=r\"Hierarchical predictive ($\\tau$-driven)\",\n",
")\n",
"ax.axvline(0.0, color=\"grey\", linestyle=\":\", alpha=0.6)\n",
"ax.set_xlabel(r\"Effect in a new market $\\theta_{\\text{new}}$\")\n",
"ax.set_ylabel(\"Prior density\")\n",
"ax.set_title(\"Static power prior versus dynamic hierarchical borrowing\")\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "d91959be",
"metadata": {},
"source": [
"At $\\alpha = 1$ the static power prior is the tightest curve, far more confident about a new market than the spread across markets warrants. Matching the hierarchical predictive takes a large deviation from full borrowing: the dashed curve marks the small $\\alpha$ at which the static prior finally reaches the $\\tau$-driven width, and that value has to be set by hand. The hierarchical model arrives there on its own, because $\\tau$ reads the between-market spread from the data.\n",
"\n",
"Either prior becomes the belief the next market inherits, and that inheritance is legitimate only when the new market is drawn from the same population the past markets describe. Borrowing sharpens the posterior when that holds and pulls it toward the wrong centre when it fails, so the strength of borrowing has to be earned rather than assumed. A prior-data conflict check is the gate {cite:p}`evans2006checking`: locate the incoming estimate in the prior predictive distribution, and read a small tail probability as the new market disagreeing with the borrowed belief."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "b0b7bf16",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
incoming estimate
\n",
"
prior-predictive tail probability
\n",
"
\n",
" \n",
" \n",
"
\n",
"
concordant market
\n",
"
0.28
\n",
"
0.796
\n",
"
\n",
"
\n",
"
conflicting market
\n",
"
-1.00
\n",
"
0.028
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" incoming estimate prior-predictive tail probability\n",
"concordant market 0.28 0.796\n",
"conflicting market -1.00 0.028"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def prior_data_conflict_tail(d_new, prior_pred_samples):\n",
" centre = np.median(prior_pred_samples)\n",
" return float(np.mean(np.abs(prior_pred_samples - centre) >= abs(d_new - centre)))\n",
"\n",
"\n",
"concordant_d_new = 0.28 # a new market in line with the population\n",
"conflicting_d_new = -1.0 # a new market that contradicts the population\n",
"pd.DataFrame(\n",
" {\n",
" \"incoming estimate\": [concordant_d_new, conflicting_d_new],\n",
" \"prior-predictive tail probability\": [\n",
" prior_data_conflict_tail(concordant_d_new, d_hat_new_samples),\n",
" prior_data_conflict_tail(conflicting_d_new, d_hat_new_samples),\n",
" ],\n",
" },\n",
" index=[\"concordant market\", \"conflicting market\"],\n",
").round(3)"
]
},
{
"cell_type": "markdown",
"id": "690ea5aa",
"metadata": {},
"source": [
"The concordant market sits in the body of the predictive and the tail probability is large; the prior and the new data describe one population, so the experiment can borrow at full strength and keep the precision that buys. The conflicting market sits far out and the tail probability is small, the trigger the guidance names for reassessing how much to borrow {cite:p}`fda2026bayesian`: lower $\\alpha$, widen the prior, or hold the borrowed estimate aside until the discrepancy is understood. Dynamic borrowing through $\\tau$ softens this failure on its own, since a heterogeneous set of markets produces a wide predictive that absorbs a surprising estimate, while a static power prior never adapts, so the analyst must run the check every time. Whatever borrowing strength passes the check is the prior the next experiment plans with."
]
},
{
"cell_type": "markdown",
"id": "469f684d",
"metadata": {},
"source": [
"## Predicting the next experiment\n",
"\n",
"The predictive we drew to calibrate borrowing also answers the question that occasioned the whole exercise: what will happen if we run the redesign in a market we have not tested yet. The two flavours now do decision work. The true-effect predictive $\\theta_{\\text{new}}$ is the best estimate of the effect in a new market; the observation predictive $\\hat d_{\\text{new}}$ is what to expect the next experiment to actually return, noise included. The gap between them is the experimental-noise envelope that a single-market estimate conflates with population variation."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "1a090549",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"
"
],
"text/plain": [
" posterior probability > 0\n",
"$\\theta_{\\text{new}}$ (true effect) 0.825\n",
"$\\hat d_{\\text{new}}$ (observed estimate) 0.784"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"prob_theta_new_positive = float((theta_new_samples > 0).mean())\n",
"prob_d_hat_new_positive = float((d_hat_new_samples > 0).mean())\n",
"pd.DataFrame(\n",
" {\"posterior probability > 0\": [prob_theta_new_positive, prob_d_hat_new_positive]},\n",
" index=[r\"$\\theta_{\\text{new}}$ (true effect)\", r\"$\\hat d_{\\text{new}}$ (observed estimate)\"],\n",
").round(3)"
]
},
{
"cell_type": "markdown",
"id": "cb419ca8",
"metadata": {},
"source": [
"The probability the true effect is positive in the next market is higher than the probability the next experiment will return a positive estimate. The gap is the experimental-noise tax: each individual experiment is a noisy realisation of an underlying truth, and the team will sometimes see a negative estimate even when the true effect is positive. Reporting the meta-analytic posterior on $\\theta_{\\text{new}}$ as the planning input for the next market, which {ref}`assurance_planning` then consumes as its prior, is the way to feed accumulating evidence forward without losing track of the noise."
]
},
{
"cell_type": "markdown",
"id": "c9a8d6b4",
"metadata": {},
"source": [
"## The synthesis becomes the next plan\n",
"\n",
"The predictive that calibrated borrowing also answers the question the planning notebook opens with. Read off its centre and width and the loop is closed explicitly: this synthesis is the prior {ref}`assurance_planning` integrates over."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "8be48397",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
value
\n",
"
\n",
" \n",
" \n",
"
\n",
"
planning prior mean μ
\n",
"
0.400
\n",
"
\n",
"
\n",
"
planning prior sd σ
\n",
"
0.500
\n",
"
\n",
"
\n",
"
assurance ceiling P(θ_new > 0)
\n",
"
0.788
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" value\n",
"planning prior mean μ 0.400\n",
"planning prior sd σ 0.500\n",
"assurance ceiling P(θ_new > 0) 0.788"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The true-effect predictive is exactly what the planning notebook treats as its\n",
"# prior: a Normal summarised by a location and a width.\n",
"planning_mu = round(float(theta_new_mean), 1)\n",
"planning_sigma = round(float(theta_new_sd), 1)\n",
"assurance_ceiling_next = 1.0 - stats.norm.cdf(0.0, planning_mu, planning_sigma)\n",
"\n",
"pd.DataFrame(\n",
" {\"value\": [planning_mu, planning_sigma, round(float(assurance_ceiling_next), 3)]},\n",
" index=[\n",
" \"planning prior mean μ\",\n",
" \"planning prior sd σ\",\n",
" \"assurance ceiling P(θ_new > 0)\",\n",
" ],\n",
")"
]
},
{
"cell_type": "markdown",
"id": "93470378",
"metadata": {},
"source": [
"`EffectPrior(mu=planning_mu, sigma=planning_sigma)` is the object {ref}`assurance_planning` opens with."
]
},
{
"cell_type": "markdown",
"id": "e7c2c1c7",
"metadata": {},
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"## Replication as the data-generating process\n",
"\n",
"A single experiment is overheard speech. Eight experiments are conversation. The hierarchical model is what lets us hear them as conversation, and the posterior on the population describes the very population our experiments were drawn from.\n",
"\n",
"Replication is often described as a verification protocol, a post-hoc check on a result already in hand. It is better understood as the data-generating process whose distribution we are trying to learn. Each new market is a draw from a population we never observed directly; pooling constructs that population from the draws; the next experiment tests whether the constructed population keeps predicting new markets. The three notebooks make the same move on three problems. Planning became a posterior over the posteriors a future experiment will compute. Interpretation became a posterior over the bias a single experiment cannot rule out. Synthesis became a posterior over the population a series of experiments samples from. The likelihood changed from Gaussian to Bernoulli each time and the picture held. In each, an assumption a conventional analysis leaves implicit is made a parameter with a posterior, something to argue about rather than assume. The problem changes; its proper characterisation is always a posterior.\n",
"\n",
"And the last question feeds the first. The population this notebook inferred is the prior the planning notebook consumes: $\\theta_{\\text{new}} \\sim \\mathcal{N}(\\mu, \\tau)$ is the kind of belief {ref}`assurance_planning` integrates over before the next experiment is run. The synthesis that ends one experiment's lifecycle is the input to the design of the next. The lifecycle runs as a loop rather than a line from plan to verdict, and the posterior is what travels around it: each notebook's synthesis becomes the next notebook's prior, and each overheard conversation becomes the next one's opening question.\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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"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"
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"source": [
"%load_ext watermark\n",
"%watermark -n -u -v -iv -w -p pytensor,xarray"
]
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":::{include} ../page_footer.md\n",
":::"
]
}
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