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{
"cells": [
{
"cell_type": "markdown",
"id": "711508cb",
"metadata": {},
"source": [
"<!-- SOURCE ONLY -->\n",
"> **This is the master. Edit this file, then run `make`.** Student and solutions notebooks are generated.\n",
">\n",
"> **TF timing (60 min):** intro 4 · Part 1 19 (Exercise 1: 4) · Part 2 19 (Exercise 2: 5) · Part 3a 8 (Exercise 3: 3) · takeaways 3 · Part 3b 7.\n",
"> Keep both Part 1 demonstrations, the interval table in Part 2, and the shared-probability model before logistic regression.\n",
"> The bootstrap is a Section 5 review: run the cell and read the one-line summary; do not walk through the loop.\n",
"> The takeaways summarize Parts 1–3a and sit before 3b on purpose, so that they are not the thing that gets cut.\n",
"> If behind, give out Exercise 1's function rather than cutting 3b. Appendices are not part of the live section.\n",
"> The plan and Opus 5.5 critique are saved alongside this master."
]
},
{
"cell_type": "markdown",
"id": "6eacc5d9",
"metadata": {},
"source": [
"<img 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\" alt=\"Harvard John A. Paulson School of Engineering and Applied Sciences\" width=\"150\" style=\"margin-bottom:8px\">\n",
"\n",
"# CS1090A Introduction to Data Science\n",
"\n",
"### Section 8 — Bayesian Inference for Heights and Health Outcomes"
]
},
{
"cell_type": "markdown",
"id": "d5dce77c",
"metadata": {},
"source": [
"<div style=\"background:#E8F1FF; border-left:6px solid #2563EB; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🎯 Objectives — what you should be able to do by the end</div>\n",
"<div>\n",
"<ul>\n",
"<li>Name the prior, the likelihood, and the posterior in a model, and combine them with Bayes' rule.</li>\n",
"<li>Compute a normal posterior mean, standard deviation, and 95% credible interval, and write the posterior mean as a weighted average of the prior mean and the sample mean.</li>\n",
"<li>Predict how a narrower prior and a larger sample each change the posterior.</li>\n",
"<li>Apply the same update to a regression slope, and compare its credible interval with bootstrap and confidence intervals.</li>\n",
"<li>Update a Beta prior for a probability that is shared by everyone in a population.</li>\n",
"<li>Explain why a normal prior on logistic-regression coefficients does not give a posterior with a closed-form formula.</li>\n",
"</ul>\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "716b4e56",
"metadata": {},
"source": [
"**Coloured boxes:** 🤔 commit to a prediction before running the code · 🏋️ write code (look for `# your code here`) · 💬 stop running cells and discuss · ⭐ the point of the exercise · 🧠 what to carry out of the room · 🔍 an appendix item to work through on your own afterwards."
]
},
{
"cell_type": "markdown",
"id": "c88618cf",
"metadata": {},
"source": [
"**Bayesian inference** treats an unknown parameter, such as a population mean, as a quantity\n",
"with a probability distribution. Every model in this section has the same pieces. For a parameter $\\theta$ and data $\\mathbf y$:\n",
"\n",
"- **Prior** $p(\\theta)$: what we believe about $\\theta$ before seeing these data, written as a probability distribution.\n",
"- **Likelihood** $p(\\mathbf y\\mid\\theta)$: how probable the observed data are for each candidate value of $\\theta$. It comes from our model for the observations.\n",
"- **Posterior** $p(\\theta\\mid\\mathbf y)$: what we believe about $\\theta$ after seeing the data.\n",
"- **Bayes' rule** combines likelihood and prior into the posterior:\n",
"$$p(\\theta\\mid\\mathbf y)=\\frac{p(\\mathbf y\\mid\\theta)\\,p(\\theta)}{p(\\mathbf y)}\\;\\propto\\;p(\\mathbf y\\mid\\theta)\\,p(\\theta).$$\n",
"The denominator $p(\\mathbf y)$ does not depend on $\\theta$. Its only job is to make the posterior integrate to 1, so we often write \"$\\propto$\" (proportional to) and leave it out.\n",
"\n",
"We apply this three times, adding one step each time:\n",
"\n",
"1. **Part 1:** the mean height of a population. One unknown number, no predictors.\n",
"2. **Part 2:** the slope of a regression line. We add a predictor.\n",
"3. **Part 3:** the probability of a yes/no health outcome, first the same probability for everyone (3a), then a probability that depends on age (3b).\n",
"\n",
"In Parts 1, 2 and 3a the posterior has a closed-form formula. In Part 3b it does not, and that is the problem Section 9 solves.\n",
"\n",
"All data in this section are simulated. Because we choose the true parameter values, we can check every estimate against them. The data are not real measurements and say nothing about real populations."
]
},
{
"cell_type": "markdown",
"id": "e673258b",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "52152301",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"from scipy import stats\n",
"from scipy.special import expit\n",
"from sklearn.linear_model import LinearRegression, Ridge\n",
"\n",
"plt.rcParams.update({\"figure.figsize\": (8, 4), \"axes.spines.top\": False,\n",
" \"axes.spines.right\": False, \"font.size\": 11})"
]
},
{
"cell_type": "markdown",
"id": "ba8a7f9b",
"metadata": {},
"source": [
"### Simulated adult heights\n",
"\n",
"We simulate heights from a normal distribution with mean `true_mu` = 175 cm and standard deviation `sigma` = 7 cm.\n",
"In the analysis we pretend that we do not know the mean, but we treat `sigma` as known, which keeps the formulas short.\n",
"We draw 1,200 heights once. Most of Part 1 uses the first 12; later we use the first 120 and then all 1,200.\n",
"\n",
"Our prior for the mean is $N(168, 2^2)$: before seeing data, we believe the mean is near 168 cm and very likely within\n",
"about 4 cm (two prior standard deviations) of it. We chose a prior that is centred away from the true value on purpose,\n",
"so that its effect on the posterior is easy to see."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c868eb82",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"n 12.000\n",
"sample mean (cm) 175.568\n",
"known observation SD (cm) 7.000\n",
"prior mean (cm) 168.000\n",
"prior SD (cm) 2.000\n",
"dtype: float64"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rng_height = np.random.default_rng(109)\n",
"true_mu, sigma = 175.0, 7.0 # generating mean and known observation SD (cm)\n",
"height_sequence = rng_height.normal(true_mu, sigma, 1200)\n",
"y_height = height_sequence[:12] # the first 12 heights\n",
"mu_p, sigma_p = 168.0, 2.0 # prior mean and prior SD for the population mean (cm)\n",
"pd.Series({\"n\": len(y_height), \"sample mean (cm)\": y_height.mean(),\n",
" \"known observation SD (cm)\": sigma, \"prior mean (cm)\": mu_p,\n",
" \"prior SD (cm)\": sigma_p}).round(3)"
]
},
{
"cell_type": "markdown",
"id": "806395d1-373a-4132-a6fd-dfd5629cd89f",
"metadata": {
"nbinlineai": {
"isPromptCell": true
}
},
"source": [
"make me a plot of this prior against a normalized histogram (ie probability density) of the data"
]
},
{
"cell_type": "markdown",
"id": "667f9015-c19c-41db-a232-a9110b43cfe3",
"metadata": {
"nbinlineai": {
"isOutputCell": true,
"promptCellId": "806395d1-373a-4132-a6fd-dfd5629cd89f",
"status": "done"
}
},
"source": [
"```python\n",
"x = np.linspace(min(y_height.min(), mu_p - 4*sigma_p),\n",
" max(y_height.max(), mu_p + 4*sigma_p), 500)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.hist(y_height, bins=\"auto\", density=True, alpha=0.4,\n",
" label=\"Observed heights (n=12)\")\n",
"ax.plot(x, stats.norm.pdf(x, loc=mu_p, scale=sigma_p),\n",
" lw=2, label=\"Prior on mean: N(168, 2²)\")\n",
"ax.set(xlabel=\"Height (cm)\", ylabel=\"Probability density\")\n",
"ax.legend()\n",
"plt.show()\n",
"```\n",
"\n",
"Note: the prior describes uncertainty about the **population mean**, while the histogram shows variation among **individual heights**."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "bdc5c0dd-dda9-4264-bec5-1afba3fcae71",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(min(y_height.min(), mu_p - 4*sigma_p),\n",
" max(y_height.max(), mu_p + 4*sigma_p), 500)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.hist(y_height, bins=4, density=True, alpha=0.4,\n",
" label=\"Observed heights (n=12)\")\n",
"ax.plot(x, stats.norm.pdf(x, loc=mu_p, scale=sigma_p),\n",
" lw=2, label=\"Prior on mean: N(168, 2²)\")\n",
"ax.set(xlabel=\"Height (cm)\", ylabel=\"Probability density\")\n",
"ax.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "28b809c6",
"metadata": {},
"source": [
"## Part 1. A normal model for a population mean"
]
},
{
"cell_type": "markdown",
"id": "997a7a38",
"metadata": {},
"source": [
"### The model, the prior, and the likelihood\n",
"\n",
"Each height is the population mean plus random noise:\n",
"\n",
"$$y_i=\\mu+\\epsilon_i,\\qquad \\epsilon_i\\overset{\\mathrm{ind}}{\\sim}N(0,\\sigma^2),\n",
"\\qquad\\text{so}\\qquad y_i\\mid\\mu\\sim N(\\mu,\\sigma^2).$$\n",
"\n",
"This is the intercept-only regression model: every person has the same predicted height, $\\mu$.\n",
"\n",
"Two normal distributions appear in this part, and they describe different things:\n",
"\n",
"| | What it describes | Standard deviation |\n",
"|---|---|---|\n",
"| Observation model $y_i\\mid\\mu\\sim N(\\mu,\\sigma^2)$ | how **individual heights** vary around the mean | $\\sigma = 7$ cm, known |\n",
"| Prior $\\mu\\sim N(\\mu_p,\\sigma_p^2)$ | our uncertainty about the **population mean** before seeing data | $\\sigma_p = 2$ cm, chosen by us |\n",
"\n",
"The **likelihood** is the probability density of the observed data, viewed as a function of a candidate value of $\\mu$.\n",
"Because the observations are independent, we multiply their normal densities:\n",
"\n",
"$$L(\\mu)=p(\\mathbf y\\mid\\mu)\\propto\\exp\\left[-\\frac{\\sum_i(y_i-\\mu)^2}{2\\sigma^2}\\right].$$\n",
"\n",
"The likelihood is not a probability distribution over $\\mu$; it does not have to integrate to 1.\n",
"Multiplying it by the prior gives the posterior, up to a constant:\n",
"\n",
"$$p(\\mu\\mid\\mathbf y)\\propto\n",
"\\underbrace{\\exp\\left[-\\frac{\\sum_i(y_i-\\mu)^2}{2\\sigma^2}\\right]}_{\\text{likelihood}}\\;\n",
"\\underbrace{\\exp\\left[-\\frac{(\\mu-\\mu_p)^2}{2\\sigma_p^2}\\right]}_{\\text{prior}}.$$"
]
},
{
"cell_type": "markdown",
"id": "ed2ed266-be4d-4b5e-b1ba-b3a13989952d",
"metadata": {
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"source": [
"Can you write for me the base theorem formulas which make the above equation come out? "
]
},
{
"cell_type": "markdown",
"id": "4c175c9c-5125-4e5b-826f-1e3bd95a32a9",
"metadata": {
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"source": [
"Three formulas give the posterior equation above:\n",
"\n",
"**1. Normal probability density**\n",
"$$X\\sim N(m,s^2)\\quad\\Rightarrow\\quad f(x)=\\frac{1}{\\sqrt{2\\pi s^2}}\\exp\\left[-\\frac{(x-m)^2}{2s^2}\\right].$$\n",
"\n",
"**2. Conditional independence: multiply observation densities**\n",
"$$p(\\mathbf y\\mid\\mu)=\\prod_{i=1}^n p(y_i\\mid\\mu)\n",
"=(2\\pi\\sigma^2)^{-n/2}\\exp\\left[-\\frac{\\sum_{i=1}^n(y_i-\\mu)^2}{2\\sigma^2}\\right].$$\n",
"\n",
"**3. Bayes’ theorem**\n",
"$$p(\\mu\\mid\\mathbf y)=\\frac{p(\\mathbf y\\mid\\mu)p(\\mu)}{p(\\mathbf y)}\\propto p(\\mathbf y\\mid\\mu)p(\\mu).$$\n",
"\n",
"Substitute the likelihood from (2) and the normal prior $\\mu\\sim N(\\mu_p,\\sigma_p^2)$ from (1):\n",
"$$\\boxed{p(\\mu\\mid\\mathbf y)\\propto\n",
"\\exp\\left[-\\frac{\\sum_i(y_i-\\mu)^2}{2\\sigma^2}\\right]\n",
"\\exp\\left[-\\frac{(\\mu-\\mu_p)^2}{2\\sigma_p^2}\\right].}$$\n",
"Here $\\propto$ drops factors that do **not depend on $\\mu$**."
]
},
{
"cell_type": "markdown",
"id": "9501e733",
"metadata": {},
"source": [
"### Prior times likelihood, computed on a grid\n",
"\n",
"Before using any formula, we can compute the posterior directly. The provided code evaluates prior × likelihood at\n",
"2,401 candidate means between 150 and 195 cm, then divides by the sum so that the values add to 1.\n",
"We add logarithms instead of multiplying densities: a product of many small densities can round to zero on a computer,\n",
"and subtracting the largest log value before exponentiating prevents that."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "528806dd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Grid posterior: mean 171.745 cm, SD 1.421 cm\n"
]
}
],
"source": [
"mu_grid = np.linspace(150, 195, 2401) # candidate values of the mean\n",
"log_prior = stats.norm.logpdf(mu_grid, mu_p, sigma_p)\n",
"log_likelihood = stats.norm.logpdf(y_height[:, None], mu_grid, sigma).sum(axis=0) # sum over the 12 heights\n",
"log_product = log_prior + log_likelihood\n",
"grid_mass = np.exp(log_product - log_product.max()) # subtract the maximum so exp() does not round to 0\n",
"grid_mass /= grid_mass.sum() # normalize: the grid values now add to 1\n",
"grid_mean = np.sum(mu_grid * grid_mass)\n",
"grid_sd = np.sqrt(np.sum((mu_grid - grid_mean)**2 * grid_mass))\n",
"print(f\"Grid posterior: mean {grid_mean:.3f} cm, SD {grid_sd:.3f} cm\")"
]
},
{
"cell_type": "markdown",
"id": "d0cfb219-97a6-4d61-a586-af4186fe3e19",
"metadata": {
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"keepAnswer": true
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},
"source": [
"Explain the nearest code cell above this question. Use earlier context where helpful. Specifically explain this line: `grid_mass = np.exp(log_product - log_product.max()) # subtract the maximum so exp() does not round to 0\n",
"`\n"
]
},
{
"cell_type": "markdown",
"id": "d39a209f-7ad2-49e6-aa61-77facfd3bcae",
"metadata": {
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"promptCellId": "d0cfb219-97a6-4d61-a586-af4186fe3e19",
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},
"source": [
"The cell approximates the posterior distribution of the population mean $\\mu$ on a grid:\n",
"\n",
"1. Evaluate the log prior and log likelihood at each candidate mean.\n",
"2. Add them: `log_product` is the log of prior × likelihood.\n",
"3. Exponentiate and normalize to obtain posterior grid probabilities.\n",
"4. Compute their weighted mean and standard deviation.\n",
"\n",
"**The key line:**\n",
"```python\n",
"grid_mass = np.exp(log_product - log_product.max())\n",
"```\n",
"Directly exponentiating very negative numbers can **underflow**—round to zero. Subtracting the maximum shifts the largest log value to zero, so the largest resulting weight is $e^0=1$, and all others lie between 0 and 1.\n",
"\n",
"For example:\n",
"```text\n",
"Log values: [-1001, -1000, -1002]\n",
"After subtracting max: [ -1, 0, -2]\n",
"Exponentiating: [0.368, 1.000, 0.135]\n",
"```\n",
"This preserves the posterior because it multiplies every weight by the same constant, which cancels in the next line:\n",
"$$w_j=\\frac{e^{\\ell_j-M}}{\\sum_k e^{\\ell_k-M}}\n",
"=\\frac{e^{\\ell_j}}{\\sum_k e^{\\ell_k}}.$$\n",
"\n",
"The comment is slightly simplified: extremely small tail weights can still round to zero, but **the weights cannot all become zero**, making normalization safe."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "80b8ea4d",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"grid_density = grid_mass / (mu_grid[1] - mu_grid[0]) # probabilities -> density\n",
"scaled_likelihood = np.exp(log_likelihood - log_likelihood.max()) * grid_density.max()\n",
"fig, ax = plt.subplots()\n",
"ax.plot(mu_grid, np.exp(log_prior), label=\"Prior\")\n",
"ax.plot(mu_grid, scaled_likelihood, linestyle=\"--\", label=\"Likelihood (rescaled to fit)\")\n",
"ax.plot(mu_grid, grid_density, linewidth=3, label=\"Posterior (grid)\")\n",
"ax.axvline(y_height.mean(), color=\"grey\", alpha=0.6, label=\"Sample mean\")\n",
"ax.set(xlim=(158, 186), xlabel=\"Candidate population mean (cm)\", ylabel=\"Density\")\n",
"ax.legend(loc=\"upper left\", bbox_to_anchor=(1.02, 1), fontsize=9)\n",
"fig.tight_layout(); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "bc2e1e01-6ddd-4047-9783-6723af5947d5",
"metadata": {
"nbinlineai": {
"isPromptCell": true
}
},
"source": [
"What is `scaled_likelihood = np.exp(log_likelihood - log_likelihood.max()) * grid_density.max()\n",
"` doing in the code above?"
]
},
{
"cell_type": "markdown",
"id": "96dac98b-4ac6-4f3a-8eef-1891e958a2de",
"metadata": {
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"source": [
"It rescales the likelihood curve **for plotting**, so its peak matches the posterior’s peak.\n",
"\n",
"```python\n",
"np.exp(log_likelihood - log_likelihood.max())\n",
"```\n",
"Computes the likelihood relative to its maximum: its peak becomes **1**, while preserving its shape and avoiding numerical underflow at the peak.\n",
"\n",
"```python\n",
"* grid_density.max()\n",
"```\n",
"Then makes its peak equal to the maximum posterior density.\n",
"\n",
"Thus, the dashed curve shows the likelihood’s **shape and location**, but its height is arbitrary. It is **not normalized to integrate to 1**, and this rescaling does not affect the posterior calculation."
]
},
{
"cell_type": "markdown",
"id": "49b54313",
"metadata": {},
"source": [
"The peak of the posterior is between the peak of the prior, at 168 cm, and the peak of the likelihood, at the sample mean of 175.6 cm.\n",
"The posterior is also narrower than either of them, because it combines the information in both."
]
},
{
"cell_type": "markdown",
"id": "4d6a367d",
"metadata": {},
"source": [
"### The closed-form normal posterior\n",
"\n",
"A prior is **conjugate** to a likelihood when the posterior belongs to the same family of distributions as the prior.\n",
"Here both exponents above are quadratic in $\\mu$. Adding them and completing the square (Appendix A4) gives another normal distribution,\n",
"$\\mu\\mid\\mathbf y\\sim N(\\mu_{\\mathrm{post}},\\sigma_{\\mathrm{post}}^2)$, with\n",
"\n",
"$$\\boxed{\\mu_{\\mathrm{post}}=\n",
"\\frac{n\\sigma_p^2}{n\\sigma_p^2+\\sigma^2}\\bar y+\n",
"\\frac{\\sigma^2}{n\\sigma_p^2+\\sigma^2}\\mu_p},\\qquad\n",
"\\boxed{\\sigma_{\\mathrm{post}}^2=\\frac{\\sigma^2\\sigma_p^2}{n\\sigma_p^2+\\sigma^2}}.$$\n",
"\n",
"This is the formula from lecture, where the prior mean and SD are written $\\mu_0$ and $\\sigma_0$.\n",
"\n",
"The posterior mean is a **weighted average** of the sample mean $\\bar y$ and the prior mean $\\mu_p$. Write the weight on the data as\n",
"\n",
"$$w=\\frac{n\\sigma_p^2}{n\\sigma_p^2+\\sigma^2},\\qquad\\text{so}\\qquad \\mu_{\\mathrm{post}}=w\\,\\bar y+(1-w)\\,\\mu_p.$$\n",
"\n",
"The weight $w$ grows when $n$ grows and when the prior SD $\\sigma_p$ grows. In our example $n\\sigma_p^2=12\\times4=48$ and $\\sigma^2=49$,\n",
"so $w=48/97\\approx0.49$: the data and the prior get almost equal weight.\n",
"\n",
"The posterior standard deviation $\\sigma_{\\mathrm{post}}$ is the square root of the posterior variance. It measures our uncertainty about\n",
"the **mean**. The standard deviation of individual heights stays $\\sigma=7$ cm."
]
},
{
"cell_type": "markdown",
"id": "a28f53da-0cf3-4257-94a7-66f0e69737dd",
"metadata": {
"nbinlineai": {
"isPromptCell": true
}
},
"source": [
"The above formula may be better represented by thinking about the data and prior variances or the data and prior precisions. Gimme formulas in terms of both of these for the weights and for the entire d you know form of the posterior mean and the yeah for the posterior mean. also if you have an intuitive way of explaining this formula and explaining why the posterior is Gaussian, that would be super. "
]
},
{
"cell_type": "markdown",
"id": "a41c98bc-eb9e-4a46-ab76-ae5e084bbb90",
"metadata": {
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"source": [
"### In terms of variances\n",
"The relevant **data variance is the variance of the sample mean**, not of individual heights:\n",
"$$V_d=\\frac{\\sigma^2}{n},\\qquad V_p=\\sigma_p^2.$$\n",
"\n",
"The weights and posterior mean are\n",
"$$w_d=\\frac{V_p}{V_d+V_p},\\qquad w_p=\\frac{V_d}{V_d+V_p},$$\n",
"$$\\boxed{\\mu_{\\mathrm{post}}=\\frac{V_p\\bar y+V_d\\mu_p}{V_d+V_p}.}$$\n",
"Notice the **opposite variance** in each numerator: a larger prior variance gives the data more weight.\n",
"\n",
"### In terms of precisions\n",
"Precision is inverse variance:\n",
"$$\\tau_d=\\frac{1}{V_d}=\\frac{n}{\\sigma^2},\\qquad \\tau_p=\\frac{1}{V_p}=\\frac{1}{\\sigma_p^2}.$$\n",
"Now each weight is its **own precision divided by total precision**:\n",
"$$w_d=\\frac{\\tau_d}{\\tau_d+\\tau_p},\\qquad w_p=\\frac{\\tau_p}{\\tau_d+\\tau_p},$$\n",
"$$\\boxed{\\mu_{\\mathrm{post}}=\\frac{\\tau_d\\bar y+\\tau_p\\mu_p}{\\tau_d+\\tau_p}.}$$\n",
"The full posterior is\n",
"$$\\boxed{\\mu\\mid\\mathbf y\\sim N\\!\\left(\\mu_{\\mathrm{post}},\\frac{1}{\\tau_d+\\tau_p}\\right).}$$\n",
"\n",
"### Intuition—and why Gaussian?\n",
"Think of the prior and data as two estimates of the same mean. **Trust the more precise estimate more.** More observations increase data precision; a tighter prior increases prior precision. Their precisions add, making the posterior narrower.\n",
"\n",
"Gaussianity follows because the log likelihood and log prior are both quadratic in $\\mu$:\n",
"$$\\log p(\\mu\\mid\\mathbf y)\n",
"=-\\frac12\\left[\\tau_d(\\mu-\\bar y)^2+\\tau_p(\\mu-\\mu_p)^2\\right]+C.$$\n",
"Completing the square gives\n",
"$$\\log p(\\mu\\mid\\mathbf y)\n",
"=-\\frac12(\\tau_d+\\tau_p)(\\mu-\\mu_{\\mathrm{post}})^2+C',$$\n",
"which is exactly the log of a Gaussian density. Here $C,C'$ do not depend on $\\mu$."
]
},
{
"cell_type": "markdown",
"id": "73941edf",
"metadata": {},
"source": [
"<div style=\"background:#E9F8EE; border-left:6px solid #16A34A; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🏋️ Exercise 1: update the mean (4 min)</div>\n",
"<div>\n",
"Complete the two formulas in <code>normal_mean_posterior</code>, using the boxed formulas above. Return the posterior mean and the posterior\n",
"<em>standard deviation</em>, not the variance. The next cell compares your answer with the grid; if the two columns match, your function is correct.\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ae3421f9",
"metadata": {},
"outputs": [],
"source": [
"def normal_mean_posterior(y, sigma, mu_p, sigma_p):\n",
" n = len(y)\n",
" denominator = n * sigma_p**2 + sigma**2\n",
" # BEGIN SOLUTION\n",
" mean = (n * sigma_p**2 * np.mean(y) + sigma**2 * mu_p) / denominator\n",
" variance = sigma**2 * sigma_p**2 / denominator\n",
" # END SOLUTION\n",
" # BEGIN STUDENT\n",
" # mean = ... # your code here\n",
" # variance = ... # your code here\n",
" # END STUDENT\n",
" return mean, np.sqrt(variance)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "5a1481a5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"95% credible interval for the mean: (168.96, 174.53) cm\n"
]
},
{
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>your formula</th>\n",
" <th>grid</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>posterior mean (cm)</th>\n",
" <td>171.745</td>\n",
" <td>171.745</td>\n",
" </tr>\n",
" <tr>\n",
" <th>posterior SD (cm)</th>\n",
" <td>1.421</td>\n",
" <td>1.421</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" your formula grid\n",
"posterior mean (cm) 171.745 171.745\n",
"posterior SD (cm) 1.421 1.421"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_post, sd_post = normal_mean_posterior(y_height, sigma, mu_p, sigma_p)\n",
"mean_interval = stats.norm.interval(0.95, loc=mean_post, scale=sd_post) # central 95% credible interval\n",
"print(f\"95% credible interval for the mean: ({mean_interval[0]:.2f}, {mean_interval[1]:.2f}) cm\")\n",
"pd.DataFrame({\"your formula\": [mean_post, sd_post], \"grid\": [grid_mean, grid_sd]},\n",
" index=[\"posterior mean (cm)\", \"posterior SD (cm)\"]).round(3)"
]
},
{
"cell_type": "markdown",
"id": "d2a7c0dd",
"metadata": {},
"source": [
"<div style=\"background:#FDECEC; border-left:6px solid #DC2626; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">💬 Discuss — Checkpoint 1: interpreting the interval</div>\n",
"<div>\n",
"<ol><li>What does the 95% credible interval say about the unknown mean?</li><li>Is it an interval that contains 95% of individual heights?</li><li>Which standard deviation describes how individual heights vary, and which describes our prior uncertainty about the mean?</li></ol>\n",
"</div>\n",
"\n",
"<details>\n",
"<summary><strong>Worked answer</strong></summary>\n",
"<div style=\"margin-top:10px; padding-top:8px; border-top:1px dashed #999;\">\n",
"<p>A 95% <strong>credible interval</strong> contains 95% posterior probability for the population mean, conditional on these data and the stipulated prior and likelihood. Here, given our data and our N(168, 2²) prior, the mean lies between about 169.0 and 174.5 cm with probability 0.95.</p>\n",
"<p>It is not an interval for individual heights. Individual heights vary with standard deviation σ = 7 cm, so about 95% of them lie within roughly ±14 cm of the mean, a much wider range. The prior SD σ<sub>p</sub> = 2 cm describes our uncertainty about the mean before seeing data, and the posterior SD of 1.42 cm describes it after.</p>\n",
"</div>\n",
"</details>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "a0b09913",
"metadata": {},
"source": [
"### Changing the prior standard deviation"
]
},
{
"cell_type": "markdown",
"id": "127e8475",
"metadata": {},
"source": [
"<div style=\"background:#FFF7CC; border-left:6px solid #D97706; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🤔 Predict — a narrower or wider prior</div>\n",
"<div>\n",
"Keep the data and the prior mean (168 cm) fixed, and try prior SDs of 0.7, 2 and 10 cm. As the prior SD gets smaller, will the posterior mean move\n",
"toward the prior mean or toward the sample mean? Will the posterior SD get larger or smaller? Commit before running the cell.\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "26668047",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1200x360 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior SD</th>\n",
" <th>weight on sample mean</th>\n",
" <th>posterior mean</th>\n",
" <th>posterior SD</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.7</td>\n",
" <td>0.107</td>\n",
" <td>168.811</td>\n",
" <td>0.661</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2.0</td>\n",
" <td>0.495</td>\n",
" <td>171.745</td>\n",
" <td>1.421</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>10.0</td>\n",
" <td>0.961</td>\n",
" <td>175.271</td>\n",
" <td>1.981</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prior SD weight on sample mean posterior mean posterior SD\n",
"0 0.7 0.107 168.811 0.661\n",
"1 2.0 0.495 171.745 1.421\n",
"2 10.0 0.961 175.271 1.981"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig, axes = plt.subplots(1, 3, figsize=(12, 3.6), sharex=True, sharey=True)\n",
"prior_rows = []\n",
"for ax, prior_sd in zip(axes, [0.7, 2.0, 10.0]):\n",
" m, s = normal_mean_posterior(y_height, sigma, mu_p, prior_sd)\n",
" w = len(y_height) * prior_sd**2 / (len(y_height) * prior_sd**2 + sigma**2) # weight on the sample mean\n",
" ax.plot(mu_grid, stats.norm.pdf(mu_grid, mu_p, prior_sd), label=\"Prior\")\n",
" ax.plot(mu_grid, stats.norm.pdf(mu_grid, m, s), label=\"Posterior\")\n",
" ax.axvline(y_height.mean(), color=\"grey\", linestyle=\"--\", label=\"Sample mean\")\n",
" ax.set(title=f\"Prior SD = {prior_sd} cm\", xlabel=\"Population mean (cm)\", xlim=(160, 186))\n",
" prior_rows.append([prior_sd, w, m, s])\n",
"axes[0].set_ylabel(\"Density\"); axes[-1].legend(fontsize=9)\n",
"fig.tight_layout(); plt.show()\n",
"pd.DataFrame(prior_rows, columns=[\"prior SD\", \"weight on sample mean\", \"posterior mean\", \"posterior SD\"]).round(3)"
]
},
{
"cell_type": "markdown",
"id": "c0f18b02",
"metadata": {},
"source": [
"With a prior SD of 0.7 cm the data get weight 0.11, so the posterior mean (168.8 cm) stays close to the prior mean, and the posterior SD is only 0.66 cm.\n",
"With a prior SD of 10 cm the data get weight 0.96, so the posterior mean (175.3 cm) is close to the sample mean, and the posterior SD (1.98 cm) is close to\n",
"$\\sigma/\\sqrt{n}=2.02$ cm. The left panel is the case to watch for: a narrow prior gives a narrow posterior even when the prior mean is wrong.\n",
"The true mean is 175 cm, and that posterior puts almost no probability there."
]
},
{
"cell_type": "markdown",
"id": "49384711",
"metadata": {},
"source": [
"### Increasing the sample size\n",
"\n",
"Now keep the prior fixed at $N(168, 2^2)$ and use the first 12, the first 120, and all 1,200 simulated heights.\n",
"Because each larger sample contains the smaller one, the sample mean changes only because new observations are added."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "532f36f8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1200x360 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>n</th>\n",
" <th>sample mean</th>\n",
" <th>weight on sample mean</th>\n",
" <th>posterior mean</th>\n",
" <th>posterior SD</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>12</td>\n",
" <td>175.568</td>\n",
" <td>0.495</td>\n",
" <td>171.745</td>\n",
" <td>1.421</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>120</td>\n",
" <td>174.614</td>\n",
" <td>0.907</td>\n",
" <td>174.001</td>\n",
" <td>0.609</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1200</td>\n",
" <td>175.148</td>\n",
" <td>0.990</td>\n",
" <td>175.075</td>\n",
" <td>0.201</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" n sample mean weight on sample mean posterior mean posterior SD\n",
"0 12 175.568 0.495 171.745 1.421\n",
"1 120 174.614 0.907 174.001 0.609\n",
"2 1200 175.148 0.990 175.075 0.201"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig, axes = plt.subplots(1, 3, figsize=(12, 3.6), sharex=True)\n",
"size_rows = []\n",
"for ax, n in zip(axes, [12, 120, 1200]):\n",
" y_n = height_sequence[:n]\n",
" m, s = normal_mean_posterior(y_n, sigma, mu_p, sigma_p)\n",
" w = n * sigma_p**2 / (n * sigma_p**2 + sigma**2) # weight on the sample mean\n",
" ax.plot(mu_grid, stats.norm.pdf(mu_grid, mu_p, sigma_p), label=\"Fixed prior\")\n",
" ax.plot(mu_grid, stats.norm.pdf(mu_grid, m, s), label=\"Posterior\")\n",
" ax.axvline(y_n.mean(), color=\"grey\", linestyle=\"--\", label=\"Sample mean\")\n",
" ax.axvline(true_mu, color=\"black\", linestyle=\":\", label=\"True mean\")\n",
" ax.set(title=f\"n = {n}\", xlabel=\"Population mean (cm)\", xlim=(160, 186))\n",
" size_rows.append([n, y_n.mean(), w, m, s])\n",
"axes[0].set_ylabel(\"Density\"); axes[-1].legend(fontsize=8)\n",
"fig.tight_layout(); plt.show()\n",
"pd.DataFrame(size_rows, columns=[\"n\", \"sample mean\", \"weight on sample mean\", \"posterior mean\", \"posterior SD\"]).round(3)"
]
},
{
"cell_type": "markdown",
"id": "d3a2b293",
"metadata": {},
"source": [
"<div style=\"background:#F3E8FF; border-left:6px solid #7E22CE; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">⭐ Insight — what controls the posterior</div>\n",
"<div>\n",
"<ul>\n",
"<li><strong>A smaller prior SD σ<sub>p</sub> puts more weight on the prior mean.</strong> The posterior mean moves toward μ<sub>p</sub> and the posterior SD shrinks. If μ<sub>p</sub> is far from the truth, the result is a narrow posterior around the wrong value.</li>\n",
"<li><strong>A larger sample size n puts more weight on the sample mean.</strong> The weight on the data went from 0.49 at n = 12 to 0.99 at n = 1,200, and the posterior SD shrank from 1.42 to 0.20 cm. This holds for any normal prior. A prior that gives zero probability to some values is different: no amount of data can move the posterior to those values.</li>\n",
"<li>The prior and the data get equal weight when nσ<sub>p</sub>² = σ². With σ<sub>p</sub> = 2 and σ = 7 that happens at n ≈ 12, which is why our first posterior sat halfway between 168 and 175.6 cm.</li>\n",
"</ul>\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "1fc94415",
"metadata": {},
"source": [
"### A very wide prior and the confidence interval\n",
"\n",
"If we make the prior SD very large ($\\sigma_p\\to\\infty$), the prior has almost no preference among candidate means. Then $w\\to1$ and\n",
"\n",
"$$\\mu_{\\mathrm{post}}\\to\\bar y,\\qquad \\sigma_{\\mathrm{post}}\\to\\frac{\\sigma}{\\sqrt n}.$$\n",
"\n",
"A prior like this is called **diffuse**. With known $\\sigma$, the 95% credible interval then has the same endpoints as the familiar\n",
"confidence interval $\\bar y\\pm1.96\\,\\sigma/\\sqrt n$, as the table below shows. The two intervals still mean different things:\n",
"\n",
"- The **credible interval** says: given these data and this prior, the mean lies in the interval with probability 0.95.\n",
"- A 95% **confidence-interval procedure** says: if we repeated the whole study many times and built an interval each time, 95% of those intervals\n",
"would contain the fixed true mean. It does not give a probability for the mean from one observed interval."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "16fc1e0b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>centre</th>\n",
" <th>SD or SE</th>\n",
" <th>95% lower</th>\n",
" <th>95% upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Diffuse-prior credible interval</th>\n",
" <td>175.568</td>\n",
" <td>2.021</td>\n",
" <td>171.608</td>\n",
" <td>179.529</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Confidence interval</th>\n",
" <td>175.568</td>\n",
" <td>2.021</td>\n",
" <td>171.608</td>\n",
" <td>179.529</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" centre SD or SE 95% lower 95% upper\n",
"Diffuse-prior credible interval 175.568 2.021 171.608 179.529\n",
"Confidence interval 175.568 2.021 171.608 179.529"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"diffuse_mean, diffuse_sd = normal_mean_posterior(y_height, sigma, mu_p, 1e6) # prior SD of a million cm\n",
"se = sigma / np.sqrt(len(y_height))\n",
"pd.DataFrame({\"centre\": [diffuse_mean, y_height.mean()],\n",
" \"SD or SE\": [diffuse_sd, se],\n",
" \"95% lower\": [diffuse_mean - 1.96 * diffuse_sd, y_height.mean() - 1.96 * se],\n",
" \"95% upper\": [diffuse_mean + 1.96 * diffuse_sd, y_height.mean() + 1.96 * se]},\n",
" index=[\"Diffuse-prior credible interval\", \"Confidence interval\"]).round(3)"
]
},
{
"cell_type": "markdown",
"id": "37b92bf4",
"metadata": {},
"source": [
"## Part 2. Adding a predictor: a regression slope"
]
},
{
"cell_type": "markdown",
"id": "8440a8f9",
"metadata": {},
"source": [
"### From one mean to a regression line\n",
"\n",
"Now we also record each person's parent's height, $x_i$. Instead of one mean for everyone, the mean height depends on $x_i$:\n",
"\n",
"$$y_i=\\beta_0+\\beta_1x_i+\\epsilon_i,\\qquad\n",
" y_i\\mid x_i,\\beta_0,\\beta_1\\sim N(\\beta_0+\\beta_1x_i,\\sigma^2).$$\n",
"\n",
"These are the usual linear-regression assumptions: the mean is linear in $x$; the errors are independent, so the likelihood is a product;\n",
"every observation has the same error variance $\\sigma^2$ (**homoscedasticity**); and the errors are normal. As in Part 1, $\\sigma=7$ cm is known.\n",
"\n",
"We simulate 80 parent–child pairs with a true slope of 0.65: each extra centimetre of parent height adds 0.65 cm to the expected adult-child height.\n",
"This is a simulation for practising the method, not a study of how height is inherited."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "9e075dc6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OLS slope: 0.649 cm per cm (true slope: 0.65)\n"
]
}
],
"source": [
"rng_regression = np.random.default_rng(110)\n",
"x = rng_regression.normal(170, 8, 80) # parent heights (cm)\n",
"true_slope = 0.65\n",
"sigma_reg = 7.0 # known observation SD (cm)\n",
"reg_y = 175 + true_slope * (x - 170) + rng_regression.normal(0, sigma_reg, len(x))\n",
"x_bar, y_bar = x.mean(), reg_y.mean()\n",
"x_c, y_c = x - x_bar, reg_y - y_bar # centred predictor and response\n",
"ols = LinearRegression().fit(x[:, None], reg_y)\n",
"beta_hat = ols.coef_[0]\n",
"print(f\"OLS slope: {beta_hat:.3f} cm per cm (true slope: {true_slope})\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "916ee509",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_line = np.linspace(x.min() - 2, x.max() + 2, 150)\n",
"fig, ax = plt.subplots()\n",
"ax.scatter(x, reg_y, alpha=0.6, label=\"Simulated observations\")\n",
"ax.plot(x_line, ols.predict(x_line[:, None]), color=\"black\", label=\"OLS mean response\")\n",
"ax.set(xlabel=\"Parent height (cm)\", ylabel=\"Adult-child height (cm)\")\n",
"ax.legend(); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "eb3304d4",
"metadata": {},
"source": [
"### Bootstrap uncertainty for the slope (review from Section 5)\n",
"\n",
"This is the paired bootstrap from Section 5, Part 2: resample the 80 rows with replacement, refit, record the slope, and repeat 3,000 times.\n",
"The spread of those slopes estimates how much the OLS slope would vary from one sample to another. It is not a posterior:\n",
"no prior is involved, and it does not give a probability for the slope itself. The loop is provided."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "8d57ddf4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Bootstrap slopes: mean 0.648, SD 0.098\n"
]
}
],
"source": [
"rng_boot = np.random.default_rng(111)\n",
"boot_slopes = np.empty(3000)\n",
"for b in range(len(boot_slopes)):\n",
" idx = rng_boot.integers(0, len(x), size=len(x)) # resample rows with replacement\n",
" xb, yb = x[idx], reg_y[idx]\n",
" xb_c, yb_c = xb - xb.mean(), yb - yb.mean()\n",
" boot_slopes[b] = np.dot(xb_c, yb_c) / np.dot(xb_c, xb_c) # OLS slope on the resample\n",
"bootstrap_interval = np.quantile(boot_slopes, [0.025, 0.975])\n",
"print(f\"Bootstrap slopes: mean {boot_slopes.mean():.3f}, SD {boot_slopes.std(ddof=1):.3f}\")"
]
},
{
"cell_type": "markdown",
"id": "558668a2",
"metadata": {},
"source": [
"### A normal prior on the slope\n",
"\n",
"We put a normal prior on the slope only:\n",
"\n",
"$$\\beta_1\\sim N(\\mu_{\\beta_1},\\sigma_{\\beta_1}^2).$$\n",
"\n",
"We put no prior information on the intercept. Mathematically, this is a **flat prior**: every intercept value is treated as equally plausible.\n",
"\n",
"The update for the slope is the Part 1 update with three substitutions:\n",
"\n",
"| | Part 1: the mean | Part 2: the slope |\n",
"|---|---|---|\n",
"| Estimate from the data | sample mean $\\bar y$ | OLS slope $\\hat\\beta_1=\\dfrac{\\sum_i(x_i-\\bar x)(y_i-\\bar y)}{S_{xx}}$ |\n",
"| Amount of information in the data | sample size $n$ | $S_{xx}=\\sum_i(x_i-\\bar x)^2$ |\n",
"| Prior | $N(\\mu_p,\\sigma_p^2)$ | $N(\\mu_{\\beta_1},\\sigma_{\\beta_1}^2)$ |\n",
"\n",
"Making those substitutions in the Part 1 formulas gives\n",
"\n",
"$$\\boxed{\\mu_{\\beta_1,\\mathrm{post}}=\n",
"\\frac{S_{xx}\\sigma_{\\beta_1}^2}{S_{xx}\\sigma_{\\beta_1}^2+\\sigma^2}\\hat\\beta_1+\n",
"\\frac{\\sigma^2}{S_{xx}\\sigma_{\\beta_1}^2+\\sigma^2}\\mu_{\\beta_1}},\\qquad\n",
"\\boxed{\\sigma_{\\beta_1,\\mathrm{post}}^2=\n",
"\\frac{\\sigma^2\\sigma_{\\beta_1}^2}{S_{xx}\\sigma_{\\beta_1}^2+\\sigma^2}}.$$\n",
"\n",
"**Why $S_{xx}$ takes the place of $n$.** The sample mean has sampling variance $\\sigma^2/n$, and the OLS slope has sampling variance $\\sigma^2/S_{xx}$.\n",
"$S_{xx}$ is large when there are many observations *and* their $x$ values are spread out. If every $x_i$ were the same, $S_{xx}$ would be 0 and the\n",
"data would say nothing about the slope.\n",
"\n",
"**Where the intercept went.** Integrating out the free intercept, which means averaging the likelihood over every possible intercept value as the flat prior allows,\n",
"leaves a likelihood for the slope alone that is proportional to $\\exp[-S_{xx}(\\beta_1-\\hat\\beta_1)^2/(2\\sigma^2)]$. This has the same form as the\n",
"Part 1 likelihood, with $\\hat\\beta_1$ in place of $\\bar y$ and $S_{xx}$ in place of $n$. Centering $x$ is what separates the slope from the intercept in this calculation;\n",
"centering $y$ only shortens the code. The intercept is still uncertain, and Appendix A3 shows how that uncertainty enters predictions."
]
},
{
"cell_type": "markdown",
"id": "9057f343-4af3-4bd5-a16c-9419e9186b57",
"metadata": {
"nbinlineai": {
"isPromptCell": true
}
},
"source": [
"lets start with the bayesian formulas first here. indeed lets put priors both on the slope and intercept. Then show how the uniform prior on the intercept integrates out (marginalization). We still have to do the posterior for the slope. explain how this formula comes about, and why $S_{xx}$ playys the role of n. And just like in the last case, recast this formula in terms of variances and precisions."
]
},
{
"cell_type": "markdown",
"id": "c3bbf242-4ff2-4d1f-88c0-89bcbaa6bf1a",
"metadata": {
"nbinlineai": {
"isOutputCell": true,
"promptCellId": "9057f343-4af3-4bd5-a16c-9419e9186b57",
"status": "done"
}
},
"source": [
"## 1. Bayes’ rule: priors on both coefficients\n",
"\n",
"Assume independent errors with **known** variance $\\sigma^2$:\n",
"$$y_i=\\beta_0+\\beta_1x_i+\\epsilon_i,\\qquad \\epsilon_i\\sim N(0,\\sigma^2).$$\n",
"\n",
"Assign independent priors $p(\\beta_0)$ and\n",
"$$\\beta_1\\sim N(m_p,V_p).$$\n",
"Then Bayes’ rule gives\n",
"$$p(\\beta_0,\\beta_1\\mid\\mathbf y,\\mathbf x)\n",
"\\propto\n",
"\\underbrace{\\exp\\!\\left[-\\frac{\\sum_i(y_i-\\beta_0-\\beta_1x_i)^2}{2\\sigma^2}\\right]}_{\\text{likelihood}}\n",
"p(\\beta_0)\\,p(\\beta_1).$$\n",
"\n",
"For the intercept, choose $p(\\beta_0)\\propto1$. This is an **improper flat prior**, not a proper uniform distribution on the whole real line. It represents no preference among intercept values.\n",
"\n",
"## 2. Integrate out the intercept\n",
"\n",
"Define $x_{ci}=x_i-\\bar x$ and $y_{ci}=y_i-\\bar y$. The crucial identity is\n",
"$$\\sum_i(y_i-\\beta_0-\\beta_1x_i)^2\n",
"=\\sum_i(y_{ci}-\\beta_1x_{ci})^2\n",
"+n(\\beta_0-\\bar y+\\beta_1\\bar x)^2.$$\n",
"The cross term vanishes because centered values sum to zero.\n",
"\n",
"Marginalization means integrating the joint posterior over $\\beta_0$:\n",
"$$\\begin{aligned}\n",
"p(\\beta_1\\mid\\mathbf y,\\mathbf x)\n",
"&\\propto p(\\beta_1)\n",
"\\exp\\!\\left[-\\frac{\\sum_i(y_{ci}-\\beta_1x_{ci})^2}{2\\sigma^2}\\right]\\\\\n",
"&\\quad\\times\\int_{-\\infty}^{\\infty}\n",
"\\exp\\!\\left[-\\frac{n(\\beta_0-\\bar y+\\beta_1\\bar x)^2}{2\\sigma^2}\\right]d\\beta_0.\n",
"\\end{aligned}$$\n",
"\n",
"The integral equals $\\sqrt{2\\pi\\sigma^2/n}$, **independent of the slope**, so it disappears into the normalization constant. We have averaged over the uncertain intercept—not fixed it at an estimate.\n",
"\n",
"## 3. Obtain the slope likelihood and posterior\n",
"\n",
"Write\n",
"$$S_{xx}=\\sum_i x_{ci}^2,\\qquad\n",
"\\hat\\beta_1=\\frac{\\sum_i x_{ci}y_{ci}}{S_{xx}},$$\n",
"assuming $S_{xx}>0$. Completing the square gives\n",
"$$\\sum_i(y_{ci}-\\beta_1x_{ci})^2\n",
"=S_{xx}(\\beta_1-\\hat\\beta_1)^2+C,$$\n",
"where $C$ does not depend on $\\beta_1$.\n",
"\n",
"Thus\n",
"$$p(\\beta_1\\mid\\mathbf y,\\mathbf x)\n",
"\\propto\\exp\\!\\left[-\\frac12\\left\\{\n",
"\\frac{S_{xx}}{\\sigma^2}(\\beta_1-\\hat\\beta_1)^2\n",
"+\\frac{1}{V_p}(\\beta_1-m_p)^2\\right\\}\\right].$$\n",
"\n",
"Both terms are quadratic in the slope; their sum is another quadratic. Completing its square yields a **Gaussian posterior**:\n",
"$$\\beta_1\\mid\\mathbf y,\\mathbf x\\sim N(m_{\\mathrm{post}},V_{\\mathrm{post}}),$$\n",
"$$\\boxed{m_{\\mathrm{post}}=\n",
"\\frac{S_{xx}V_p}{S_{xx}V_p+\\sigma^2}\\hat\\beta_1\n",
"+\\frac{\\sigma^2}{S_{xx}V_p+\\sigma^2}m_p,\\qquad\n",
"V_{\\mathrm{post}}=\\frac{\\sigma^2V_p}{S_{xx}V_p+\\sigma^2}.}$$\n",
"\n",
"## 4. Why does $S_{xx}$ replace $n$?\n",
"\n",
"Compare the sampling variances:\n",
"$$\\operatorname{Var}(\\bar y\\mid\\mu)=\\frac{\\sigma^2}{n},\\qquad\n",
"\\operatorname{Var}(\\hat\\beta_1\\mid\\mathbf x,\\beta_1)=\\frac{\\sigma^2}{S_{xx}}.$$\n",
"\n",
"For a mean, each observation adds equal information. For a slope, observations **farther from the average predictor value provide more leverage**: changing the slope changes their predicted responses more.\n",
"\n",
"Consequently, slope information increases with both sample size and predictor spread. If all predictors are identical, $S_{xx}=0$: with a free intercept, the data cannot identify the slope, and its posterior remains its prior.\n",
"\n",
"## 5. Variance and precision forms\n",
"\n",
"The relevant data variance is the **variance of the slope estimate**, not the observation variance:\n",
"$$V_d=\\frac{\\sigma^2}{S_{xx}},\\qquad V_p=\\sigma_{\\beta_1}^2,\\qquad m_p=\\mu_{\\beta_1}.$$\n",
"\n",
"**Using variances:**\n",
"$$w_d=\\frac{V_p}{V_d+V_p},\\qquad w_p=\\frac{V_d}{V_d+V_p},$$\n",
"$$\\boxed{m_{\\mathrm{post}}=\\frac{V_p\\hat\\beta_1+V_dm_p}{V_d+V_p},\\qquad\n",
"V_{\\mathrm{post}}=\\frac{V_dV_p}{V_d+V_p}.}$$\n",
"\n",
"**Using precisions** $\\tau_d=1/V_d=S_{xx}/\\sigma^2$ and $\\tau_p=1/V_p$:\n",
"$$w_d=\\frac{\\tau_d}{\\tau_d+\\tau_p},\\qquad w_p=\\frac{\\tau_p}{\\tau_d+\\tau_p},$$\n",
"$$\\boxed{m_{\\mathrm{post}}=\\frac{\\tau_d\\hat\\beta_1+\\tau_pm_p}{\\tau_d+\\tau_p},\\qquad\n",
"V_{\\mathrm{post}}=\\frac{1}{\\tau_d+\\tau_p}.}$$\n",
"\n",
"**Same principle as before:** average the prior estimate and data estimate according to their precision; add their precisions to obtain posterior precision."
]
},
{
"cell_type": "markdown",
"id": "ef97bf8d",
"metadata": {},
"source": [
"<div style=\"background:#E9F8EE; border-left:6px solid #16A34A; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🏋️ Exercise 2: update the slope (5 min)</div>\n",
"<div>\n",
"Complete the posterior mean and variance in <code>slope_posterior</code>, using the boxed formulas. Return the mean and the standard deviation.\n",
"<br><br>\n",
"The prior used below is <em>N</em>(0, 0.12²). It is a sceptical prior: before seeing data, it says the slope is probably within about ±0.24 cm per cm of zero (two prior SDs).\n",
"The OLS slope is 0.649. <strong>Predict before running:</strong> will the posterior mean be closer to 0 or to 0.649, and will the credible interval be wider or narrower than the OLS interval?\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "e40e4089",
"metadata": {},
"outputs": [],
"source": [
"sxx = np.dot(x_c, x_c) # S_xx, the spread of the predictor\n",
"mu_beta1, sigma_beta1 = 0.0, 0.12\n",
"\n",
"def slope_posterior(beta_hat, sxx, sigma, mu_beta1, sigma_beta1):\n",
" denominator = sxx * sigma_beta1**2 + sigma**2\n",
" # BEGIN SOLUTION\n",
" mean = (sxx * sigma_beta1**2 * beta_hat + sigma**2 * mu_beta1) / denominator\n",
" variance = sigma**2 * sigma_beta1**2 / denominator\n",
" # END SOLUTION\n",
" # BEGIN STUDENT\n",
" # mean = ... # your code here\n",
" # variance = ... # your code here\n",
" # END STUDENT\n",
" return mean, np.sqrt(variance)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "8bd0d5a1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"S_xx = 4970; weight on the OLS slope = 0.59, weight on the prior mean = 0.41\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>method</th>\n",
" <th>centre</th>\n",
" <th>SD or SE</th>\n",
" <th>95% lower</th>\n",
" <th>95% upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Analytical CI (known sigma)</td>\n",
" <td>0.649</td>\n",
" <td>0.099</td>\n",
" <td>0.454</td>\n",
" <td>0.843</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Diffuse-prior credible interval</td>\n",
" <td>0.649</td>\n",
" <td>0.099</td>\n",
" <td>0.454</td>\n",
" <td>0.843</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Informative-prior credible interval</td>\n",
" <td>0.385</td>\n",
" <td>0.077</td>\n",
" <td>0.235</td>\n",
" <td>0.535</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Bootstrap percentile CI</td>\n",
" <td>0.648</td>\n",
" <td>0.098</td>\n",
" <td>0.452</td>\n",
" <td>0.842</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" method centre SD or SE 95% lower 95% upper\n",
"0 Analytical CI (known sigma) 0.649 0.099 0.454 0.843\n",
"1 Diffuse-prior credible interval 0.649 0.099 0.454 0.843\n",
"2 Informative-prior credible interval 0.385 0.077 0.235 0.535\n",
"3 Bootstrap percentile CI 0.648 0.098 0.452 0.842"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"slope_mean, slope_sd = slope_posterior(beta_hat, sxx, sigma_reg, mu_beta1, sigma_beta1)\n",
"diffuse_slope_mean, diffuse_slope_sd = slope_posterior(beta_hat, sxx, sigma_reg, 0, 1e6)\n",
"analytical_se = sigma_reg / np.sqrt(sxx)\n",
"w_slope = sxx * sigma_beta1**2 / (sxx * sigma_beta1**2 + sigma_reg**2)\n",
"print(f\"S_xx = {sxx:.0f}; weight on the OLS slope = {w_slope:.2f}, weight on the prior mean = {1 - w_slope:.2f}\")\n",
"\n",
"interval_rows = []\n",
"for label, m, s in [(\"Analytical CI (known sigma)\", beta_hat, analytical_se),\n",
" (\"Diffuse-prior credible interval\", diffuse_slope_mean, diffuse_slope_sd),\n",
" (\"Informative-prior credible interval\", slope_mean, slope_sd)]:\n",
" lo, hi = stats.norm.interval(0.95, loc=m, scale=s)\n",
" interval_rows.append([label, m, s, lo, hi])\n",
"interval_rows.append([\"Bootstrap percentile CI\", boot_slopes.mean(), boot_slopes.std(ddof=1), *bootstrap_interval])\n",
"interval_table = pd.DataFrame(interval_rows, columns=[\"method\", \"centre\", \"SD or SE\", \"95% lower\", \"95% upper\"])\n",
"interval_table.round(3)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "9385d42c",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"slope_grid = np.linspace(min(0, slope_mean - 5*slope_sd), beta_hat + 5*analytical_se, 1000)\n",
"fig, ax = plt.subplots()\n",
"ax.hist(boot_slopes, bins=40, density=True, alpha=0.3, label=\"Bootstrap estimates\")\n",
"ax.plot(slope_grid, stats.norm.pdf(slope_grid, diffuse_slope_mean, diffuse_slope_sd), label=\"Diffuse-prior posterior\")\n",
"ax.plot(slope_grid, stats.norm.pdf(slope_grid, slope_mean, slope_sd), label=\"Informative-prior posterior\")\n",
"ax.axvline(beta_hat, color=\"grey\", linestyle=\"--\", label=\"OLS slope\")\n",
"ax.axvline(true_slope, color=\"black\", linestyle=\":\", label=\"Generating slope\")\n",
"ax.set(xlabel=\"Slope (cm per cm of parent height)\", ylabel=\"Density\")\n",
"ax.legend(fontsize=9); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "30b1234a",
"metadata": {},
"source": [
"### Comparing the four intervals\n",
"\n",
"- The **analytical CI** is $\\hat\\beta_1\\pm1.96\\,\\sigma/\\sqrt{S_{xx}}$, the frequentist confidence interval when $\\sigma$ is known.\n",
"- The **diffuse-prior credible interval** comes from a very wide prior. Then the posterior is $N(\\hat\\beta_1,\\sigma^2/S_{xx})$, so its endpoints equal the analytical CI's.\n",
"- In the **informative-prior credible interval**, the $N(0, 0.12^2)$ prior gets weight 0.41, which moves the centre from 0.649 to 0.385 and makes the interval narrower.\n",
"Its interval does not contain the true slope of 0.65: this is the narrow-prior-around-a-wrong-value case from Part 1.\n",
"- The **bootstrap percentile CI** uses the 2.5th and 97.5th percentiles of the 3,000 bootstrap slopes. It is close to the analytical CI here.\n",
"Its 95% coverage is approximate, not exact.\n",
"\n",
"Three of the four rows give nearly the same numbers, but a credible interval and a confidence interval answer different questions, as in Part 1."
]
},
{
"cell_type": "markdown",
"id": "c427c9e1",
"metadata": {},
"source": [
"<div style=\"background:#FDECEC; border-left:6px solid #DC2626; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">💬 Discuss — Checkpoint 2: the interval comparison</div>\n",
"<div>\n",
"<ol><li>Which rows of the table use a prior? Why do the two credible intervals differ?</li><li>What does \"95%\" refer to for a credible interval, and what does it refer to for a confidence interval?</li><li>Would running 100 times as many bootstrap resamples make the bootstrap interval agree with the informative-prior interval?</li></ol>\n",
"</div>\n",
"\n",
"<details>\n",
"<summary><strong>Worked answer</strong></summary>\n",
"<div style=\"margin-top:10px; padding-top:8px; border-top:1px dashed #999;\">\n",
"<p>Only the two credible-interval rows use a prior. The diffuse prior has almost no weight, so it reproduces the analytical CI. The N(0, 0.12²) prior has weight 0.41 on its mean of 0, so its posterior is centred at 0.385 instead of 0.649 and is narrower.</p>\n",
"<p>A credible interval contains 95% posterior probability for the slope, given the observed data, the stipulated likelihood, and the prior. A confidence-interval procedure covers the fixed true slope in 95% of repeated samples.</p>\n",
"<p>No. More resamples make the bootstrap percentiles less affected by random resampling, so they settle near (0.45, 0.84). The informative-prior interval differs because of the prior, and the bootstrap uses no prior at all.</p>\n",
"</div>\n",
"</details>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "49c2b58b",
"metadata": {},
"source": [
"## Part 3. A yes/no outcome: one shared probability, then predictors"
]
},
{
"cell_type": "markdown",
"id": "3191dd4c",
"metadata": {},
"source": [
"### 3a. A shared probability for a health outcome\n",
"\n",
"We simulate 24 adults, each with an age and a yes/no heart-disease outcome (1 = disease, 0 = no disease).\n",
"In the simulation, the probability of disease rises with age. This is a teaching simulation, not a clinical risk estimate.\n",
"\n",
"We start by ignoring age. Every person gets the same unknown probability $p$ of disease:\n",
"\n",
"$$y_i\\sim\\mathrm{Bernoulli}(p),\\quad\\text{independently}.$$\n",
"\n",
"This is the yes/no version of Part 1, where everyone had the same mean $\\mu$. A Bernoulli observation is a binomial with one trial,\n",
"so the number of positive outcomes, $k=\\sum_i y_i$, follows a $\\mathrm{Binomial}(n,p)$ distribution."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "b41197c4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Observed disease outcomes: 9 of 24; proportion = 0.375\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>age</th>\n",
" <th>heart_disease</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>36.7</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>59.4</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>44.2</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>52.1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>40.5</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age heart_disease\n",
"0 36.7 0\n",
"1 59.4 1\n",
"2 44.2 0\n",
"3 52.1 0\n",
"4 40.5 0"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rng_health = np.random.default_rng(112)\n",
"age_z = rng_health.normal(size=24)\n",
"age = 50 + 10 * age_z # ages, mean 50 and SD 10 years\n",
"true_prob = expit(-0.6 + 0.8 * age_z) # true disease probability rises with age\n",
"y_health = rng_health.binomial(1, true_prob)\n",
"health = pd.DataFrame({\"age\": age, \"heart_disease\": y_health})\n",
"n_health, k_health = len(y_health), y_health.sum()\n",
"print(f\"Observed disease outcomes: {k_health} of {n_health}; proportion = {k_health/n_health:.3f}\")\n",
"health.head().round(1)"
]
},
{
"cell_type": "markdown",
"id": "dfb09a1c",
"metadata": {},
"source": [
"### A Beta prior and posterior\n",
"\n",
"The parameter $p$ is a probability, so its prior must only allow values between 0 and 1. The **Beta distribution** $\\mathrm{Beta}(a,b)$\n",
"is a distribution on $[0,1]$ with density proportional to $p^{a-1}(1-p)^{b-1}$ and mean $a/(a+b)$. $\\mathrm{Beta}(1,1)$ is flat: every value of $p$ is equally plausible.\n",
"\n",
"For $k$ positive outcomes among $n$ independent observations, the likelihood is proportional to $p^k(1-p)^{n-k}$.\n",
"Multiplying it by the Beta prior adds the exponents:\n",
"\n",
"$$p(p\\mid\\mathbf y)\\propto p^{a+k-1}(1-p)^{b+n-k-1},\\qquad\\text{so}\\qquad\n",
"p\\mid\\mathbf y\\sim\\mathrm{Beta}(a+k,b+n-k).$$\n",
"\n",
"The posterior is again a Beta distribution, so the Beta prior is conjugate here. The update adds the $k$ observed positive outcomes to $a$ and the $n-k$\n",
"observed negative outcomes to $b$. For this reason you can read $a$ and $b$ as counts of positive and negative outcomes from an earlier sample of size $a+b$.\n",
"\n",
"The posterior mean is again a weighted average, this time of the prior mean and the observed proportion:\n",
"\n",
"$$\\mathbb E[p\\mid\\mathbf y]=\\frac{a+b}{a+b+n}\\cdot\\frac{a}{a+b}+\\frac{n}{a+b+n}\\cdot\\frac{k}{n}.$$\n",
"\n",
"The prior mean gets weight $a+b$ and the observed proportion gets weight $n$. To specify a prior by its mean $m$ and weight $w$, set $a=mw$ and $b=(1-m)w$.\n",
"\n",
"We compare two priors: the flat $\\mathrm{Beta}(1,1)$, with weight 2, and $\\mathrm{Beta}(20,20)$, with mean 0.5 and weight 40, which is more than our $n=24$."
]
},
{
"cell_type": "markdown",
"id": "260c2807-8284-473f-93be-bf7802ab23a7",
"metadata": {
"nbinlineai": {
"isPromptCell": true
}
},
"source": [
"Do a similar treatment here like we did for the Gaussian for both the mean and the variance, understanding how it goes in terms of the prior mean and the data mean and the prior variance and the datavariance. "
]
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"Here we use the **Beta–Bernoulli model**. Unlike the Gaussian case, its weights are not generally inverse-variance weights.\n",
"\n",
"### 1. Bayes’ rule\n",
"For $k$ positive outcomes in $n$ observations,\n",
"$$L(p)\\propto p^k(1-p)^{n-k},\\qquad \\pi(p)\\propto p^{a-1}(1-p)^{b-1}.$$\n",
"Multiplying gives\n",
"$$\\boxed{p\\mid\\mathbf y\\sim\\operatorname{Beta}(a+k,b+n-k).}$$\n",
"\n",
"### 2. Posterior mean: prior mean versus data mean\n",
"Define the prior strength $w$, prior mean $m_p$, and data mean $m_d$:\n",
"$$w=a+b,\\qquad m_p=\\frac{a}{a+b},\\qquad m_d=\\frac{k}{n}.$$\n",
"Then\n",
"$$\\boxed{m_{\\mathrm{post}}=\\frac{w}{w+n}m_p+\\frac{n}{w+n}m_d.}$$\n",
"**Intuition:** the prior contributes an effective weight of $w$ observations; the data contribute $n$. These are pseudocounts, not necessarily a literal earlier sample.\n",
"\n",
"### 3. Prior and posterior variances\n",
"The Beta prior variance is\n",
"$$V_p=\\frac{ab}{(a+b)^2(a+b+1)}=\\frac{m_p(1-m_p)}{w+1}.$$\n",
"Thus, specifying the prior mean and variance determines its strength:\n",
"$$\\boxed{w=\\frac{m_p(1-m_p)}{V_p}-1.}$$\n",
"For a proper Beta prior, $0<m_p<1$ and $0<V_p<m_p(1-m_p)$.\n",
"\n",
"The posterior has strength $w+n$, so\n",
"$$\\boxed{V_{\\mathrm{post}}=\\frac{m_{\\mathrm{post}}(1-m_{\\mathrm{post}})}{w+n+1}.}$$\n",
"Together, these formulas express the posterior mean and variance entirely through $m_p,V_p,m_d,n$.\n",
"\n",
"Unlike the Gaussian case, **posterior variance depends on the observed outcomes**, through $m_{\\mathrm{post}}$. More data increase concentration, but a particular update can increase variance if it moves a very extreme prior mean toward $0.5$.\n",
"\n",
"### 4. What is the “data variance”?\n",
"Distinguish individual observations from their mean:\n",
"$$\\operatorname{Var}(y_i\\mid p)=p(1-p),\\qquad\n",
"V_d(p)=\\operatorname{Var}(m_d\\mid p)=\\frac{p(1-p)}{n}.$$\n",
"Unlike the known Gaussian noise variance, this depends on the **unknown parameter**. A plug-in estimate is\n",
"$$\\widehat V_d=\\frac{m_d(1-m_d)}{n}.$$\n",
"It can be misleading near 0 or 1: all-zero observations do not imply zero uncertainty about $p$.\n",
"\n",
"An exact, useful variance decomposition is\n",
"$$\\boxed{V_{\\mathrm{post}}=\n",
"\\frac{w\\,m_p(1-m_p)+n\\,m_d(1-m_d)+\\frac{wn}{w+n}(m_p-m_d)^2}\n",
"{(w+n)(w+n+1)}.}$$\n",
"Here $m_p(1-m_p)=(w+1)V_p$ and $m_d(1-m_d)=n\\widehat V_d$. The extra squared-difference term shows how **prior–data disagreement** enters posterior uncertainty.\n",
"\n",
"### 5. Comparison with Gaussian precision weighting\n",
"For the Gaussian model, exactly:\n",
"$$m_{\\mathrm{post}}=\\frac{m_p/V_p+m_d/V_d}{1/V_p+1/V_d},\\qquad\n",
"V_{\\mathrm{post}}=\\frac{1}{1/V_p+1/V_d}.$$\n",
"These are **not exact Beta-update formulas**. They become useful approximations when both prior and likelihood are approximately Gaussian, concentrated away from the boundaries.\n",
"\n",
"**Bottom line:** Gaussian updates add precisions; Beta updates add positive and negative pseudocounts. Both yield a weighted posterior mean, but their variance updates differ."
]
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p_grid = np.linspace(0.001, 0.999, 1000)\n",
"health_priors = {\"Flat: Beta(1, 1)\": (1, 1), \"Stronger: Beta(20, 20)\": (20, 20)}\n",
"fig, ax = plt.subplots()\n",
"for label, (a, b) in health_priors.items():\n",
" ax.plot(p_grid, stats.beta.pdf(p_grid, a, b), label=label)\n",
"ax.set(xlabel=\"Shared disease probability p\", ylabel=\"Prior density\")\n",
"ax.legend(); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "9b004fc1",
"metadata": {},
"source": [
"<div style=\"background:#E9F8EE; border-left:6px solid #16A34A; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🏋️ Exercise 3: update a shared probability (3 min)</div>\n",
"<div>\n",
"For each prior, fill in the two posterior shape parameters, <code>a_post</code> and <code>b_post</code>. The rest of the code reports the posterior mean and the central 95% credible interval.\n",
"It uses <code>stats.beta.ppf</code>, which computes quantiles of the Beta distribution. A Beta posterior need not be symmetric, so we do not use mean ± 1.96 SD.\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "f3271c8c",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior</th>\n",
" <th>posterior mean</th>\n",
" <th>95% lower</th>\n",
" <th>95% upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Flat: Beta(1, 1)</td>\n",
" <td>0.385</td>\n",
" <td>0.211</td>\n",
" <td>0.575</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Stronger: Beta(20, 20)</td>\n",
" <td>0.453</td>\n",
" <td>0.334</td>\n",
" <td>0.575</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prior posterior mean 95% lower 95% upper\n",
"0 Flat: Beta(1, 1) 0.385 0.211 0.575\n",
"1 Stronger: Beta(20, 20) 0.453 0.334 0.575"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"beta_rows = []\n",
"health_posteriors = {}\n",
"for label, (a, b) in health_priors.items():\n",
" # BEGIN SOLUTION\n",
" a_post = a + k_health\n",
" b_post = b + n_health - k_health\n",
" # END SOLUTION\n",
" # BEGIN STUDENT\n",
" # a_post = ... # your code here\n",
" # b_post = ... # your code here\n",
" # END STUDENT\n",
" health_posteriors[label] = (a_post, b_post)\n",
" lo, hi = stats.beta.ppf([0.025, 0.975], a_post, b_post)\n",
" beta_rows.append([label, a_post/(a_post+b_post), lo, hi])\n",
"pd.DataFrame(beta_rows, columns=[\"prior\", \"posterior mean\", \"95% lower\", \"95% upper\"]).round(3)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "d779d77e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"for label, (a_post, b_post) in health_posteriors.items():\n",
" ax.plot(p_grid, stats.beta.pdf(p_grid, a_post, b_post), label=label)\n",
"ax.axvline(k_health/n_health, color=\"black\", linestyle=\"--\", label=\"Observed proportion\")\n",
"ax.set(xlabel=\"Shared disease probability p\", ylabel=\"Posterior density\")\n",
"ax.legend(); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e2769537",
"metadata": {},
"source": [
"Under the flat prior the posterior mean, 0.385, is close to the observed proportion of 0.375, because the prior's weight of 2 is small next to n = 24.\n",
"Under Beta(20, 20) the prior's weight of 40 is larger than n = 24, so the posterior mean, 0.453, is closer to the prior mean of 0.5 than to the data."
]
},
{
"cell_type": "markdown",
"id": "4705a152",
"metadata": {},
"source": [
"<div style=\"background:#FDECEC; border-left:6px solid #DC2626; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">💬 Discuss — Checkpoint 3: adding predictors</div>\n",
"<div>\n",
"<ol><li>What do we assume when we give everyone the same disease probability?</li><li>Which recorded variable could explain why some people have a higher probability than others?</li><li>Could a Beta prior on one shared probability describe those differences?</li></ol>\n",
"</div>\n",
"\n",
"<details>\n",
"<summary><strong>Worked answer</strong></summary>\n",
"<div style=\"margin-top:10px; padding-top:8px; border-top:1px dashed #999;\">\n",
"<p>The model assumes that every person has the same probability, whatever their age. Age is recorded, and in our simulation the probability rises with age. A prior on one shared probability still produces only one probability, so it cannot describe a relationship with age. We need to change the model for the probability itself, just as Part 2 replaced one mean height with a regression line.</p>\n",
"</div>\n",
"</details>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "b75aaf70",
"metadata": {},
"source": [
"<div style=\"background:#F3F4F6; border-left:6px solid #4B5563; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🧠 Takeaways — the three closed-form updates (Parts 1–3a)</div>\n",
"<div>\n",
"<ol>\n",
"<li><strong>The posterior is proportional to the likelihood times the prior.</strong> The likelihood comes from our model for the observations and the prior is our choice, so every posterior statement holds only under both of those assumptions.</li>\n",
"<li><strong>In all three conjugate models, the posterior mean is a weighted average of an estimate from the data and the prior mean.</strong> The estimate is ȳ, β̂<sub>1</sub> or k/n. Its weight grows with the amount of data (n, S<sub>xx</sub>, or n), and the prior's weight grows as the prior gets narrower (smaller σ<sub>p</sub> or σ<sub>β1</sub>, larger a + b).</li>\n",
"<li><strong>A credible interval and a confidence interval can have the same endpoints and still answer different questions.</strong> A credible interval gives a probability for the parameter, given the data and the prior. A confidence interval describes how often the procedure would cover the true value over repeated samples.</li>\n",
"</ol>\n",
"<p><strong>Final check:</strong> In the height model, which of σ, σ<sub>p</sub> and n describes how individual heights vary, our prior uncertainty about the mean, and the amount of data? In the Beta model, which expression plays the role of the prior's weight?</p>\n",
"</div>\n",
"\n",
"<details>\n",
"<summary><strong>Worked answer</strong></summary>\n",
"<div style=\"margin-top:10px; padding-top:8px; border-top:1px dashed #999;\">\n",
"<p>σ is the standard deviation of individual heights; σ<sub>p</sub> is our prior uncertainty about their mean; n is the number of observations. In the Beta model the prior's weight in the posterior mean is a + b, which is compared with the sample size n.</p>\n",
"</div>\n",
"</details>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "04a076c8",
"metadata": {},
"source": [
"### 3b. Logistic regression: a probability that depends on age\n",
"\n",
"Now we use age. Each person gets their own probability $p_i$, which depends on their standardized age $x_i$ through the logistic function from Section 7:\n",
"\n",
"$$\\eta_i=\\beta_0+\\beta_1x_i,\\qquad p_i=\\frac{1}{1+e^{-\\eta_i}},\\qquad\n",
" y_i\\mid x_i,\\boldsymbol\\beta\\sim\\mathrm{Bernoulli}(p_i).$$\n",
"\n",
"The outcome is still Bernoulli. What changed is the probability: one shared $p$ has become a $p_i$ for each person.\n",
"\n",
"The unknowns are now the coefficients $\\beta_0$ and $\\beta_1$, which can be any real numbers, so a Beta prior no longer applies. We give **both** coefficients\n",
"independent normal priors, $\\beta_j\\sim N(0,2^2)$. Unlike Part 2, the intercept gets a proper prior too, which guarantees the posterior is a valid distribution even in a small sample.\n",
"Because age is standardized, a prior SD of 2 says that, before seeing data, a one-SD (10-year) increase in age is very unlikely to change the log-odds by more than about 4.\n",
"\n",
"The likelihood is $\\prod_i p_i^{y_i}(1-p_i)^{1-y_i}$, and we multiply it by the prior once:\n",
"\n",
"$$p(\\boldsymbol\\beta\\mid\\mathbf x,\\mathbf y)\\propto\n",
"\\left[\\prod_i p_i^{y_i}(1-p_i)^{1-y_i}\\right]\n",
"\\exp\\left[-\\frac{\\beta_0^2}{2\\sigma_{\\beta_0}^2}-\\frac{\\beta_1^2}{2\\sigma_{\\beta_1}^2}\\right].$$\n",
"\n",
"Taking logs gives\n",
"\n",
"$$\\log p(\\boldsymbol\\beta\\mid\\mathbf x,\\mathbf y)=\n",
"\\underbrace{\\sum_i\\left[y_i\\eta_i-\\log(1+e^{\\eta_i})\\right]}_{\\text{log-likelihood}}\n",
"\\;\\underbrace{-\\frac{\\beta_0^2}{2\\sigma_{\\beta_0}^2}-\\frac{\\beta_1^2}{2\\sigma_{\\beta_1}^2}}_{\\text{log prior}}+C.$$\n",
"\n",
"The log-likelihood part is the negative of Section 7's binary cross-entropy. The likelihood is a function of the parameters; its maximum is the maximum-likelihood estimate,\n",
"which is what `LogisticRegression(penalty=None)` finds. A single maximum is not enough here, though: we want the posterior mean and a credible interval.\n",
"\n",
"The code below evaluates the log posterior at any pair of coefficients. `np.logaddexp(0, eta)` computes $\\log(1+e^{\\eta})$ without overflowing when $\\eta$ is large.\n",
"We do not know the constant $C$, but it cancels when we subtract two log-posterior values, so we can still compare two points."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "a3cea28c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Log posterior + C at (0, 0): -16.636\n",
"Log posterior + C at (-0.5, 1): -15.095\n",
"Posterior density at (-0.5, 1) is 4.7 times the density at (0, 0)\n"
]
}
],
"source": [
"x_health = (age - age.mean()) / age.std(ddof=0) # standardized age\n",
"sigma_beta_health = np.array([2.0, 2.0]) # prior SDs for the intercept and the slope\n",
"\n",
"def logistic_log_posterior(beta):\n",
" eta = beta[0] + beta[1] * x_health\n",
" log_likelihood = np.sum(y_health * eta - np.logaddexp(0, eta))\n",
" log_prior = -0.5 * np.sum((np.asarray(beta) / sigma_beta_health)**2)\n",
" return log_likelihood + log_prior # up to the unknown constant C\n",
"\n",
"lp_a, lp_b = logistic_log_posterior([0, 0]), logistic_log_posterior([-0.5, 1])\n",
"print(f\"Log posterior + C at (0, 0): {lp_a:.3f}\")\n",
"print(f\"Log posterior + C at (-0.5, 1): {lp_b:.3f}\")\n",
"print(f\"Posterior density at (-0.5, 1) is {np.exp(lp_b - lp_a):.1f} times the density at (0, 0)\")"
]
},
{
"cell_type": "markdown",
"id": "775e8b20",
"metadata": {},
"source": [
"### Computing the logistic posterior\n",
"\n",
"In Parts 1 and 2 the log posterior was a quadratic function of the parameter, and an exponent that is quadratic in the parameter is a normal distribution.\n",
"Here the term $\\log(1+e^{\\eta_i})$ is not quadratic in the coefficients, so the posterior is not a normal distribution: the normal prior is **not conjugate** here.\n",
"We can evaluate the posterior at any pair $(\\beta_0,\\beta_1)$, as above, but there is no formula for its mean or its credible intervals.\n",
"\n",
"**We can evaluate this posterior up to a constant. How do we obtain its mean, credible intervals, and predictions?**\n",
"With two coefficients we could evaluate it on a grid, as in Part 1. But the grid grows quickly: 100 values for each of 10 coefficients is $100^{10}$ grid points.\n",
"Section 9 introduces Markov chain Monte Carlo (MCMC), which draws samples from the posterior instead of evaluating it everywhere."
]
},
{
"cell_type": "markdown",
"id": "b0bfc612",
"metadata": {},
"source": [
"---\n",
"\n",
"## Appendix — optional explorations\n",
"\n",
"The main section ends with the question above. These examples are for later and are not part of the 60-minute session.\n",
"\n",
"- **A1:** multiple predictors and a multivariate normal posterior.\n",
"- **A2:** a zero-mean normal prior on the slope and ridge regression.\n",
"- **A3:** uncertainty in a mean response and in a new observation.\n",
"- **A4:** deriving the updates, and allowing the observation noise to be unknown."
]
},
{
"cell_type": "markdown",
"id": "f428267b",
"metadata": {},
"source": [
"<div style=\"background:#F1F5F9; border-left:6px solid #64748B; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🔍 Explore — A1. Multiple linear regression</div>\n",
"<div>\n",
"With multiple predictors, a multivariate normal prior yields a multivariate normal posterior when observation variance is known. Run the provided example and interpret the joint contour: what does its orientation tell you about coefficient uncertainty?\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "5e6def73",
"metadata": {},
"source": [
"### A multivariate normal update\n",
"\n",
"For design matrix $X$, write $\\mathbf y\\mid\\boldsymbol\\beta\\sim N(X\\boldsymbol\\beta,\\sigma^2I)$ and $\\boldsymbol\\beta\\sim N(\\mathbf m_0,V_0)$. Then\n",
"\n",
"$$V_{\\mathrm{post}}=\\left(\\frac{X^{\\mathsf T}X}{\\sigma^2}+V_0^{-1}\\right)^{-1},\\qquad\n",
"\\mathbf m_{\\mathrm{post}}=V_{\\mathrm{post}}\\left(\\frac{X^{\\mathsf T}\\mathbf y}{\\sigma^2}+V_0^{-1}\\mathbf m_0\\right).$$\n",
"\n",
"Here the intercept also has a proper normal prior, unlike the flat intercept in Part 2. We use two correlated parent-height predictors, centered in centimetres; the slope priors are defined on this same scale. Nonzero off-diagonal posterior covariances describe how coefficient uncertainties are related. The code uses linear solves rather than directly inverting a matrix."
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "1e7bd095",
"metadata": {},
"outputs": [
{
"data": {
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>posterior mean</th>\n",
" <th>posterior SD</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Intercept at mean parent heights</th>\n",
" <td>175.666</td>\n",
" <td>0.780</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Parent 1 slope</th>\n",
" <td>0.576</td>\n",
" <td>0.138</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Parent 2 slope</th>\n",
" <td>0.219</td>\n",
" <td>0.127</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
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"text/plain": [
" posterior mean posterior SD\n",
"Intercept at mean parent heights 175.666 0.780\n",
"Parent 1 slope 0.576 0.138\n",
"Parent 2 slope 0.219 0.127"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rng_multi = np.random.default_rng(113)\n",
"parents = rng_multi.multivariate_normal([170, 170], [[64, 48], [48, 64]], size=80)\n",
"parents_c = parents - parents.mean(axis=0)\n",
"X_multi = np.column_stack([np.ones(len(parents)), parents_c])\n",
"y_multi = 175 + parents_c @ np.array([0.4, 0.3]) + rng_multi.normal(0, sigma_reg, len(parents))\n",
"m0, V0 = np.array([175, 0, 0]), np.diag([10**2, 0.5**2, 0.5**2])\n",
"V0_inverse = np.linalg.solve(V0, np.eye(3))\n",
"posterior_system = X_multi.T @ X_multi / sigma_reg**2 + V0_inverse\n",
"V_multi = np.linalg.solve(posterior_system, np.eye(3))\n",
"m_multi = np.linalg.solve(posterior_system, X_multi.T @ y_multi / sigma_reg**2 + V0_inverse @ m0)\n",
"pd.DataFrame({\"posterior mean\": m_multi, \"posterior SD\": np.sqrt(np.diag(V_multi))},\n",
" index=[\"Intercept at mean parent heights\", \"Parent 1 slope\", \"Parent 2 slope\"]).round(3)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "a2f2185b",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Posterior slope correlation: -0.74\n"
]
}
],
"source": [
"b1 = np.linspace(m_multi[1]-3*np.sqrt(V_multi[1, 1]), m_multi[1]+3*np.sqrt(V_multi[1, 1]), 150)\n",
"b2 = np.linspace(m_multi[2]-3*np.sqrt(V_multi[2, 2]), m_multi[2]+3*np.sqrt(V_multi[2, 2]), 150)\n",
"B1, B2 = np.meshgrid(b1, b2)\n",
"joint = stats.multivariate_normal(m_multi[1:], V_multi[1:, 1:])\n",
"fig, ax = plt.subplots()\n",
"ax.contour(B1, B2, joint.pdf(np.dstack([B1, B2])), levels=7)\n",
"ax.plot(m_multi[1], m_multi[2], \"o\", label=\"Posterior mean\")\n",
"ax.set(xlabel=\"Parent 1 slope\", ylabel=\"Parent 2 slope\", title=\"Joint coefficient posterior\")\n",
"ax.legend(); plt.show()\n",
"print(\"Posterior slope correlation:\", round(V_multi[1, 2]/np.sqrt(V_multi[1, 1]*V_multi[2, 2]), 3))"
]
},
{
"cell_type": "markdown",
"id": "3b906a6c",
"metadata": {},
"source": [
"<div style=\"background:#F1F5F9; border-left:6px solid #64748B; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🔍 Explore — A2. A normal prior and ridge regression</div>\n",
"<div>\n",
"Compare the posterior mean with ridge at the matching penalty on the same predictor scale. The prior is centered at zero and the intercept is unpenalized. Change the prior SD and compare the results.\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "bb3ca40b",
"metadata": {},
"source": [
"### Posterior mode and the ridge objective\n",
"\n",
"For a zero-mean normal slope prior, the log posterior is $-\\mathrm{RSS}/(2\\sigma^2)-\\beta_1^2/(2\\sigma_{\\beta_1}^2)+C$. Its maximizer minimizes $\\mathrm{RSS}+\\alpha\\beta_1^2$ with $\\alpha=\\sigma^2/\\sigma_{\\beta_1}^2$. This is scikit-learn's ridge objective. A normal posterior has the same mean and mode, so its slope mean matches the ridge coefficient.\n",
"\n",
"Use the same predictor scale for the prior and ridge fit. A nonzero prior mean gives a penalty on deviations from that mean rather than from zero."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "b44066cd",
"metadata": {},
"outputs": [
{
"data": {
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" 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>prior SD</th>\n",
" <th>alpha</th>\n",
" <th>posterior mean</th>\n",
" <th>ridge slope</th>\n",
" <th>posterior SD</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.50</td>\n",
" <td>196.00000</td>\n",
" <td>0.62401</td>\n",
" <td>0.62401</td>\n",
" <td>0.09740</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.12</td>\n",
" <td>3402.77778</td>\n",
" <td>0.38500</td>\n",
" <td>0.38500</td>\n",
" <td>0.07650</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.05</td>\n",
" <td>19600.00000</td>\n",
" <td>0.13119</td>\n",
" <td>0.13119</td>\n",
" <td>0.04466</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prior SD alpha posterior mean ridge slope posterior SD\n",
"0 0.50 196.00000 0.62401 0.62401 0.09740\n",
"1 0.12 3402.77778 0.38500 0.38500 0.07650\n",
"2 0.05 19600.00000 0.13119 0.13119 0.04466"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ridge_rows = []\n",
"for prior_sd in [0.5, 0.12, 0.05]:\n",
" m, s = slope_posterior(beta_hat, sxx, sigma_reg, 0, prior_sd)\n",
" alpha = sigma_reg**2 / prior_sd**2\n",
" ridge = Ridge(alpha=alpha).fit(x_c[:, None], y_c)\n",
" ridge_rows.append([prior_sd, alpha, m, ridge.coef_[0], s])\n",
"pd.DataFrame(ridge_rows, columns=[\"prior SD\", \"alpha\", \"posterior mean\", \"ridge slope\", \"posterior SD\"]).round(5)"
]
},
{
"cell_type": "markdown",
"id": "15f63318",
"metadata": {},
"source": [
"<div style=\"background:#F1F5F9; border-left:6px solid #64748B; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🔍 Explore — A3. A mean response and a new observation</div>\n",
"<div>\n",
"At a given predictor value, distinguish uncertainty about the conditional mean from variation in a new measured response. Why are the new-observation intervals wider?\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "61043d58",
"metadata": {},
"source": [
"### Retaining intercept uncertainty\n",
"\n",
"Let $a=\\beta_0+\\beta_1\\bar x$ be the intercept at mean predictor height. With the flat intercept prior, $a\\mid\\mathbf y\\sim N(\\bar y,\\sigma^2/n)$ and is independent of the slope posterior: $\\sum_i(x_i-\\bar x)=0$ removes the cross term in the likelihood.\n",
"\n",
"At $x^*$ the posterior mean response is $\\bar y+\\mu_{\\beta_1,\\mathrm{post}}(x^*-\\bar x)$, with variance\n",
"\n",
"$$v_{\\mathrm{mean}}(x^*)=\\frac{\\sigma^2}{n}+(x^*-\\bar x)^2\\sigma_{\\beta_1,\\mathrm{post}}^2.$$\n",
"\n",
"A new observation adds independent noise, so $v_{\\mathrm{new}}(x^*)=v_{\\mathrm{mean}}(x^*)+\\sigma^2$. Constant observation variance does not imply constant prediction uncertainty: slope uncertainty increases the bands away from the mean predictor."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "bc12bae7",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"prediction_mean = y_bar + slope_mean * (x_line - x_bar)\n",
"mean_sd = np.sqrt(sigma_reg**2/len(x) + (x_line-x_bar)**2 * slope_sd**2)\n",
"new_sd = np.sqrt(mean_sd**2 + sigma_reg**2)\n",
"fig, ax = plt.subplots()\n",
"ax.fill_between(x_line, prediction_mean-1.96*new_sd, prediction_mean+1.96*new_sd,\n",
" alpha=0.18, label=\"95% posterior predictive interval\")\n",
"ax.fill_between(x_line, prediction_mean-1.96*mean_sd, prediction_mean+1.96*mean_sd,\n",
" alpha=0.45, label=\"95% credible interval for mean response\")\n",
"ax.plot(x_line, prediction_mean, color=\"black\", label=\"Posterior mean response\")\n",
"ax.scatter(x, reg_y, s=15, alpha=0.4)\n",
"ax.set(xlabel=\"Parent height (cm)\", ylabel=\"Adult-child height (cm)\")\n",
"ax.legend(fontsize=9); plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c278c0ac",
"metadata": {},
"source": [
"<div style=\"background:#F1F5F9; border-left:6px solid #64748B; padding:14px 18px; margin:16px 0; border-radius:6px; color:#1F2937;\">\n",
"<div style=\"font-size:1.15em; font-weight:700; margin-bottom:6px;\">🔍 Explore — A4. Derivations and unknown noise</div>\n",
"<div>\n",
"The main section fixes the observation variance at its known simulation value. Review the algebra below, then compare a plug-in normal interval with an interval that accounts for unknown observation variance in a small sample.\n",
"</div>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "5068a1b9",
"metadata": {},
"source": [
"### Completing the square\n",
"\n",
"For the mean, $\\sum_i(y_i-\\mu)^2=\\sum_i(y_i-\\bar y)^2+n(\\mu-\\bar y)^2$. The first term does not depend on $\\mu$. In the log posterior, the coefficient of $\\mu^2$ is $-\\tfrac12(n/\\sigma^2+1/\\sigma_p^2)$ and the coefficient of $\\mu$ is $n\\bar y/\\sigma^2+\\mu_p/\\sigma_p^2$. Completing the square gives the Part 1 formulas.\n",
"\n",
"For the slope, use $a=\\beta_0+\\beta_1\\bar x$, the height of the regression line at the mean parent height. The residual sum of squares separates as\n",
"\n",
"$$\\mathrm{RSS}(a,\\beta_1)=n(a-\\bar y)^2+\\mathrm{RSS}_{\\mathrm{OLS}}+S_{xx}(\\beta_1-\\hat\\beta_1)^2.$$\n",
"\n",
"Integrating over the intercept with its flat prior contributes a factor that does not depend on $\\beta_1$. What is left is the Part 1 calculation with $S_{xx}$ in place of $n$ and $\\hat\\beta_1$ in place of $\\bar y$.\n",
"\n",
"### Unknown observation variance\n",
"\n",
"With real data, $\\sigma$ is usually unknown. Replacing it with the residual SD in the known-$\\sigma$ formulas is a **plug-in approximation**: it ignores our uncertainty about $\\sigma$, so the intervals come out too narrow.\n",
"\n",
"For the comparison below, we use flat priors on the coefficients and the prior $p(\\sigma)\\propto1/\\sigma$ on the noise SD. Integrating over the intercept and $\\sigma$ then gives a Student t posterior for the slope with $n-2$ degrees of freedom, centred at the OLS slope, with scale $s/\\sqrt{S_{xx}}$, where $s^2=\\mathrm{RSS}_{\\mathrm{OLS}}/(n-2)$. Its central interval equals the classical t interval. These are different priors from the informative slope prior in Part 2. With only 8 observations, the t interval is noticeably wider."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "8b539cc3",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>95% lower</th>\n",
" <th>95% upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Plug-in normal interval</th>\n",
" <td>-0.393</td>\n",
" <td>1.254</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Unknown-sigma t interval</th>\n",
" <td>-0.597</td>\n",
" <td>1.459</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" 95% lower 95% upper\n",
"Plug-in normal interval -0.393 1.254\n",
"Unknown-sigma t interval -0.597 1.459"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n_small = 8\n",
"xs, ys = x[:n_small], reg_y[:n_small]\n",
"xsc, ysc = xs-xs.mean(), ys-ys.mean()\n",
"sxx_small = np.dot(xsc, xsc)\n",
"slope_small = np.dot(xsc, ysc) / sxx_small\n",
"residuals_small = ysc - slope_small * xsc\n",
"residual_sd = np.sqrt(np.dot(residuals_small, residuals_small)/(n_small-2))\n",
"scale_small = residual_sd / np.sqrt(sxx_small)\n",
"normal_limits = stats.norm.interval(0.95, loc=slope_small, scale=scale_small)\n",
"t_limits = stats.t.interval(0.95, df=n_small-2, loc=slope_small, scale=scale_small)\n",
"pd.DataFrame([normal_limits, t_limits], index=[\"Plug-in normal interval\", \"Unknown-sigma t interval\"],\n",
" columns=[\"95% lower\", \"95% upper\"]).round(3)"
]
}
],
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