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+# PR: Add notebook — Unit-level counterfactuals with abduction, action, and prediction
+
+Closes #851
+
+## Issue Summary
+
+The PyMC examples gallery had no notebook demonstrating unit-level counterfactuals (rung 3 of Pearl's causal ladder). Users may assume `pm.do` is sufficient for individual-level "what if?" questions, when it actually answers a population-level question (rung 2).
+
+## Root Cause
+
+No existing example demonstrated the three-step counterfactual procedure (abduction, action, prediction) or explained the conceptual difference between interventional and counterfactual queries.
+
+## Solution
+
+New notebook `unit_level_counterfactuals.ipynb` implementing the encouragement design from Pearl, Glymour, and Jewell (2016), *Causal Inference in Statistics: A Primer*, §4.2.3–4.2.4.
+
+The notebook:
+- Opens with Joe's concrete question (examples-first pedagogy)
+- Simulates data from a known SCM, fits it with PyMC, and verifies coefficient recovery
+- Computes the population intervention E[Y|do(H=2)] ≈ 0.8 and shows it gives the wrong answer for Joe
+- Explains the conceptual shift from "residuals as noise" to "U as individual property"
+- Implements all three steps (abduction, action, prediction) per posterior draw
+- Shows both comparison figure (intervention vs counterfactual) and counterfactual posterior
+- Includes summary table mapping intervention vs counterfactual to Pearl's causal ladder
+- Ends with bolded-key-term summary and domain-transfer reflection prompt
+
+## Changes Made
+
+- `examples/causal_inference/unit_level_counterfactuals.ipynb`: New notebook (41 cells)
+- `examples/causal_inference/unit_level_counterfactuals.myst.md`: Auto-generated MyST companion
+
+## Testing
+
+- [x] Valid JSON notebook structure verified
+- [x] All 41 cells present with correct types
+- [x] MyST companion file generated via jupytext
+- [x] Cross-reference to existing `interventional_distribution` notebook included
+- [x] Citation key `pearl2016causal` exists in `examples/references.bib`
+
+## Notes
+
+- Notebook is not yet executed (no outputs). Execution requires a PyMC environment with graphviz.
+- Figures follow figure-excellence conventions: `FIG_WIDTH`/`FIG_HEIGHT` constants, semantic colors (`COLOR_POPULATION`, `COLOR_JOE`), technical captions.
+- Narrative follows educational-narrative skill: examples-first, progressive complexity, callouts for pedagogical functions, summary with bolded key terms, reflection prompt.
diff --git a/examples/causal_inference/unit_level_counterfactuals.ipynb b/examples/causal_inference/unit_level_counterfactuals.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "cell-01",
+ "metadata": {},
+ "source": [
+ "(unit_level_counterfactuals)=\n",
+ "# Unit-level counterfactuals: abduction, action, and prediction\n",
+ "\n",
+ ":::{post} March, 2026\n",
+ ":tags: causal inference, counterfactuals, structural causal models, Pearl\n",
+ ":category: intermediate, explanation\n",
+ ":author: Benjamin T. Vincent\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-02",
+ "metadata": {},
+ "source": [
+ "Joe participated in an after-school encouragement program. He spent moderate time in the program ($X = 0.5$), did 1 hour of homework ($H = 1.0$), and scored 1.5 on his exam ($Y = 1.5$). His teacher asks: **\"What would Joe's exam score have been if he had doubled his homework to $H = 2$?\"**\n",
+ "\n",
+ "This is not a question about what happens on average when we assign everyone to do 2 hours of homework. It is about one specific student whose abilities, motivation, and circumstances have already been observed.\n",
+ "\n",
+ "The standard causal tool for \"what if?\" questions is the do-operator: $E[Y \\mid \\operatorname{do}(H\\!=\\!2)]$. But the do-operator answers a population-level question — rung 2 of Pearl's causal ladder — not an individual one. For Joe, it predicts a score of approximately $0.8$, which is *below* his actual score of $1.5$. The population intervention treats Joe as if he were average, discarding the individual characteristics that made him score above average.\n",
+ "\n",
+ "A **unit-level counterfactual** (rung 3) conditions on Joe's observed data before intervening. It infers that Joe has above-average inherent ability, and predicts a counterfactual score of approximately $1.9$. The gap — $0.8$ versus $1.9$ — is the difference between \"what happens in general?\" and \"what would have happened to *this person*?\"\n",
+ "\n",
+ "This notebook implements Pearl's three-step counterfactual procedure (**abduction, action, prediction**) using a structural causal model fit with PyMC. The worked example follows {cite:t}`pearl2016causal`, §4.2."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-03",
+ "metadata": {},
+ "source": [
+ ":::{note} Pearl's causal ladder\n",
+ "- **Rung 1 — Association**: \"What do we observe?\" $P(Y \\mid X)$\n",
+ "- **Rung 2 — Intervention**: \"What happens if we set $H = 2$ for everyone?\" $P(Y \\mid \\operatorname{do}(H\\!=\\!2))$\n",
+ "- **Rung 3 — Counterfactual**: \"What *would have happened* to Joe if he had done $H\\!=\\!2$, given what we already observed?\" $Y_{H=2} \\mid X\\!=\\!0.5, H\\!=\\!1, Y\\!=\\!1.5$\n",
+ "\n",
+ "The existing {ref}`interventional_distribution` notebook demonstrates rung 2 using `pm.do`. This notebook tackles rung 3.\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-04",
+ "metadata": {},
+ "source": [
+ "## Set up the notebook\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "cell-05",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import arviz as az\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import pymc as pm\n",
+ "\n",
+ "from graphviz import Digraph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "cell-06",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "RANDOM_SEED = 42\n",
+ "rng = np.random.default_rng(RANDOM_SEED)\n",
+ "\n",
+ "az.style.use(\"arviz-darkgrid\")\n",
+ "%config InlineBackend.figure_format = 'retina'\n",
+ "\n",
+ "FIG_WIDTH = 10\n",
+ "FIG_HEIGHT = 4\n",
+ "\n",
+ "COLOR_POPULATION = \"C0\"\n",
+ "COLOR_JOE = \"C1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-07",
+ "metadata": {},
+ "source": [
+ "## The encouragement design\n",
+ "\n",
+ "The example comes from {cite:t}`pearl2016causal`, §4.2.3. Three variables, all standardized:\n",
+ "\n",
+ "- $X$ — time in an after-school encouragement program (randomized)\n",
+ "- $H$ — hours of homework\n",
+ "- $Y$ — exam score\n",
+ "\n",
+ "Encouragement ($X$) has both a direct effect on the exam score and an indirect effect through homework. The structural equations that generate the data are:\n",
+ "\n",
+ "$$\n",
+ "\\begin{align}\n",
+ "X &= U_X \\\\\n",
+ "H &= aX + U_H \\\\\n",
+ "Y &= bX + cH + U_Y\n",
+ "\\end{align}\n",
+ "$$\n",
+ "\n",
+ "where $a = 0.5$, $b = 0.7$, $c = 0.4$, and $U_X, U_H, U_Y$ are mutually independent standard normals."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "cell-08",
+ "metadata": {
+ "tags": [
+ "hide-input"
+ ]
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dag = Digraph()\n",
+ "dag.attr(rankdir=\"LR\")\n",
+ "dag.node(\"X\", \"X\\n(Encouragement)\")\n",
+ "dag.node(\"H\", \"H\\n(Homework)\")\n",
+ "dag.node(\"Y\", \"Y\\n(Exam score)\")\n",
+ "dag.edge(\"X\", \"H\", label=\" a\")\n",
+ "dag.edge(\"H\", \"Y\", label=\" c\")\n",
+ "dag.edge(\"X\", \"Y\", label=\" b\")\n",
+ "dag"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-09",
+ "metadata": {},
+ "source": [
+ "**Caption:** DAG for the encouragement design. Encouragement ($X$) affects exam score ($Y$) directly (coefficient $b$) and indirectly through homework ($H$, coefficients $a$ and $c$)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-10",
+ "metadata": {},
+ "source": [
+ "## Simulate data and fit the structural model\n",
+ "\n",
+ "We generate $N = 500$ observations from the structural equations, then fit a PyMC model to recover the coefficients."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "cell-11",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Analytical E[Y | do(H=2)] = 0.80\n",
+ "Analytical Y_{H=2} for Joe = 1.90\n"
+ ]
+ }
+ ],
+ "source": [
+ "N = 500\n",
+ "\n",
+ "TRUE_A = 0.5\n",
+ "TRUE_B = 0.7\n",
+ "TRUE_C = 0.4\n",
+ "\n",
+ "U_X = rng.normal(0, 1, N)\n",
+ "U_H = rng.normal(0, 1, N)\n",
+ "U_Y = rng.normal(0, 1, N)\n",
+ "\n",
+ "X_data = U_X\n",
+ "H_data = TRUE_A * X_data + U_H\n",
+ "Y_data = TRUE_B * X_data + TRUE_C * H_data + U_Y\n",
+ "\n",
+ "# Joe's observed values\n",
+ "joe_X = 0.5\n",
+ "joe_H = 1.0\n",
+ "joe_Y = 1.5\n",
+ "\n",
+ "# Analytical reference values\n",
+ "ANALYTICAL_INTERVENTION = 2 * TRUE_C\n",
+ "ANALYTICAL_COUNTERFACTUAL = joe_Y + TRUE_C * (2 - joe_H)\n",
+ "\n",
+ "print(f\"Analytical E[Y | do(H=2)] = {ANALYTICAL_INTERVENTION:.2f}\")\n",
+ "print(f\"Analytical Y_{{H=2}} for Joe = {ANALYTICAL_COUNTERFACTUAL:.2f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-12",
+ "metadata": {},
+ "source": [
+ "The PyMC model mirrors the structural equations. Each equation becomes a likelihood statement, and we place weakly informative priors on the coefficients and noise standard deviations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "cell-13",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Initializing NUTS using jitter+adapt_diag...\n",
+ "Multiprocess sampling (4 chains in 4 jobs)\n",
+ "NUTS: [a, b, c, sigma_X, sigma_H, sigma_Y]\n"
+ ]
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "676f6b091c1b4df49c3a1d0570eaee5b",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "Output()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n"
+ ],
+ "text/plain": []
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 1 seconds.\n"
+ ]
+ }
+ ],
+ "source": [
+ "with pm.Model() as scm:\n",
+ " a = pm.Normal(\"a\", mu=0, sigma=2)\n",
+ " b = pm.Normal(\"b\", mu=0, sigma=2)\n",
+ " c = pm.Normal(\"c\", mu=0, sigma=2)\n",
+ "\n",
+ " sigma_X = pm.HalfNormal(\"sigma_X\", sigma=2)\n",
+ " sigma_H = pm.HalfNormal(\"sigma_H\", sigma=2)\n",
+ " sigma_Y = pm.HalfNormal(\"sigma_Y\", sigma=2)\n",
+ "\n",
+ " X = pm.Normal(\"X\", mu=0, sigma=sigma_X, observed=X_data)\n",
+ " H = pm.Normal(\"H\", mu=a * X, sigma=sigma_H, observed=H_data)\n",
+ " Y = pm.Normal(\"Y\", mu=b * X + c * H, sigma=sigma_Y, observed=Y_data)\n",
+ "\n",
+ " idata = pm.sample(draws=2000, random_seed=RANDOM_SEED)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "cell-14",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
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+ "\n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
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+ "
mean
\n",
+ "
sd
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+ "
hdi_3%
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+ "
hdi_97%
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+ "
true_value
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+ "
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+ " \n",
+ " \n",
+ "
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+ "
a
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+ "
0.491
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0.048
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0.400
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0.579
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0.5
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b
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0.773
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0.052
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0.675
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0.871
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0.7
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c
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0.363
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0.045
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0.281
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0.451
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0.4
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+ "
sigma_X
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+ "
0.961
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0.030
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0.904
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1.016
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1.0
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sigma_H
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1.021
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0.962
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1.082
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sigma_Y
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+ " \n",
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+ "
"
+ ],
+ "text/plain": [
+ " mean sd hdi_3% hdi_97% true_value\n",
+ "a 0.491 0.048 0.400 0.579 0.5\n",
+ "b 0.773 0.052 0.675 0.871 0.7\n",
+ "c 0.363 0.045 0.281 0.451 0.4\n",
+ "sigma_X 0.961 0.030 0.904 1.016 1.0\n",
+ "sigma_H 1.021 0.032 0.962 1.082 1.0\n",
+ "sigma_Y 1.023 0.032 0.960 1.082 1.0"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "summary = az.summary(\n",
+ " idata,\n",
+ " var_names=[\"a\", \"b\", \"c\", \"sigma_X\", \"sigma_H\", \"sigma_Y\"],\n",
+ " kind=\"stats\",\n",
+ ")\n",
+ "summary[\"true_value\"] = [TRUE_A, TRUE_B, TRUE_C, 1.0, 1.0, 1.0]\n",
+ "summary[[\"mean\", \"sd\", \"hdi_3%\", \"hdi_97%\", \"true_value\"]]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-15",
+ "metadata": {},
+ "source": [
+ "The posterior means are close to the true values, and all true values fall within the 94% HDI. The model has recovered the structural relationships."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-16",
+ "metadata": {},
+ "source": [
+ "## The population intervention: $E[Y \\mid \\operatorname{do}(H\\!=\\!2)]$\n",
+ "\n",
+ "The do-operator answers: \"What happens on average if we set everyone's homework to 2?\" Under $\\operatorname{do}(H\\!=\\!2)$, the structural equation for $H$ is replaced with the constant $H = 2$, severing the causal link from $X$ to $H$. The equation for $Y$ becomes:\n",
+ "\n",
+ "$$Y = bX + c \\cdot 2 + U_Y$$\n",
+ "\n",
+ "Taking expectations over the population ($E[X] = 0$, $E[U_Y] = 0$):\n",
+ "\n",
+ "$$E[Y \\mid \\operatorname{do}(H\\!=\\!2)] = 2c$$\n",
+ "\n",
+ "We compute this for each posterior draw to propagate coefficient uncertainty."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "cell-17",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Posterior mean of E[Y | do(H=2)]: 0.727\n",
+ "Analytical value: 0.800\n"
+ ]
+ }
+ ],
+ "source": [
+ "posterior = idata.posterior\n",
+ "c_draws = posterior[\"c\"].values.flatten()\n",
+ "b_draws = posterior[\"b\"].values.flatten()\n",
+ "\n",
+ "intervention_ey = 2 * c_draws\n",
+ "\n",
+ "print(f\"Posterior mean of E[Y | do(H=2)]: {intervention_ey.mean():.3f}\")\n",
+ "print(f\"Analytical value: {ANALYTICAL_INTERVENTION:.3f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-18",
+ "metadata": {},
+ "source": [
+ "For Joe, the population intervention predicts a score of approximately $0.8$ — below his observed $1.5$. The do-operator averages over all possible individual characteristics. It knows nothing about Joe's above-average ability, his specific level of encouragement, or any other factor that made him who he is. It treats him as a generic member of the population.\n",
+ "\n",
+ "To answer Joe's question, we need to preserve his individual characteristics."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-19",
+ "metadata": {},
+ "source": [
+ "## The exogenous terms are not noise\n",
+ "\n",
+ "The key insight that separates counterfactual from interventional reasoning is a reinterpretation of the exogenous terms $U$.\n",
+ "\n",
+ "In standard regression, residuals are exchangeable estimation error — interchangeable across individuals, carrying no individual meaning. In a structural causal model, $U_Y$ encodes everything about a specific person that causally affects $Y$ but is not measured: inherent ability, sleep quality, motivation, prior knowledge. Across the population, these factors look like zero-mean noise. For a specific individual, they are **fixed causal properties**."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-20",
+ "metadata": {},
+ "source": [
+ ":::{important} The dual nature of $U$\n",
+ "Across the population, $U_Y$ behaves like noise: zero mean, uncorrelated with measured variables. For a specific individual, $U_Y$ is a fixed property encoding all unmeasured causal factors that affect the outcome. This reinterpretation — from \"discardable error\" to \"signal about the individual\" — is what enables counterfactual reasoning.\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-21",
+ "metadata": {},
+ "source": [
+ "For Joe, his exogenous value is:\n",
+ "\n",
+ "$$U_Y^{\\text{Joe}} = Y - bX - cH = 1.5 - 0.7 \\cdot 0.5 - 0.4 \\cdot 1.0 = 0.75$$\n",
+ "\n",
+ "Joe has above-average inherent ability. The counterfactual procedure preserves this; the population intervention discards it."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-22",
+ "metadata": {},
+ "source": [
+ "## Pearl's three-step counterfactual procedure\n",
+ "\n",
+ "The population intervention asks what happens when we change the world for everyone. A counterfactual asks what would have happened to a specific individual in a world that *did not occur*, given what we observed in the world that *did*.\n",
+ "\n",
+ "Pearl's three-step procedure turns a fitted structural causal model into a counterfactual engine."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-23",
+ "metadata": {},
+ "source": [
+ "### Step 1: Abduction — infer Joe's exogenous values\n",
+ "\n",
+ "Given Joe's observed data $(X = 0.5, H = 1.0, Y = 1.5)$ and the structural equations, we solve for his individual exogenous values. For each posterior draw, the coefficients differ slightly, so Joe's inferred $U_Y$ varies across draws:\n",
+ "\n",
+ "$$U_Y^{\\text{Joe}} = Y_{\\text{obs}} - b \\cdot X_{\\text{obs}} - c \\cdot H_{\\text{obs}}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "cell-24",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Posterior mean of U_Y (Joe): 0.750\n",
+ "Analytical U_Y (Joe): 0.750\n"
+ ]
+ }
+ ],
+ "source": [
+ "u_y_joe = joe_Y - b_draws * joe_X - c_draws * joe_H\n",
+ "\n",
+ "analytical_u_y = joe_Y - TRUE_B * joe_X - TRUE_C * joe_H\n",
+ "print(f\"Posterior mean of U_Y (Joe): {u_y_joe.mean():.3f}\")\n",
+ "print(f\"Analytical U_Y (Joe): {analytical_u_y:.3f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-25",
+ "metadata": {},
+ "source": [
+ "### Step 2: Action — set the intervention\n",
+ "\n",
+ "Replace the structural equation for homework with the counterfactual value $H = 2$. All other equations and Joe's abducted exogenous values remain unchanged.\n",
+ "\n",
+ "### Step 3: Prediction — compute the counterfactual outcome\n",
+ "\n",
+ "Propagate through the modified model using Joe's individual $U_Y$:\n",
+ "\n",
+ "$$Y_{H=2}^{\\text{Joe}} = b \\cdot X_{\\text{obs}} + c \\cdot 2 + U_Y^{\\text{Joe}}$$\n",
+ "\n",
+ "Substituting the abduction result reveals a clean simplification:\n",
+ "\n",
+ "$$Y_{H=2}^{\\text{Joe}} = Y_{\\text{obs}} + c \\cdot (2 - H_{\\text{obs}})$$\n",
+ "\n",
+ "In a linear SEM, the counterfactual reduces to the observed outcome plus the structural coefficient times the change in the intervened variable. The $b$ terms and the exogenous term cancel exactly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "cell-26",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Posterior mean of Y_{H=2} (Joe): 1.863\n",
+ "Analytical Y_{H=2} (Joe): 1.900\n"
+ ]
+ }
+ ],
+ "source": [
+ "y_cf_joe = joe_Y + c_draws * (2 - joe_H)\n",
+ "\n",
+ "print(f\"Posterior mean of Y_{{H=2}} (Joe): {y_cf_joe.mean():.3f}\")\n",
+ "print(f\"Analytical Y_{{H=2}} (Joe): {ANALYTICAL_COUNTERFACTUAL:.3f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-27",
+ "metadata": {},
+ "source": [
+ ":::{tip} Linear SEM shortcut\n",
+ "In a linear structural equation model, the counterfactual change in $Y$ when intervening on a direct parent $H$ is $c \\cdot (H' - H_{\\text{obs}})$, where $c$ is the structural coefficient. This elegant cancellation does not hold in nonlinear models, where the full three-step procedure is necessary.\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-28",
+ "metadata": {},
+ "source": [
+ "## Intervention versus counterfactual"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "cell-29",
+ "metadata": {
+ "tags": [
+ "hide-input"
+ ]
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/var/folders/r0/nf1kgxsx6zx3rw16xc3wnnzr0000gn/T/ipykernel_12360/1678486857.py:25: UserWarning: The figure layout has changed to tight\n",
+ " plt.tight_layout()\n"
+ ]
+ },
+ {
+ "data": {
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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 387,
+ "width": 989
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(FIG_WIDTH, FIG_HEIGHT))\n",
+ "\n",
+ "az.plot_kde(\n",
+ " intervention_ey,\n",
+ " ax=ax,\n",
+ " plot_kwargs={\"color\": COLOR_POPULATION, \"lw\": 2},\n",
+ " fill_kwargs={\"color\": COLOR_POPULATION, \"alpha\": 0.3},\n",
+ " label=rf\"Population $E[Y \\mid do(H\\!=\\!2)]$ (analytical: {ANALYTICAL_INTERVENTION:.2f})\",\n",
+ ")\n",
+ "\n",
+ "az.plot_kde(\n",
+ " y_cf_joe,\n",
+ " ax=ax,\n",
+ " plot_kwargs={\"color\": COLOR_JOE, \"lw\": 2},\n",
+ " fill_kwargs={\"color\": COLOR_JOE, \"alpha\": 0.3},\n",
+ " label=rf\"Joe's counterfactual $Y_{{H=2}}$ (analytical: {ANALYTICAL_COUNTERFACTUAL:.2f})\",\n",
+ ")\n",
+ "\n",
+ "ax.axvline(ANALYTICAL_INTERVENTION, color=\"black\", ls=\"--\", lw=1.5, alpha=0.7)\n",
+ "ax.axvline(ANALYTICAL_COUNTERFACTUAL, color=\"black\", ls=\"--\", lw=1.5, alpha=0.7)\n",
+ "\n",
+ "ax.set_xlabel(\"Exam score ($Y$)\")\n",
+ "ax.set_ylabel(\"Density\")\n",
+ "ax.legend(fontsize=10)\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-30",
+ "metadata": {},
+ "source": [
+ "**Caption:** Posterior distributions of the population-level intervention $E[Y \\mid \\operatorname{do}(H\\!=\\!2)]$ and Joe's unit-level counterfactual $Y_{H=2}$. Black dashed lines mark the analytical values. The gap reflects Joe's above-average individual characteristics ($U_Y \\approx 0.75$), which the population intervention averages away."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-31",
+ "metadata": {},
+ "source": [
+ "## Joe's counterfactual posterior"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "cell-32",
+ "metadata": {
+ "tags": [
+ "hide-input"
+ ]
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/var/folders/r0/nf1kgxsx6zx3rw16xc3wnnzr0000gn/T/ipykernel_12360/3557695747.py:28: UserWarning: The figure layout has changed to tight\n",
+ " plt.tight_layout()\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 387,
+ "width": 989
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(FIG_WIDTH, FIG_HEIGHT))\n",
+ "\n",
+ "az.plot_kde(\n",
+ " y_cf_joe,\n",
+ " ax=ax,\n",
+ " plot_kwargs={\"color\": COLOR_JOE, \"lw\": 2},\n",
+ " fill_kwargs={\"color\": COLOR_JOE, \"alpha\": 0.3},\n",
+ ")\n",
+ "\n",
+ "ax.axvline(\n",
+ " ANALYTICAL_COUNTERFACTUAL,\n",
+ " color=\"black\",\n",
+ " ls=\"--\",\n",
+ " lw=1.5,\n",
+ " label=f\"Analytical counterfactual: {ANALYTICAL_COUNTERFACTUAL:.2f}\",\n",
+ ")\n",
+ "ax.axvline(\n",
+ " joe_Y,\n",
+ " color=\"gray\",\n",
+ " ls=\"--\",\n",
+ " lw=1.5,\n",
+ " label=f\"Joe's observed score: {joe_Y:.2f}\",\n",
+ ")\n",
+ "\n",
+ "ax.set_xlabel(\"Exam score ($Y$)\")\n",
+ "ax.set_ylabel(\"Density\")\n",
+ "ax.legend(fontsize=10)\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-33",
+ "metadata": {},
+ "source": [
+ "**Caption:** Posterior distribution of Joe's counterfactual exam score under $H = 2$, with the analytical counterfactual (1.90, black dashed) and Joe's observed score (1.50, gray dashed). The counterfactual is higher than the observed score because additional homework has a positive causal effect ($c > 0$), and Joe's above-average ability is preserved."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-34",
+ "metadata": {},
+ "source": [
+ "## Putting it together\n",
+ "\n",
+ "| | Intervention: $E[Y \\mid \\operatorname{do}(H\\!=\\!2)]$ | Counterfactual: $Y_{H=2}$ for Joe |\n",
+ "|---|---|---|\n",
+ "| **Question** | What happens on average if we set everyone's homework to 2? | What would Joe's score have been if he had done $H\\!=\\!2$? |\n",
+ "| **Uses individual data?** | No | Yes — conditions on Joe's observed $(X, H, Y)$ |\n",
+ "| **Exogenous values** | Population mean ($U \\approx 0$) | Joe's inferred values ($U_Y \\approx 0.75$) |\n",
+ "| **Causal ladder** | Rung 2 (intervention) | Rung 3 (counterfactual) |\n",
+ "| **Result** | $\\approx 0.80$ | $\\approx 1.90$ |"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-35",
+ "metadata": {},
+ "source": [
+ ":::{warning}\n",
+ "`pm.do` alone does not produce unit-level counterfactuals. It computes interventional distributions (rung 2), which average over all individual characteristics. For unit-level counterfactuals (rung 3), the additional abduction step — inferring the individual's exogenous values from observed data — is essential.\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-36",
+ "metadata": {},
+ "source": [
+ "## Summary\n",
+ "\n",
+ "- **The exogenous terms ($U$) are not noise** — they encode everything about a specific individual that causally affects the outcome but is not measured. Across the population they look like zero-mean error; for a specific person they are fixed causal properties.\n",
+ "- **Counterfactuals** answer questions about specific individuals under hypothetical conditions by conditioning on observed evidence before intervening.\n",
+ "- **Pearl's three-step procedure** — abduction, action, prediction — turns a fitted structural causal model into a counterfactual engine.\n",
+ "- **`do()` answers a different question**: the population-level average effect of an intervention. For Joe, $\\operatorname{do}(H\\!=\\!2)$ predicts $\\approx 0.8$; the counterfactual predicts $\\approx 1.9$.\n",
+ "- **In a Bayesian framework**, the three-step procedure yields a full posterior over the counterfactual outcome, naturally propagating coefficient uncertainty through every step.\n",
+ "- **In linear SEMs**, the counterfactual simplifies: $Y_{H=h'} = Y_{\\text{obs}} + c \\cdot (h' - H_{\\text{obs}})$. In nonlinear models, the full three-step procedure is required."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-37",
+ "metadata": {},
+ "source": [
+ "## Reflection\n",
+ "\n",
+ "When have you wanted to answer a question about a *specific case* rather than a population average?\n",
+ "\n",
+ "- **Medicine**: A patient took drug A and recovered slowly. Would drug B have worked better *for this patient*, given their specific medical history?\n",
+ "- **Marketing**: A customer saw campaign A and didn't convert. Would they have converted under campaign B, given their browsing behavior and demographics?\n",
+ "- **Education**: A student attended tutoring but still struggled. Would a different teaching method have helped *this student*, given their prior performance and learning style?\n",
+ "\n",
+ "In each case, the population-level answer ($\\operatorname{do}$) and the individual answer (counterfactual) can diverge substantially — especially for individuals far from the population mean."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-38",
+ "metadata": {},
+ "source": [
+ "## Authors\n",
+ "\n",
+ "- Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in March 2026"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-39",
+ "metadata": {},
+ "source": [
+ "## References\n",
+ "\n",
+ ":::{bibliography}\n",
+ ":filter: docname in docnames\n",
+ ":::"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "cell-40",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Last updated: Thu, 05 Mar 2026\n",
+ "\n",
+ "Python implementation: CPython\n",
+ "Python version : 3.12.12\n",
+ "IPython version : 9.11.0\n",
+ "\n",
+ "pytensor: 2.38.1\n",
+ "xarray : 2026.2.0\n",
+ "\n",
+ "arviz : 0.23.4\n",
+ "graphviz : 0.21\n",
+ "matplotlib: 3.10.8\n",
+ "numpy : 2.4.2\n",
+ "pymc : 5.28.1\n",
+ "\n",
+ "Watermark: 2.6.0\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "%load_ext watermark\n",
+ "%watermark -n -u -v -iv -w -p pytensor,xarray"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cell-41",
+ "metadata": {},
+ "source": [
+ ":::{include} ../page_footer.md\n",
+ ":::"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "pymc-examples",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.12.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/examples/causal_inference/unit_level_counterfactuals.myst.md b/examples/causal_inference/unit_level_counterfactuals.myst.md
new file mode 100644
index 000000000..2825a16dc
--- /dev/null
+++ b/examples/causal_inference/unit_level_counterfactuals.myst.md
@@ -0,0 +1,412 @@
+---
+jupytext:
+ text_representation:
+ extension: .md
+ format_name: myst
+ format_version: 0.13
+kernelspec:
+ display_name: pymc-examples
+ language: python
+ name: python3
+---
+
+(unit_level_counterfactuals)=
+# Unit-level counterfactuals: abduction, action, and prediction
+
+:::{post} March, 2026
+:tags: causal inference, counterfactuals, structural causal models, Pearl
+:category: intermediate, explanation
+:author: Benjamin T. Vincent
+:::
+
++++
+
+Joe participated in an after-school encouragement program. He spent moderate time in the program ($X = 0.5$), did 1 hour of homework ($H = 1.0$), and scored 1.5 on his exam ($Y = 1.5$). His teacher asks: **"What would Joe's exam score have been if he had doubled his homework to $H = 2$?"**
+
+This is not a question about what happens on average when we assign everyone to do 2 hours of homework. It is about one specific student whose abilities, motivation, and circumstances have already been observed.
+
+The standard causal tool for "what if?" questions is the do-operator: $E[Y \mid \operatorname{do}(H\!=\!2)]$. But the do-operator answers a population-level question — rung 2 of Pearl's causal ladder — not an individual one. For Joe, it predicts a score of approximately $0.8$, which is *below* his actual score of $1.5$. The population intervention treats Joe as if he were average, discarding the individual characteristics that made him score above average.
+
+A **unit-level counterfactual** (rung 3) conditions on Joe's observed data before intervening. It infers that Joe has above-average inherent ability, and predicts a counterfactual score of approximately $1.9$. The gap — $0.8$ versus $1.9$ — is the difference between "what happens in general?" and "what would have happened to *this person*?"
+
+This notebook implements Pearl's three-step counterfactual procedure (**abduction, action, prediction**) using a structural causal model fit with PyMC. The worked example follows {cite:t}`pearl2016causal`, §4.2.
+
++++
+
+:::{note} Pearl's causal ladder
+- **Rung 1 — Association**: "What do we observe?" $P(Y \mid X)$
+- **Rung 2 — Intervention**: "What happens if we set $H = 2$ for everyone?" $P(Y \mid \operatorname{do}(H\!=\!2))$
+- **Rung 3 — Counterfactual**: "What *would have happened* to Joe if he had done $H\!=\!2$, given what we already observed?" $Y_{H=2} \mid X\!=\!0.5, H\!=\!1, Y\!=\!1.5$
+
+The existing {ref}`interventional_distribution` notebook demonstrates rung 2 using `pm.do`. This notebook tackles rung 3.
+:::
+
++++
+
+## Set up the notebook
+
+```{code-cell} ipython3
+import arviz as az
+import matplotlib.pyplot as plt
+import numpy as np
+import pymc as pm
+
+from graphviz import Digraph
+```
+
+```{code-cell} ipython3
+RANDOM_SEED = 42
+rng = np.random.default_rng(RANDOM_SEED)
+
+az.style.use("arviz-darkgrid")
+%config InlineBackend.figure_format = 'retina'
+
+FIG_WIDTH = 10
+FIG_HEIGHT = 4
+
+COLOR_POPULATION = "C0"
+COLOR_JOE = "C1"
+```
+
+## The encouragement design
+
+The example comes from {cite:t}`pearl2016causal`, §4.2.3. Three variables, all standardized:
+
+- $X$ — time in an after-school encouragement program (randomized)
+- $H$ — hours of homework
+- $Y$ — exam score
+
+Encouragement ($X$) has both a direct effect on the exam score and an indirect effect through homework. The structural equations that generate the data are:
+
+$$
+\begin{align}
+X &= U_X \\
+H &= aX + U_H \\
+Y &= bX + cH + U_Y
+\end{align}
+$$
+
+where $a = 0.5$, $b = 0.7$, $c = 0.4$, and $U_X, U_H, U_Y$ are mutually independent standard normals.
+
+```{code-cell} ipython3
+:tags: [hide-input]
+
+dag = Digraph()
+dag.attr(rankdir="LR")
+dag.node("X", "X\n(Encouragement)")
+dag.node("H", "H\n(Homework)")
+dag.node("Y", "Y\n(Exam score)")
+dag.edge("X", "H", label=" a")
+dag.edge("H", "Y", label=" c")
+dag.edge("X", "Y", label=" b")
+dag
+```
+
+**Caption:** DAG for the encouragement design. Encouragement ($X$) affects exam score ($Y$) directly (coefficient $b$) and indirectly through homework ($H$, coefficients $a$ and $c$).
+
++++
+
+## Simulate data and fit the structural model
+
+We generate $N = 500$ observations from the structural equations, then fit a PyMC model to recover the coefficients.
+
+```{code-cell} ipython3
+N = 500
+
+TRUE_A = 0.5
+TRUE_B = 0.7
+TRUE_C = 0.4
+
+U_X = rng.normal(0, 1, N)
+U_H = rng.normal(0, 1, N)
+U_Y = rng.normal(0, 1, N)
+
+X_data = U_X
+H_data = TRUE_A * X_data + U_H
+Y_data = TRUE_B * X_data + TRUE_C * H_data + U_Y
+
+# Joe's observed values
+joe_X = 0.5
+joe_H = 1.0
+joe_Y = 1.5
+
+# Analytical reference values
+ANALYTICAL_INTERVENTION = 2 * TRUE_C
+ANALYTICAL_COUNTERFACTUAL = joe_Y + TRUE_C * (2 - joe_H)
+
+print(f"Analytical E[Y | do(H=2)] = {ANALYTICAL_INTERVENTION:.2f}")
+print(f"Analytical Y_{{H=2}} for Joe = {ANALYTICAL_COUNTERFACTUAL:.2f}")
+```
+
+The PyMC model mirrors the structural equations. Each equation becomes a likelihood statement, and we place weakly informative priors on the coefficients and noise standard deviations.
+
+```{code-cell} ipython3
+with pm.Model() as scm:
+ a = pm.Normal("a", mu=0, sigma=2)
+ b = pm.Normal("b", mu=0, sigma=2)
+ c = pm.Normal("c", mu=0, sigma=2)
+
+ sigma_X = pm.HalfNormal("sigma_X", sigma=2)
+ sigma_H = pm.HalfNormal("sigma_H", sigma=2)
+ sigma_Y = pm.HalfNormal("sigma_Y", sigma=2)
+
+ X = pm.Normal("X", mu=0, sigma=sigma_X, observed=X_data)
+ H = pm.Normal("H", mu=a * X, sigma=sigma_H, observed=H_data)
+ Y = pm.Normal("Y", mu=b * X + c * H, sigma=sigma_Y, observed=Y_data)
+
+ idata = pm.sample(draws=2000, random_seed=RANDOM_SEED)
+```
+
+```{code-cell} ipython3
+summary = az.summary(
+ idata,
+ var_names=["a", "b", "c", "sigma_X", "sigma_H", "sigma_Y"],
+ kind="stats",
+)
+summary["true_value"] = [TRUE_A, TRUE_B, TRUE_C, 1.0, 1.0, 1.0]
+summary[["mean", "sd", "hdi_3%", "hdi_97%", "true_value"]]
+```
+
+The posterior means are close to the true values, and all true values fall within the 94% HDI. The model has recovered the structural relationships.
+
++++
+
+## The population intervention: $E[Y \mid \operatorname{do}(H\!=\!2)]$
+
+The do-operator answers: "What happens on average if we set everyone's homework to 2?" Under $\operatorname{do}(H\!=\!2)$, the structural equation for $H$ is replaced with the constant $H = 2$, severing the causal link from $X$ to $H$. The equation for $Y$ becomes:
+
+$$Y = bX + c \cdot 2 + U_Y$$
+
+Taking expectations over the population ($E[X] = 0$, $E[U_Y] = 0$):
+
+$$E[Y \mid \operatorname{do}(H\!=\!2)] = 2c$$
+
+We compute this for each posterior draw to propagate coefficient uncertainty.
+
+```{code-cell} ipython3
+posterior = idata.posterior
+c_draws = posterior["c"].values.flatten()
+b_draws = posterior["b"].values.flatten()
+
+intervention_ey = 2 * c_draws
+
+print(f"Posterior mean of E[Y | do(H=2)]: {intervention_ey.mean():.3f}")
+print(f"Analytical value: {ANALYTICAL_INTERVENTION:.3f}")
+```
+
+For Joe, the population intervention predicts a score of approximately $0.8$ — below his observed $1.5$. The do-operator averages over all possible individual characteristics. It knows nothing about Joe's above-average ability, his specific level of encouragement, or any other factor that made him who he is. It treats him as a generic member of the population.
+
+To answer Joe's question, we need to preserve his individual characteristics.
+
++++
+
+## The exogenous terms are not noise
+
+The key insight that separates counterfactual from interventional reasoning is a reinterpretation of the exogenous terms $U$.
+
+In standard regression, residuals are exchangeable estimation error — interchangeable across individuals, carrying no individual meaning. In a structural causal model, $U_Y$ encodes everything about a specific person that causally affects $Y$ but is not measured: inherent ability, sleep quality, motivation, prior knowledge. Across the population, these factors look like zero-mean noise. For a specific individual, they are **fixed causal properties**.
+
++++
+
+:::{important} The dual nature of $U$
+Across the population, $U_Y$ behaves like noise: zero mean, uncorrelated with measured variables. For a specific individual, $U_Y$ is a fixed property encoding all unmeasured causal factors that affect the outcome. This reinterpretation — from "discardable error" to "signal about the individual" — is what enables counterfactual reasoning.
+:::
+
++++
+
+For Joe, his exogenous value is:
+
+$$U_Y^{\text{Joe}} = Y - bX - cH = 1.5 - 0.7 \cdot 0.5 - 0.4 \cdot 1.0 = 0.75$$
+
+Joe has above-average inherent ability. The counterfactual procedure preserves this; the population intervention discards it.
+
++++
+
+## Pearl's three-step counterfactual procedure
+
+The population intervention asks what happens when we change the world for everyone. A counterfactual asks what would have happened to a specific individual in a world that *did not occur*, given what we observed in the world that *did*.
+
+Pearl's three-step procedure turns a fitted structural causal model into a counterfactual engine.
+
++++
+
+### Step 1: Abduction — infer Joe's exogenous values
+
+Given Joe's observed data $(X = 0.5, H = 1.0, Y = 1.5)$ and the structural equations, we solve for his individual exogenous values. For each posterior draw, the coefficients differ slightly, so Joe's inferred $U_Y$ varies across draws:
+
+$$U_Y^{\text{Joe}} = Y_{\text{obs}} - b \cdot X_{\text{obs}} - c \cdot H_{\text{obs}}$$
+
+```{code-cell} ipython3
+u_y_joe = joe_Y - b_draws * joe_X - c_draws * joe_H
+
+analytical_u_y = joe_Y - TRUE_B * joe_X - TRUE_C * joe_H
+print(f"Posterior mean of U_Y (Joe): {u_y_joe.mean():.3f}")
+print(f"Analytical U_Y (Joe): {analytical_u_y:.3f}")
+```
+
+### Step 2: Action — set the intervention
+
+Replace the structural equation for homework with the counterfactual value $H = 2$. All other equations and Joe's abducted exogenous values remain unchanged.
+
+### Step 3: Prediction — compute the counterfactual outcome
+
+Propagate through the modified model using Joe's individual $U_Y$:
+
+$$Y_{H=2}^{\text{Joe}} = b \cdot X_{\text{obs}} + c \cdot 2 + U_Y^{\text{Joe}}$$
+
+Substituting the abduction result reveals a clean simplification:
+
+$$Y_{H=2}^{\text{Joe}} = Y_{\text{obs}} + c \cdot (2 - H_{\text{obs}})$$
+
+In a linear SEM, the counterfactual reduces to the observed outcome plus the structural coefficient times the change in the intervened variable. The $b$ terms and the exogenous term cancel exactly.
+
+```{code-cell} ipython3
+y_cf_joe = joe_Y + c_draws * (2 - joe_H)
+
+print(f"Posterior mean of Y_{{H=2}} (Joe): {y_cf_joe.mean():.3f}")
+print(f"Analytical Y_{{H=2}} (Joe): {ANALYTICAL_COUNTERFACTUAL:.3f}")
+```
+
+:::{tip} Linear SEM shortcut
+In a linear structural equation model, the counterfactual change in $Y$ when intervening on a direct parent $H$ is $c \cdot (H' - H_{\text{obs}})$, where $c$ is the structural coefficient. This elegant cancellation does not hold in nonlinear models, where the full three-step procedure is necessary.
+:::
+
++++
+
+## Intervention versus counterfactual
+
+```{code-cell} ipython3
+:tags: [hide-input]
+
+fig, ax = plt.subplots(figsize=(FIG_WIDTH, FIG_HEIGHT))
+
+az.plot_kde(
+ intervention_ey,
+ ax=ax,
+ plot_kwargs={"color": COLOR_POPULATION, "lw": 2},
+ fill_kwargs={"color": COLOR_POPULATION, "alpha": 0.3},
+ label=rf"Population $E[Y \mid do(H\!=\!2)]$ (analytical: {ANALYTICAL_INTERVENTION:.2f})",
+)
+
+az.plot_kde(
+ y_cf_joe,
+ ax=ax,
+ plot_kwargs={"color": COLOR_JOE, "lw": 2},
+ fill_kwargs={"color": COLOR_JOE, "alpha": 0.3},
+ label=rf"Joe's counterfactual $Y_{{H=2}}$ (analytical: {ANALYTICAL_COUNTERFACTUAL:.2f})",
+)
+
+ax.axvline(ANALYTICAL_INTERVENTION, color="black", ls="--", lw=1.5, alpha=0.7)
+ax.axvline(ANALYTICAL_COUNTERFACTUAL, color="black", ls="--", lw=1.5, alpha=0.7)
+
+ax.set_xlabel("Exam score ($Y$)")
+ax.set_ylabel("Density")
+ax.legend(fontsize=10)
+plt.tight_layout()
+plt.show()
+```
+
+**Caption:** Posterior distributions of the population-level intervention $E[Y \mid \operatorname{do}(H\!=\!2)]$ and Joe's unit-level counterfactual $Y_{H=2}$. Black dashed lines mark the analytical values. The gap reflects Joe's above-average individual characteristics ($U_Y \approx 0.75$), which the population intervention averages away.
+
++++
+
+## Joe's counterfactual posterior
+
+```{code-cell} ipython3
+:tags: [hide-input]
+
+fig, ax = plt.subplots(figsize=(FIG_WIDTH, FIG_HEIGHT))
+
+az.plot_kde(
+ y_cf_joe,
+ ax=ax,
+ plot_kwargs={"color": COLOR_JOE, "lw": 2},
+ fill_kwargs={"color": COLOR_JOE, "alpha": 0.3},
+)
+
+ax.axvline(
+ ANALYTICAL_COUNTERFACTUAL,
+ color="black",
+ ls="--",
+ lw=1.5,
+ label=f"Analytical counterfactual: {ANALYTICAL_COUNTERFACTUAL:.2f}",
+)
+ax.axvline(
+ joe_Y,
+ color="gray",
+ ls="--",
+ lw=1.5,
+ label=f"Joe's observed score: {joe_Y:.2f}",
+)
+
+ax.set_xlabel("Exam score ($Y$)")
+ax.set_ylabel("Density")
+ax.legend(fontsize=10)
+plt.tight_layout()
+plt.show()
+```
+
+**Caption:** Posterior distribution of Joe's counterfactual exam score under $H = 2$, with the analytical counterfactual (1.90, black dashed) and Joe's observed score (1.50, gray dashed). The counterfactual is higher than the observed score because additional homework has a positive causal effect ($c > 0$), and Joe's above-average ability is preserved.
+
++++
+
+## Putting it together
+
+| | Intervention: $E[Y \mid \operatorname{do}(H\!=\!2)]$ | Counterfactual: $Y_{H=2}$ for Joe |
+|---|---|---|
+| **Question** | What happens on average if we set everyone's homework to 2? | What would Joe's score have been if he had done $H\!=\!2$? |
+| **Uses individual data?** | No | Yes — conditions on Joe's observed $(X, H, Y)$ |
+| **Exogenous values** | Population mean ($U \approx 0$) | Joe's inferred values ($U_Y \approx 0.75$) |
+| **Causal ladder** | Rung 2 (intervention) | Rung 3 (counterfactual) |
+| **Result** | $\approx 0.80$ | $\approx 1.90$ |
+
++++
+
+:::{warning}
+`pm.do` alone does not produce unit-level counterfactuals. It computes interventional distributions (rung 2), which average over all individual characteristics. For unit-level counterfactuals (rung 3), the additional abduction step — inferring the individual's exogenous values from observed data — is essential.
+:::
+
++++
+
+## Summary
+
+- **The exogenous terms ($U$) are not noise** — they encode everything about a specific individual that causally affects the outcome but is not measured. Across the population they look like zero-mean error; for a specific person they are fixed causal properties.
+- **Counterfactuals** answer questions about specific individuals under hypothetical conditions by conditioning on observed evidence before intervening.
+- **Pearl's three-step procedure** — abduction, action, prediction — turns a fitted structural causal model into a counterfactual engine.
+- **`do()` answers a different question**: the population-level average effect of an intervention. For Joe, $\operatorname{do}(H\!=\!2)$ predicts $\approx 0.8$; the counterfactual predicts $\approx 1.9$.
+- **In a Bayesian framework**, the three-step procedure yields a full posterior over the counterfactual outcome, naturally propagating coefficient uncertainty through every step.
+- **In linear SEMs**, the counterfactual simplifies: $Y_{H=h'} = Y_{\text{obs}} + c \cdot (h' - H_{\text{obs}})$. In nonlinear models, the full three-step procedure is required.
+
++++
+
+## Reflection
+
+When have you wanted to answer a question about a *specific case* rather than a population average?
+
+- **Medicine**: A patient took drug A and recovered slowly. Would drug B have worked better *for this patient*, given their specific medical history?
+- **Marketing**: A customer saw campaign A and didn't convert. Would they have converted under campaign B, given their browsing behavior and demographics?
+- **Education**: A student attended tutoring but still struggled. Would a different teaching method have helped *this student*, given their prior performance and learning style?
+
+In each case, the population-level answer ($\operatorname{do}$) and the individual answer (counterfactual) can diverge substantially — especially for individuals far from the population mean.
+
++++
+
+## Authors
+
+- Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in March 2026
+
++++
+
+## References
+
+:::{bibliography}
+:filter: docname in docnames
+:::
+
+```{code-cell} ipython3
+%load_ext watermark
+%watermark -n -u -v -iv -w -p pytensor,xarray
+```
+
+:::{include} ../page_footer.md
+:::