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Start of Bayesian notebooks -- imported various sample codez
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@ivanistheone
ivanistheone committed Aug 21, 2024
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401 changes: 401 additions & 0 deletions datasets/movies.csv
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12 changes: 6 additions & 6 deletions notebooks/46_generalized_linear_models.ipynb
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},
{
"cell_type": "code",
"execution_count": 11,
"execution_count": 122,
"id": "f3357c58-0d49-4019-84b7-34f16a452685",
"metadata": {},
"outputs": [
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"\n",
"# plot the expit function, a.k.a. the logistic function\n",
"xs = np.linspace(-6, 6, 500)\n",
"sns.lineplot(x=xs, y=expit(xs), ax=ax1, label=\"$\\\\text{expit}(x)$\")\n",
"sns.lineplot(x=xs, y=expit(xs), ax=ax1, label=\"$\\\\mathrm{expit}(x)$\")\n",
"ax1.set_xlabel(\"$x$\")\n",
"ax1.set_ylabel(\"$p$\")\n",
"\n",
"# plot the logit function\n",
"ps = np.linspace(0, 1, 600)\n",
"sns.lineplot(x=ps, y=logit(ps), ax=ax2, label=\"$\\\\text{logit}(p)$\", color=\"C1\")\n",
"sns.lineplot(x=ps, y=logit(ps), ax=ax2, label=\"$\\\\mathrm{logit}(p)$\", color=\"C1\")\n",
"ax2.set_xlabel(\"$p$\")\n",
"ax2.set_ylabel(\"$x$\")\n",
"\n",
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},
{
"cell_type": "code",
"execution_count": 14,
"execution_count": 123,
"id": "104042bd-f21c-4e6b-8b81-bd92932ddb0c",
"metadata": {},
"outputs": [
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" # Plot the logistic regression model\n",
" xs = np.linspace(xlims[0], xlims[1], 200)\n",
" ps = expit_model(xs)\n",
" sns.lineplot(x=xs, y=ps, ax=ax, label=r\"$p(x) = \\text{expit}(\\beta_0 + \\beta_1x)$\", linewidth=2)\n",
" sns.lineplot(x=xs, y=ps, ax=ax, label=r\"$p(x) = \\mathrm{expit}(\\beta_0 + \\beta_1x)$\", linewidth=2)\n",
"\n",
" # Plot Bernoulli distributions at specified x positions\n",
" x_positions = [2,4,5,6,8,10]\n",
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"So the model equation is \n",
"\n",
"$$\n",
" \\log(p/(1-p)) = \\text{logit}(p) = -9.793942 + .1563404 \\cdot \\tt{math}\n",
" \\log(p/(1-p)) = \\texttt{logit}(p) = -9.793942 + .1563404 \\cdot \\texttt{math}\n",
"$$"
]
},
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247 changes: 247 additions & 0 deletions notebooks/50_extra_bayesian_stuff.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"id": "95a6eda2-a640-4817-9eaf-88bad67ca3d9",
"metadata": {},
"source": [
"# Chapter 5: Extra code, drafts, and cut material"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b818a09a-90ac-408e-b39c-f30dd038c6fc",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1ad57ed2-8583-4d1f-a16c-ddd481ee3e5f",
"metadata": {},
"source": [
"## Bayesian p-value"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "48fc8af8-bfee-4239-8ae7-8419c072ed21",
"metadata": {},
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"name": "stderr",
"output_type": "stream",
"text": [
"WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n",
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [beta0, beta1, sigma]\n",
"WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n",
"WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n",
"WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n",
"WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n"
]
},
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" 100.00% [12000/12000 00:06&lt;00:00 Sampling 4 chains, 0 divergences]\n",
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" "
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"name": "stderr",
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"text": [
"Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 17 seconds.\n"
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"source": [
"import pymc as pm\n",
"import numpy as np\n",
"import arviz as az\n",
"\n",
"# Simulated data\n",
"np.random.seed(42)\n",
"x = np.random.normal(0, 1, 100)\n",
"y = 3 + 2 * x + np.random.normal(0, 1, 100)\n",
"\n",
"# Bayesian Linear Regression Model\n",
"with pm.Model() as model:\n",
" # Priors\n",
" beta0 = pm.Normal(\"beta0\", mu=0, sigma=10)\n",
" beta1 = pm.Normal(\"beta1\", mu=0, sigma=10)\n",
" sigma = pm.HalfNormal(\"sigma\", sigma=1)\n",
" \n",
" # Likelihood\n",
" mu = beta0 + beta1 * x\n",
" y_obs = pm.Normal(\"y_obs\", mu=mu, sigma=sigma, observed=y)\n",
" \n",
" # Sampling\n",
" trace = pm.sample(2000, return_inferencedata=True)"
]
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"name": "stderr",
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"text": [
"Sampling: [y_obs]\n"
]
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"\n",
"<style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
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"source": [
"# Posterior Predictive Check\n",
"# with model:\n",
"# ppc = pm.sample_posterior_predictive(trace) \n",
"# Posterior Predictive Check\n",
"ppc = pm.sample_posterior_predictive(trace, model=model)\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b526666e-ace3-4b0c-af87-bd0fbcb95aad",
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"name": "stdout",
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"text": [
"Bayesian p-value: 0.4925\n"
]
}
],
"source": [
"# Extract the posterior predictive samples for 'y_obs'\n",
"y_rep = ppc.posterior_predictive[\"y_obs\"].values\n",
"\n",
"# Calculate Bayesian p-value for the slope\n",
"test_stat_observed = np.mean(y) # Example test statistic\n",
"test_stat_rep = np.mean(y_rep, axis=1)\n",
"bayesian_p_value = np.mean(test_stat_rep >= test_stat_observed)\n",
"print(\"Bayesian p-value:\", bayesian_p_value)"
]
},
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"pygments_lexer": "ipython3",
"version": "3.9.4"
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"nbformat": 4,
"nbformat_minor": 5
}
531 changes: 531 additions & 0 deletions notebooks/51_intro_to_Bayesian_stats.ipynb
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