{
"cells": [
{
"attachments": {
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}
},
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"source": [
"# Multilevel models\n",
"\n",
"## Departmental punctuality\n",
"\n",
"Imagine that your university hires a new president. On her first week,\n",
"she schedules a meeting with professors from three departments,\n",
"${ D = \\{ \\text{G}, ~ \\text{E}, ~ \\text{M} \\} }$. The professor from the\n",
"Department of Government (${ d{=}\\text{G} }$) shows up 1 minute late,\n",
"the professor from the Department of English (${ d{=}\\text{E} }$) shows\n",
"up 15 minutes before the scheduled meeting time, and the professor from\n",
"the Department of Math (${ d{=}\\text{M} }$) shows up 30 minutes late.\n",
"From this single meeting the new president updates her beliefs about\n",
"when professors will show up to scheduled meetings.\n",
"\n",
"But how should the president update her beliefs? It could be that\n",
"departments have different relationships with punctuality and it would\n",
"be useful to expect professors from the Math department to show up later\n",
"than professors from the English department. It could also be the case\n",
"that there is not meaningful between-department variance and she should\n",
"just learn about the greater population of professors at the university.\n",
"\n",
"A model that infers information about the population without\n",
"differentiating subpopulations is doing *“complete pooling”*, meaning\n",
"that all of the variance in the data is treated as being generated by\n",
"the same distribution. I.e. the data is pooled together and treated as\n",
"iid observations drawn from a single distribution.\n",
"\n",
"If the president thinks of each department independently, what she\n",
"learns about the punctuality of professors from one department will not\n",
"change her beliefs about professors from other departments. In this\n",
"case, there would be *“no pooling”* of information across departments.\n",
"The president’s observations of the three professors would have no\n",
"bearing on her belief about what to expect of a professor from a fourth\n",
"department (e.g. Psychology).\n",
"\n",
"*“**Partial** pooling”* models represent uncertainty at multiple levels\n",
"of abstraction. Based on her observations from this meeting, the\n",
"president will update her beliefs about these departments as well as the\n",
"greater population. In other words, what she observes about the Math\n",
"department might strongly update her beliefs about that department,\n",
"moderately update her beliefs about the broader population, and that in\n",
"turn could weakly update her beliefs about the English department.\n",
"\n",
"## Complete pooling\n",
"\n",
"Let’s build a complete pooling model of the president’s belief about the\n",
"punctuality of professors. The data observed by the president are\n",
"${ t = \\langle t_G, t_E, t_M \\rangle = \\langle 1, -15, 30 \\rangle }$.\n",
"We’ll model the president’s belief about the greater population of\n",
"professors as a normal distribution centered at $\\theta$ with standard\n",
"deviation $\\dot\\sigma$. Prior to meeting with anyone, the president\n",
"thinks that professors will, on average, show up on time, but that some\n",
"will show up early and some late. We can encode this prior belief as a\n",
"normal distribution centered at zero, with some standard deviation,\n",
"let’s say 20. I.e. the prior for $\\theta$ is:\n",
"\n",
"$$\n",
"\\theta ~\\sim~ \\mathcal{N}\\left( \\dot{\\mu}{=}0, ~ \\dot{\\tau}{=}20 \\right)\n",
"$$\n",
"\n",
"If she observes that professors tend to be late, then her posterior\n",
"estimate of $\\theta$ will have an expected value greater than zero\n",
"(i.e. ${ \\operatorname{E}[\\theta \\mid t] > 0 }$), and if she ends up\n",
"expecting professors to be early, then\n",
"${ \\operatorname{E}[\\theta \\mid t] < 0 }$.\n",
"\n",
"In this tutorial I’ll use a dot above to indicate that a variable is\n",
"fixed, not inferred. (N.B. the dot is not standard notation, just what\n",
"I’m using here.) In the graphical schematic, fixed parameters are\n",
"depicted as bare symbols rather than nodes. Note that “fixed” means the\n",
"values are not updated during inference (but you can, of course,\n",
"manually tune these values or learn suitable values by minimizing some\n",
"loss function in conjunction with a model fitting algorithm).\n",
"\n",
"Since the model infers the distribution of $\\theta$, the graphical\n",
"schematic depicts it as an open node (i.e. a latent random variable).\n",
"The data in this model are $t$.\n",
"\n",
"We specify the likelihood as,\n",
"\n",
"$$\n",
"t_d ~\\sim~ \\mathcal{N}(\\theta, ~ \\dot\\sigma{=}15)\n",
"$$\n",
"\n",
"I.e., for whatever the true value of $\\theta$ is for the population of\n",
"professors, the president thinks that when professors actually show up\n",
"will follow a normal distribution, centered on the true value of\n",
"$\\theta$, with standard deviation 15.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\theta ~\\sim&~ \\mathcal{N}\\left( \\dot{\\mu}{=}0, ~ \\dot{\\tau}{=}20 \\right) \\\\\n",
"t_d ~\\sim&~ \\mathcal{N}(\\theta, ~ \\dot\\sigma{=}15) \\\\\n",
"d ~\\in&~ D,~~~ \\text{where}~~~ D = \\{ \\text{G}, ~ \\text{E}, ~ \\text{M} \\}\n",
"\\end{align*}\n",
"$$\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a809f52a",
"metadata": {},
"outputs": [],
"source": [
"%reset -f\n",
"import jax\n",
"import jax.numpy as jnp\n",
"from memo import memo\n",
"from enum import IntEnum\n",
"from jax.scipy.stats.norm import pdf as normpdf\n",
"from jax.scipy.stats.cauchy import pdf as cauchypdf\n",
"from matplotlib import pyplot as plt\n",
"\n",
"normpdfjit = jax.jit(normpdf)\n",
"\n",
"class Department(IntEnum):\n",
" GOVERNMENT = 0\n",
" ENGLISH = 1\n",
" MATH = 2\n",
"\n",
"t = jnp.array([1, -15, 30])\n",
"sigma = 15\n",
"\n",
"Theta = jnp.linspace(-40, 40, 200)\n",
"\n",
"@jax.jit\n",
"def professor_arrival_likelihood(d, theta):\n",
" ### likelihood of a professor from department d \n",
" ### showing up t_d minutes early/late, \n",
" ### under the hypothesis given by theta and sigma.\n",
" return normpdf(t[d], loc=theta, scale=sigma)\n",
"\n",
"@memo\n",
"def complete_pooling[\n",
" _theta: Theta,\n",
"](mu=0, tau=1):\n",
" president: knows(_theta)\n",
" president: thinks[\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau))\n",
" ]\n",
" president: observes_event(\n",
" wpp=professor_arrival_likelihood({Department.GOVERNMENT}, department.theta))\n",
" president: observes_event(\n",
" wpp=professor_arrival_likelihood({Department.ENGLISH}, department.theta))\n",
" president: observes_event(\n",
" wpp=professor_arrival_likelihood({Department.MATH}, department.theta))\n",
" return president[Pr[department.theta == _theta]]\n",
"\n",
"mu_ = 0\n",
"tau_ = 20\n",
"res = complete_pooling(mu=mu_, tau=tau_)\n",
"\n",
"### check the size and sum of the output\n",
"# res.shape\n",
"# res.sum()\n",
"\n",
"fig, ax = plt.subplots()\n",
"\n",
"ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
"theta_posterior = res\n",
"theta_expectation = jnp.dot(Theta, theta_posterior)\n",
"ax.plot(Theta, theta_posterior, label=r\"$P(\\theta \\mid t)$\")\n",
"ax.axvline(\n",
" theta_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=(\n",
" r\"$\\operatorname{E}\"\n",
" + rf\"[\\theta \\mid t]={theta_expectation:6.2f}$\")\n",
")\n",
"_ = ax.set_title(r\"Posterior of $\\theta$\")\n",
"_ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
"_ = plt.suptitle(fr\"$\\dot\\tau$ = {tau_}\", y=1)\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"attachments": {
"generated/multilevel-models/no-pooling.png": {
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}
},
"cell_type": "markdown",
"id": "65cb537d-02d2-4991-80cd-e41d5921d660",
"metadata": {},
"source": [
"Try changing the data to `t = jnp.array([-20, -10, 30])`. Notice how\n",
"changing the data for one group updates the expectation of the\n",
"population.\n",
"\n",
"## No pooling\n",
"\n",
"In contrast to complete pooling, which assumes all observations are\n",
"generated by a shared population-level distribution parameterized by\n",
"$\\theta$, the no pooling model treats each department as having its own\n",
"independent parameter $\\theta_d$. The key change is that instead of\n",
"having a single $\\theta$ drawn from the prior distribution, we now have\n",
"three independent parameters $\\theta_G$, $\\theta_E$, and $\\theta_M$. The\n",
"practical meaning of this change is significant:\n",
"\n",
"In complete pooling, an observation of the Math professor being late\n",
"would shift our expectations for all departments. In no pooling,\n",
"learning that the Math professor is late only updates our beliefs about\n",
"the Math department. Each department’s parameter is estimated using only\n",
"data from that department.\n",
"\n",
"The key change in our model specification is that we have replaced the\n",
"single $\\theta$ with three parameters, $\\theta_d$.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\theta_d ~\\sim&~ \\mathcal{N}\\left( \\dot{\\mu}{=}0, ~ \\dot{\\tau}{=}20 \\right) \\\\\n",
"t_d ~\\sim&~ \\mathcal{N}(\\theta_d, ~ \\dot\\sigma{=}15) \\\\\n",
"d ~\\in&~ D,~~~ \\text{where}~~~ D = \\{ \\text{G}, ~ \\text{E}, ~ \\text{M} \\}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"\n",
"\n",
"The plate (rectangular box) with label $d$ indicates that everything\n",
"inside is repeated for each department $d \\in D$. Variables inside the\n",
"plate have a unique value for each department. Variables outside the\n",
"plate are shared across all departments.\n",
"\n",
"To change the `complete_pooling` model to the `no_pooling` model we make\n",
"a simple change, adding the conditional statement\n",
"\n",
"``` python\n",
"president: observes [department.d] is _d\n",
"```\n",
"\n",
"and the query variable `_d` in the definition, `[_d: Department, ...]`."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "60ef6ca4",
"metadata": {},
"outputs": [],
"source": [
"%reset -f\n",
"import jax\n",
"import jax.numpy as jnp\n",
"from memo import memo\n",
"from enum import IntEnum\n",
"from jax.scipy.stats.norm import pdf as normpdf\n",
"from jax.scipy.stats.cauchy import pdf as cauchypdf\n",
"from matplotlib import pyplot as plt\n",
"\n",
"normpdfjit = jax.jit(normpdf)\n",
"\n",
"class Department(IntEnum):\n",
" GOVERNMENT = 0\n",
" ENGLISH = 1\n",
" MATH = 2\n",
"\n",
"t = jnp.array([1, -15, 30])\n",
"sigma = 15\n",
"\n",
"Theta = jnp.linspace(-40, 40, 200)\n",
"\n",
"@jax.jit\n",
"def professor_arrival_likelihood(d, theta):\n",
" ### likelihood of a professor from department d \n",
" ### showing up t_d minutes early/late, \n",
" ### under the hypothesis given by theta and sigma.\n",
" return normpdf(t[d], loc=theta, scale=sigma)\n",
"\n",
"@memo\n",
"def no_pooling[\n",
" _d: Department,\n",
" _theta: Theta,\n",
"](mu=0, tau=1):\n",
" president: knows(_theta)\n",
" president: thinks[\n",
" department: chooses(d in Department, wpp=1),\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau))\n",
" ]\n",
" president: observes [department.d] is _d ### new conditional statement\n",
" president: observes_event(\n",
" wpp=professor_arrival_likelihood(department.d, department.theta))\n",
" return president[Pr[department.theta == _theta]]\n",
"\n",
"mu_ = 0\n",
"tau_ = 20\n",
"res = no_pooling(mu=mu_, tau=tau_)\n",
"\n",
"### check the size and sum of the output\n",
"# res.shape\n",
"# res.sum()\n",
"# res[0].sum()\n",
"# res[1].sum()\n",
"# res[2].sum()\n",
"\n",
"fig, ax = plt.subplots()\n",
"\n",
"ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
"for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" theta_posterior = res[d]\n",
" theta_expectation = jnp.dot(Theta, theta_posterior)\n",
" ax.plot(\n",
" Theta, \n",
" theta_posterior, \n",
" label=(\n",
" rf\"$p(\\theta_{department_abbrev} \\mid t),~ \"\n",
" + r\"\\operatorname{E}\"\n",
" + rf\"[\\theta_{department_abbrev} \\mid t]={theta_expectation:6.2f}$\")\n",
" )\n",
"_ = ax.set_title(r\"Posterior of $\\theta_d$\")\n",
"_ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
"_ = plt.suptitle(fr\"$\\dot\\tau$ = {tau_}\", y=1)\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"attachments": {
"generated/multilevel-models/partial-pooling.png": {
"image/png": 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W1FavXq3Z2YIFC+RY7927p3ooFECcsZPtZM+eXUycOFEW1vrggw9kCz3d9u3b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\n/1JShYGdyALsX0oqMbATWYD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OC829sWKmY8eOslAYqziSjoGdYoQmz9jggm49CCT6xdVM\nmTLJAIIysmzeYC38aWJDErpCXbhwQX6u70hFCV9sNKtTpw6bVFM0DOwULwT1kydPyrojqGFy69Yt\nuVEGSybJWtg1ihs2KeEdE24oE0AUFwZ2IiKX4VUWIiKXYWAnInIZBnYiIpdhYCcichkGdiIil2Fg\nJyJyGQZ2IiKXYWAnInIZBnYiIpdhYCcichkGdiIil2FgJyJyGQZ2IiKXYWAnInIZBnYiIpdhYCci\nchkGdiIi4S7/DwnpOQrzXlGuAAAAAElFTkSuQmCC\n"
}
},
"cell_type": "markdown",
"id": "6bf0d185-35fe-4f2a-82fb-ed74aab2d574",
"metadata": {},
"source": [
"Try changing the data to `t = jnp.array([-20, -15, 30])`. Notice how\n",
"changing the data for one group does not affect the expectation of the\n",
"posterior of the other groups.\n",
"\n",
"Previously, the `complete_pooling` model returned an array of shape\n",
"`(200,)` with 200 being the size of the sample space of `Theta`. With\n",
"the addition of the conditional statement, what array shape does\n",
"`no_pooling` return? Make sure you understand the shape change, what\n",
"each dimension reflects, and why the values sum in the ways that they\n",
"do.\n",
"\n",
"The key theoretical distinction is that in *no pooling*, we’re asserting\n",
"that the timing behavior of professors in different departments is\n",
"independent of the behavior of professors from other departments\n",
"(i.e. when professors from one department show up for meetings carries\n",
"no information about when professors from a different department will\n",
"show up). This is an unrealistically strong assumption.\n",
"\n",
"The `no_pooling` and `complete_pooling` models highlight an important\n",
"practical tradeoff: *no pooling* can better capture differences between\n",
"departments but may suffer from high variance in its estimates due to\n",
"small sample sizes within each department. Complete pooling has lower\n",
"variance but may miss important systematic differences between\n",
"departments.\n",
"\n",
"## Partial pooling\n",
"\n",
"In partial pooling, every observation updates beliefs across multiple\n",
"levels of abstraction. The critical insight is that while departments\n",
"may differ in their typical timing behavior, the departments are not\n",
"statistically independent. They are influenced by common causes. To\n",
"model the president’s reasoning about these multiple levels of\n",
"uncertainty, we modify the `no_pooling` model by adding priors over\n",
"$\\mu$ and $\\tau$.\n",
"\n",
"Rather than being fixed values, $\\mu$ and $\\tau$ become latent\n",
"parameters to be jointly inferred alongside $\\theta_d$.\n",
"\n",
"The higher-level latent parameters $\\mu$ and $\\tau$ characterize a\n",
"“population-level” distribution from which department-specific\n",
"$\\theta_d$ values are generated.\n",
"\n",
"The key change to the model is that rather than\n",
"${ \\theta_d ~\\sim~ \\mathcal{N}\\left( \\dot{\\mu}{=}0, ~ \\dot{\\tau}{=}20 \\right) }$,\n",
"we have ${ \\theta_d ~\\sim~ \\mathcal{N}\\left(\\mu, ~ \\tau \\right) }$ and\n",
"specify hyperpriors on these new latent parameters:\n",
"${ \\mu ~\\sim~ \\mathcal{N}(0, ~ \\dot\\sigma_{\\mu}) }$ and\n",
"${ \\tau ~\\sim~ \\text{HalfCauchy}(\\dot\\sigma_{\\tau}) }$.\n",
"\n",
"Note that there are new fixed parameters: `mu_scale`\n",
"(${ \\dot\\sigma_\\mu}$) and `tau_scale` (${ \\dot\\sigma_\\tau }$), but I am\n",
"omitting there from the graphical schematic for the sake of visual\n",
"simplicity.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\mu ~\\sim&~ \\mathcal{N}(0, ~ \\dot\\sigma_{\\mu}) \\\\\n",
"\\tau ~\\sim&~ \\text{HalfCauchy}(\\dot\\sigma_{\\tau}) \\\\\n",
"\\theta_d ~\\sim&~ \\mathcal{N}\\left(\\mu, ~ \\tau \\right) \\\\\n",
"t_d ~\\sim&~ \\mathcal{N}(\\theta_d, ~ \\dot\\sigma{=}15) \\\\\n",
"d ~\\in&~ D,~~~ \\text{where}~~~ D = \\{ \\text{G}, ~ \\text{E}, ~ \\text{M} \\}\n",
"\\end{align*}\n",
"$$\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c462b737",
"metadata": {},
"outputs": [],
"source": [
"%reset -f\n",
"import jax\n",
"import jax.numpy as jnp\n",
"from memo import memo\n",
"from enum import IntEnum\n",
"from jax.scipy.stats.norm import pdf as normpdf\n",
"from jax.scipy.stats.cauchy import pdf as cauchypdf\n",
"from matplotlib import pyplot as plt\n",
"\n",
"normpdfjit = jax.jit(normpdf)\n",
"\n",
"class Department(IntEnum):\n",
" GOVERNMENT = 0\n",
" ENGLISH = 1\n",
" MATH = 2\n",
"\n",
"t = jnp.array([1, -15, 30])\n",
"sigma = 15\n",
"\n",
"Mu = jnp.linspace(-25, 25, 100) ### sample space for new hyperprior\n",
"Tau = jnp.linspace(1, 30, 100) ### sample space for new hyperprior\n",
"Theta = jnp.linspace(-40, 40, 200)\n",
"\n",
"### PDF for new hyperprior\n",
"@jax.jit\n",
"def half_cauchy(x, scale=1.0):\n",
" return 2 * cauchypdf(x, 0, scale)\n",
"\n",
"@jax.jit\n",
"def professor_arrival_likelihood(d, theta):\n",
" ### likelihood of a professor from department d \n",
" ### showing up t_d minutes early/late, \n",
" ### under the hypothesis given by theta and sigma.\n",
" return normpdf(t[d], loc=theta, scale=sigma)\n",
"\n",
"@memo\n",
"def department_model[_mu: Mu, _tau: Tau](d):\n",
" department: knows(_mu, _tau)\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, _mu, _tau))\n",
" return E[ department[professor_arrival_likelihood(d, theta)] ]\n",
"\n",
"@memo\n",
"def partial_pooling[_mu: Mu, _tau: Tau](mu_scale=5, tau_scale=5):\n",
" president: knows(_mu, _tau)\n",
" president: thinks[\n",
" population: chooses(mu in Mu, wpp=normpdfjit(mu, 0, mu_scale)),\n",
" population: chooses(tau in Tau, wpp=half_cauchy(tau, tau_scale)),\n",
" ]\n",
"\n",
" president: observes_event(\n",
" wpp=department_model[population.mu, population.tau]({Department.GOVERNMENT}))\n",
" president: observes_event(\n",
" wpp=department_model[population.mu, population.tau]({Department.ENGLISH}))\n",
" president: observes_event(\n",
" wpp=department_model[population.mu, population.tau]({Department.MATH}))\n",
"\n",
" return president[Pr[population.mu == _mu, population.tau == _tau]]"
]
},
{
"cell_type": "markdown",
"id": "7e1908d5-eaa1-4c04-b8b4-a5df1ad748e0",
"metadata": {},
"source": [
"Let’s think about what each variable represents.\n",
"\n",
"The likelihood model `professor_arrival_likelihood` gives the\n",
"probability that a professor from department $d$ shows up $t_d$ minutes\n",
"early/late, under a given $\\theta_d$ and $\\sigma$:\n",
"\n",
"$$\n",
"t_d ~\\sim~ \\mathcal{N}(\\theta_d, ~ \\dot\\sigma{=}15)\n",
"$$\n",
"\n",
"We can write the likelihood as\n",
"${ P(t_d \\mid \\theta_d, ~ \\mu, ~\\tau ~;~ \\sigma) }$. The marginal\n",
"posterior ${ P(\\theta_d \\mid t) }$ will thus represent the president’s\n",
"belief about the true value of $\\theta_d$ for a given department $d$."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c9bd4b35",
"metadata": {},
"outputs": [],
"source": [
"@memo\n",
"def department_model_theta[_theta: Theta](d, mu_scale, tau_scale):\n",
" obs: thinks[\n",
" department: chooses(mu in Mu, tau in Tau, wpp=partial_pooling[mu, tau](mu_scale, tau_scale)),\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau))\n",
" ]\n",
" obs: observes_event(wpp=professor_arrival_likelihood(d, department.theta))\n",
" obs: knows(_theta)\n",
" return obs[Pr[department.theta == _theta]]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b6f97195",
"metadata": {},
"outputs": [],
"source": [
"def plot_model(mu_scale=1, tau_scale=1, figsize=(10, 8), verbose=False):\n",
" posterior = partial_pooling(mu_scale=mu_scale, tau_scale=tau_scale)\n",
"\n",
" # Marginal over Tau (sum over Mu)\n",
" posterior_tau = posterior.sum(axis=0)\n",
" # Marginal over Mu (sum over Tau)\n",
" posterior_mu = posterior.sum(axis=1)\n",
"\n",
" fig, axs = plt.subplots(3, 1, figsize=figsize)\n",
"\n",
" ax = axs[0]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Mu, posterior_mu, label=r\"$P(\\mu \\mid t)$\")\n",
" mu_expectation = jnp.dot(Mu, posterior_mu)\n",
" ax.axvline(\n",
" mu_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\mu \\mid t]={mu_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\mu$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[1]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Tau, posterior_tau, label=r\"$P(\\tau \\mid t)$\")\n",
" tau_expectation = jnp.dot(Tau, posterior_tau)\n",
" ax.axvline(\n",
" tau_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\tau \\mid t]={tau_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\tau$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[2]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" theta_posterior = department_model_theta(d, mu_scale, tau_scale)\n",
" theta_expectation = jnp.dot(Theta, theta_posterior)\n",
" ax.plot(\n",
" Theta, \n",
" theta_posterior, \n",
" label=(\n",
" rf\"$P(\\theta_{department_abbrev} \\mid t),~ \" \n",
" + r\"\\operatorname{E}\" \n",
" + rf\"[\\theta_{department_abbrev} \\mid t]={theta_expectation:6.2f}$\"))\n",
" _ = ax.set_title(r\"Posterior of $\\theta_d$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" _ = plt.suptitle(f\"mu_scale = {mu_scale}, tau_scale = {tau_scale}\", y=1)\n",
" plt.tight_layout()\n",
" plt.show()\n",
"\n",
" if verbose:\n",
" for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" theta_posterior = department_model_theta(d, mu_scale, tau_scale)\n",
" posterior_mean = jnp.average(Theta, weights=theta_posterior)\n",
" posterior_second_moment = jnp.average(Theta**2, weights=theta_posterior)\n",
" posterior_variance = posterior_second_moment - posterior_mean**2\n",
" print(f\"{mu_scale=}, {tau_scale=} : E[θ{department_abbrev} | t] = {posterior_mean:7.3f} , Var[θ{department_abbrev} | t] = {posterior_variance:7.3f}\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8bf2d3bc",
"metadata": {},
"outputs": [],
"source": [
"import ipywidgets as widgets\n",
"from ipywidgets import interactive\n",
"\n",
"def plot_model_widget(mu_scale=1, tau_scale=1):\n",
" plot_model(mu_scale=mu_scale, tau_scale=tau_scale, figsize=(9, 7))\n",
"\n",
"interactive_plot = interactive(\n",
" plot_model_widget, \n",
" mu_scale=widgets.IntSlider(min=1, max=40, step=1, value=1),\n",
" tau_scale=widgets.IntSlider(min=1, max=40, step=1, value=1),\n",
")\n",
"output = interactive_plot.children[-1]\n",
"output.layout.height = '700px'\n",
"interactive_plot"
]
},
{
"attachments": {
"generated/multilevel-models/partial-pooling-multipleobs.png": {
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b3FDOwHxtlALAkstmzZpF63hklguICStgxo8fr+rWrRvgOyZyBgM7uU6OHDnU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\nTkSuQmCC\n"
}
},
"cell_type": "markdown",
"id": "90c6496e-79bc-444a-9b2b-b4860589cf36",
"metadata": {},
"source": [
"When `mu_scale` is small (e.g. ${ \\dot\\sigma_{\\mu}{=}1 }$) the location\n",
"of the distribution over $\\theta_d$ will be centered near zero. When\n",
"`mu_scale` is large (e.g. ${ \\dot\\sigma_{\\mu}{=}10 }$), the center of\n",
"${ \\mathcal{N}(\\mu, ~ \\tau) }$ can move to new locations with greater\n",
"freedom. This results in a more flexible population-level mean, allowing\n",
"the model to adapt to data that suggests professors generally arrive\n",
"early or late across all departments. With a large `mu_scale`, the model\n",
"places less prior constraint on where the overall population mean should\n",
"be, letting the data have more influence on determining this parameter.\n",
"\n",
"
\n",
"\n",
"When `tau_scale` is small (e.g. ${ \\dot\\sigma_{\\tau}{=}1 }$), the\n",
"distribution ${ \\theta_d ~\\sim~ \\mathcal{N}(\\mu, ~ \\tau) }$ will be\n",
"narrow, which will result in strong shrinkage of department-specific\n",
"means toward the overall population mean. This effectively reduces the\n",
"differences between departments, making the model behave more like the\n",
"complete pooling model. The practical interpretation is that the model\n",
"assumes departments are relatively homogeneous in their timing behavior.\n",
"\n",
"When `tau_scale` is large (e.g. ${ \\dot\\sigma_{\\tau}{=}20 }$), the\n",
"${ \\theta_d }$ can diverge more freely from the population mean,\n",
"resulting in weaker shrinkage effects. Department-specific estimates\n",
"will be closer to their empirical means and less influenced by data from\n",
"other departments. This allows the model to capture more heterogeneity\n",
"between departments, making it behave more like the no pooling model\n",
"while still maintaining some information sharing.\n",
"\n",
"In this way, a large ${ \\dot\\sigma_{\\mu} }$ and small\n",
"${ \\dot\\sigma_{\\tau} }$ would create a model that assumes departments\n",
"are relatively homogeneous (due to small $\\tau$) but is very flexible\n",
"about where the overall population mean might be (due to large $\\mu$\n",
"scale). This combination would result in strong shrinkage of\n",
"department-specific estimates toward a population mean that is itself\n",
"quite adaptable to the data. Conversely, a small ${ \\dot\\sigma_{\\mu} }$\n",
"and large ${ \\dot\\sigma_{\\tau} }$ would create a model with a strong\n",
"prior belief the population mean is near zero, but allows substantial\n",
"variation between departments.\n",
"\n",
"### Multiple observations (with missing data)\n",
"\n",
"What if the president instead had a large meeting with 7 professors and\n",
"the departments were not equally represented? How would she update her\n",
"beliefs given unequal observations? Let’s say that she invited 3\n",
"professors from the Department of Government, 3 from the Department of\n",
"English, and 1 from the Department of Math. We can explore how\n",
"modulating the higher-level hyperpriors changes her posterior inference\n",
"about each department.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\mu ~\\sim&~ \\mathcal{N}(0, ~ \\dot\\sigma_{\\mu}) \\\\\n",
"\\tau ~\\sim&~ \\text{HalfCauchy}(\\dot\\sigma_{\\tau}) \\\\\n",
"\\theta_d ~\\sim&~ \\mathcal{N}\\left(\\mu, ~ \\tau \\right) \\\\\n",
"t_{d,i} ~\\sim&~ \\mathcal{N}(\\theta_d, ~ \\dot\\sigma{=}15) \\\\\n",
"d ~\\in&~ D,~~~ \\text{where}~~~ D = \\{ \\text{G}, ~ \\text{E}, ~ \\text{M} \\}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"\n",
"\n",
"In this diagram we add a new plate, $i$, which is nested in plate $d$,\n",
"to index the number of observation of each department."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "70ac0ae8",
"metadata": {},
"outputs": [],
"source": [
"%reset -f\n",
"import jax\n",
"import jax.numpy as jnp\n",
"from memo import memo\n",
"from enum import IntEnum\n",
"from jax.scipy.stats.norm import pdf as normpdf\n",
"from jax.scipy.stats.norm import logpdf as normlogpdf\n",
"from jax.scipy.stats.cauchy import pdf as cauchypdf\n",
"from matplotlib import pyplot as plt\n",
"\n",
"normpdfjit = jax.jit(normpdf)\n",
"\n",
"class Department(IntEnum):\n",
" GOVERNMENT = 0\n",
" ENGLISH = 1\n",
" MATH = 2\n",
"\n",
"###NEW\n",
"t = jnp.array([\n",
" [-10, 1, 11], \n",
" [-16, -15, -14], \n",
" [30, jnp.nan, jnp.nan],\n",
"])\n",
"\n",
"sigma = 15\n",
"\n",
"Mu = jnp.linspace(-25, 25, 100)\n",
"Tau = jnp.linspace(1, 30, 100)\n",
"Theta = jnp.linspace(-40, 40, 200)\n",
"\n",
"@jax.jit\n",
"def half_cauchy(x, scale=1.0):\n",
" return 2 * cauchypdf(x, 0, scale)\n",
"\n",
"@jax.jit\n",
"def professor_arrival_likelihood(d, theta):\n",
" ### likelihood of a professor from department d \n",
" ### showing up t_d minutes early/late, \n",
" ### under the hypothesis given by theta and sigma.\n",
" return jnp.exp(jnp.nansum(normlogpdf(t[d], theta, sigma))) ###NEW\n",
"\n",
"@memo\n",
"def department_model[_mu: Mu, _tau: Tau](d):\n",
" department: knows(_mu, _tau)\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, _mu, _tau))\n",
" return E[ department[professor_arrival_likelihood(d, theta)] ]\n",
"\n",
"@memo\n",
"def partial_pooling[_mu: Mu, _tau: Tau](mu_scale=5, tau_scale=5):\n",
" president: knows(_mu, _tau)\n",
" president: thinks[\n",
" population: chooses(mu in Mu, wpp=normpdfjit(mu, 0, mu_scale)),\n",
" population: chooses(tau in Tau, wpp=half_cauchy(tau, tau_scale)),\n",
" ]\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.GOVERNMENT}))\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.ENGLISH}))\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.MATH}))\n",
" return president[Pr[population.mu == _mu, population.tau == _tau]]\n",
"\n",
"@memo\n",
"def department_model_theta[_theta: Theta](d, mu_scale, tau_scale):\n",
" obs: thinks[\n",
" department: chooses(mu in Mu, tau in Tau, wpp=partial_pooling[mu, tau](mu_scale, tau_scale)),\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau))\n",
" ]\n",
" obs: observes_event(wpp=professor_arrival_likelihood(d, department.theta))\n",
" obs: knows(_theta)\n",
" return obs[Pr[department.theta == _theta]]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7e479317",
"metadata": {},
"outputs": [],
"source": [
"def plot_model(mu_scale=1, tau_scale=1, figsize=(10, 8)):\n",
" posterior = partial_pooling(mu_scale=mu_scale, tau_scale=tau_scale)\n",
"\n",
" # Marginal over Tau (sum over Mu)\n",
" posterior_tau = posterior.sum(axis=0)\n",
" # Marginal over Mu (sum over Tau)\n",
" posterior_mu = posterior.sum(axis=1)\n",
"\n",
" fig, axs = plt.subplots(3, 1, figsize=figsize)\n",
"\n",
" ax = axs[0]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Mu, posterior_mu, label=r\"$P(\\mu \\mid t)$\")\n",
" mu_expectation = jnp.dot(Mu, posterior_mu)\n",
" ax.axvline(\n",
" mu_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\mu \\mid t]={mu_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\mu$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[1]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Tau, posterior_tau, label=r\"$P(\\tau \\mid t)$\")\n",
" tau_expectation = jnp.dot(Tau, posterior_tau)\n",
" ax.axvline(\n",
" tau_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\tau \\mid t]={tau_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\tau$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[2]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" theta_posterior = department_model_theta(d, mu_scale, tau_scale)\n",
" theta_expectation = jnp.dot(Theta, theta_posterior)\n",
" ax.plot(\n",
" Theta, \n",
" theta_posterior, \n",
" label=(\n",
" rf\"$P(\\theta_{department_abbrev} \\mid t),~ \" \n",
" + r\"\\operatorname{E}\" \n",
" + rf\"[\\theta_{department_abbrev} \\mid t]={theta_expectation:6.2f}$\"))\n",
" _ = ax.set_title(r\"Posterior of $\\theta_d$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" _ = plt.suptitle(f\"mu_scale = {mu_scale}, tau_scale = {tau_scale}\", y=1)\n",
" plt.tight_layout()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "675eafa3",
"metadata": {},
"outputs": [],
"source": [
"import ipywidgets as widgets\n",
"from ipywidgets import interactive\n",
"\n",
"def plot_model_widget(mu_scale=1, tau_scale=1):\n",
" plot_model(mu_scale=mu_scale, tau_scale=tau_scale, figsize=(9, 7))\n",
"\n",
"interactive_plot = interactive(\n",
" plot_model_widget, \n",
" mu_scale=widgets.IntSlider(min=1, max=40, step=1, value=1),\n",
" tau_scale=widgets.IntSlider(min=1, max=40, step=1, value=1),\n",
")\n",
"output = interactive_plot.children[-1]\n",
"output.layout.height = '700px'\n",
"interactive_plot"
]
},
{
"attachments": {
"generated/multilevel-models/partial-pooling-multipleobs-learnedsigma.png": {
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41alTR86ePTvFq+bwQUCIp0yZMnH2rb3CwsJsn8Al7ub999/Xr6f06dPHuL4yZ84se/To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\n"
}
},
"cell_type": "markdown",
"id": "a328eaf8-c940-4968-9c38-dd49e63479bd",
"metadata": {},
"source": [
"When `tau_scale` is small (e.g. ${ \\dot\\sigma_{\\tau}{=}1 }$), the\n",
"distribution ${ \\theta_d ~\\sim~ \\mathcal{N}(\\mu, ~ \\tau) }$ will be\n",
"narrow, which will pressure the individual ${ \\theta_d }$ to be similar\n",
"to each other. When `tau_scale` is large\n",
"(e.g. ${ \\dot\\sigma_{\\tau}{=}20 }$), the ${ \\theta_d }$ can diverge more\n",
"freely resulting in values quite different from each other. Think about\n",
"how this will interact with the number of observations and the values of\n",
"those observations.\n",
"\n",
"When `mu_scale` is small (e.g. ${ \\dot\\sigma_{\\mu}{=}1 }$) the location\n",
"of the distribution over $\\theta_d$ will be be centered near zero. When\n",
"`mu_scale` is large (e.g. ${ \\dot\\sigma_{\\mu}{=}20 }$), the center of\n",
"${ \\mathcal{N}(\\mu, ~ \\tau) }$ can move to new locations.\n",
"\n",
"In this way, a large ${ \\dot\\sigma_{\\mu} }$ and small\n",
"${ \\dot\\sigma_{\\tau} }$ would allow ${ \\mathcal{N}(\\mu, ~ \\tau) }$ to\n",
"move to easily move to a new location that accommodates the broader\n",
"tendencies of departments and professors, but would constrain the\n",
"dispersion between departments. Notice how increasing `mu_scale` allows\n",
"the posterior ${ P(\\mu \\mid t) }$ to move away from zero towards the\n",
"mean of the combined data, whereas decreasing `mu_scale` pulls the\n",
"expectation ${ \\operatorname{E}[\\mu \\mid t] }$ towards zero. Also notice\n",
"how this effect is stronger when `tau_scale` is small.\n",
"\n",
"Pay close attention to the interaction between `mu_scale`, `tau_scale`,\n",
"and the observations for each department (including the expectation and\n",
"variance of the observations of each department).\n",
"\n",
"### Multiple observations with missing data and learned variance\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\mu ~\\sim&~ \\mathcal{N}(0, ~ \\dot\\sigma_{\\mu}) \\\\\n",
"\\tau ~\\sim&~ \\text{HalfCauchy}(\\dot\\sigma_{\\tau}) \\\\\n",
"\\theta_d ~\\sim&~ \\mathcal{N}(\\mu, ~ \\tau) \\\\\n",
"\\sigma_d ~\\sim&~ \\text{HalfCauchy}(5) \\\\\n",
"t_{d,i} ~\\sim&~ \\mathcal{N}(\\theta_d, ~ \\sigma_d)\n",
"\\end{align*}\n",
"$$\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a8181dfd",
"metadata": {},
"outputs": [],
"source": [
"%reset -f\n",
"import jax\n",
"import jax.numpy as jnp\n",
"from memo import memo\n",
"from enum import IntEnum\n",
"from jax.scipy.stats.norm import pdf as normpdf\n",
"from jax.scipy.stats.norm import logpdf as normlogpdf\n",
"from jax.scipy.stats.cauchy import pdf as cauchypdf\n",
"from matplotlib import pyplot as plt\n",
"\n",
"normpdfjit = jax.jit(normpdf)\n",
"\n",
"class Department(IntEnum):\n",
" GOVERNMENT = 0\n",
" ENGLISH = 1\n",
" MATH = 2\n",
"\n",
"t = jnp.array([\n",
" [-10, 1, 11], \n",
" [-16, -15, -14], \n",
" [30, jnp.nan, jnp.nan],\n",
"])\n",
"\n",
"Mu = jnp.linspace(-25, 25, 100)\n",
"Tau = jnp.linspace(1, 30, 100)\n",
"Theta = jnp.linspace(-40, 40, 200)\n",
"Sigma = jnp.linspace(1, 30, 100) ###NEW\n",
"\n",
"@jax.jit\n",
"def half_cauchy(x, scale=1.0):\n",
" return 2 * cauchypdf(x, 0, scale)\n",
"\n",
"@jax.jit\n",
"def professor_arrival_likelihood(d, theta, sigma): ###NEW\n",
" ### likelihood of a professor from department d \n",
" ### showing up t_d minutes early/late, \n",
" ### under the hypothesis given by theta and sigma.\n",
" return jnp.exp(jnp.nansum(normlogpdf(t[d], theta, sigma)))\n",
"\n",
"@memo(cache=True)\n",
"def department_model[_mu: Mu, _tau: Tau](d):\n",
" department: knows(_mu, _tau)\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, _mu, _tau))\n",
" department: chooses(sigma in Sigma, wpp=half_cauchy(sigma, 5)) ###NEW\n",
" return E[ department[professor_arrival_likelihood(d, theta, sigma)] ] ###NEW\n",
"\n",
"@memo(cache=True)\n",
"def partial_pooling[_mu: Mu, _tau: Tau](mu_scale=5, tau_scale=5):\n",
" president: knows(_mu, _tau)\n",
" president: thinks[\n",
" population: chooses(mu in Mu, wpp=normpdfjit(mu, 0, mu_scale)),\n",
" population: chooses(tau in Tau, wpp=half_cauchy(tau, tau_scale)),\n",
" ]\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.GOVERNMENT}))\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.ENGLISH}))\n",
" president: observes_event(wpp=department_model[population.mu, population.tau]({Department.MATH}))\n",
" return president[Pr[population.mu == _mu, population.tau == _tau]]\n",
"\n",
"@memo(cache=True)\n",
"def department_model_theta[_theta: Theta](d, mu_scale, tau_scale):\n",
" obs: thinks[\n",
" department: chooses(mu in Mu, tau in Tau, wpp=partial_pooling[mu, tau](mu_scale, tau_scale)),\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau)),\n",
" department: chooses(sigma in Sigma, wpp=half_cauchy(sigma, 5)), ###NEW\n",
" ]\n",
" obs: observes_event(wpp=professor_arrival_likelihood(d, department.theta, department.sigma)) ###NEW\n",
" obs: knows(_theta)\n",
" return obs[Pr[department.theta == _theta]]\n",
"\n",
"@memo(cache=True)\n",
"def department_model_sigma[_sigma: Sigma](d, mu_scale, tau_scale): ###NEW\n",
" obs: thinks[\n",
" department: chooses(mu in Mu, tau in Tau, wpp=partial_pooling[mu, tau](mu_scale, tau_scale)),\n",
" department: chooses(theta in Theta, wpp=normpdfjit(theta, mu, tau)),\n",
" department: chooses(sigma in Sigma, wpp=half_cauchy(sigma, 5)),\n",
" ]\n",
" obs: observes_event(wpp=professor_arrival_likelihood(d, department.theta, department.sigma))\n",
" obs: knows(_sigma)\n",
" return obs[Pr[department.sigma == _sigma]]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7878f95a",
"metadata": {},
"outputs": [],
"source": [
"# Cache for precomputed results\n",
"cache = {}\n",
"\n",
"def compute_distributions(mu_scale, tau_scale, verbose=False):\n",
" \"\"\"Retrieve from cache or compute the JAX-based distributions.\"\"\"\n",
" key = (mu_scale, tau_scale)\n",
" if key in cache:\n",
" return cache[key] # Use cached results\n",
"\n",
" if verbose:\n",
" print(f\"{mu_scale=}, {tau_scale=}\")\n",
"\n",
" # Cache results\n",
" cache[key] = (\n",
" partial_pooling(mu_scale=mu_scale, tau_scale=tau_scale).sum(axis=1), \n",
" partial_pooling(mu_scale=mu_scale, tau_scale=tau_scale).sum(axis=0), \n",
" {d: department_model_sigma(d, mu_scale, tau_scale) for d in Department}, \n",
" {d: department_model_theta(d, mu_scale, tau_scale) for d in Department},\n",
" )\n",
" return cache[key]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "821ea852",
"metadata": {},
"outputs": [],
"source": [
"def plot_model(mu_scale=1, tau_scale=1, figsize=(10, 8)):\n",
" posterior_mu, posterior_tau, sigma_posteriors, theta_posteriors = compute_distributions(mu_scale, tau_scale)\n",
"\n",
" fig, axs = plt.subplots(4, 1, figsize=figsize)\n",
"\n",
" ax = axs[0]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Mu, posterior_mu, label=r\"$P(\\mu \\mid t)$\")\n",
" mu_expectation = jnp.dot(Mu, posterior_mu)\n",
" ax.axvline(\n",
" mu_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\mu \\mid t]={mu_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\mu$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[1]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" ax.plot(Tau, posterior_tau, label=r\"$P(\\tau \\mid t)$\")\n",
" tau_expectation = jnp.dot(Tau, posterior_tau)\n",
" ax.axvline(\n",
" tau_expectation, \n",
" color='red', \n",
" linestyle='--', \n",
" label=r\"$\\operatorname{E}\" + rf\"[\\tau \\mid t]={tau_expectation:6.2f}$\")\n",
" _ = ax.set_title(r\"Posterior of $\\tau$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[2]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" sigma_posterior = sigma_posteriors[d]\n",
" sigma_expectation = jnp.dot(Sigma, sigma_posterior)\n",
" ax.plot(\n",
" Sigma, \n",
" sigma_posterior, \n",
" label=(\n",
" rf\"$P(\\sigma_{department_abbrev} \\mid t),~ \" \n",
" + r\"\\operatorname{E}\" \n",
" + rf\"[\\sigma_{department_abbrev} \\mid t]={sigma_expectation:6.2f}$\"))\n",
" _ = ax.set_xlim(-1, 20)\n",
" _ = ax.set_title(r\"Posterior of $\\sigma_d$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" ax = axs[3]\n",
" ax.axvline(0, color=\"black\", linestyle=\"-\")\n",
" for d in Department:\n",
" department_name = d.name\n",
" department_abbrev = department_name[0]\n",
" theta_posterior = theta_posteriors[d]\n",
" theta_expectation = jnp.dot(Theta, theta_posterior)\n",
" ax.plot(\n",
" Theta, \n",
" theta_posterior, \n",
" label=(\n",
" rf\"$P(\\theta_{department_abbrev} \\mid t),~ \" \n",
" + r\"\\operatorname{E}\" \n",
" + rf\"[\\theta_{department_abbrev} \\mid t]={theta_expectation:6.2f}$\"))\n",
" _ = ax.set_xlim(-20, 40)\n",
" _ = ax.set_title(r\"Posterior of $\\theta_d$\")\n",
" _ = ax.legend(bbox_to_anchor=(0.9, 0.5), loc='center left')\n",
"\n",
" _ = plt.suptitle(f\"mu_scale = {mu_scale}, tau_scale = {tau_scale}\", y=1)\n",
" plt.tight_layout()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9559f883",
"metadata": {},
"outputs": [],
"source": [
"import ipywidgets as widgets\n",
"from ipywidgets import interactive\n",
"\n",
"for mu_scale in range(1, 20, 3):\n",
" for tau_scale in range(1, 20, 3):\n",
" compute_distributions(mu_scale, tau_scale, verbose=True)\n",
"\n",
"def plot_model_widget(mu_scale=1, tau_scale=1):\n",
" plot_model(mu_scale=mu_scale, tau_scale=tau_scale, figsize=(9, 7))\n",
"\n",
"interactive_plot = interactive(\n",
" plot_model_widget, \n",
" mu_scale=widgets.IntSlider(min=1, max=19, step=3, value=1),\n",
" tau_scale=widgets.IntSlider(min=1, max=19, step=3, value=1),\n",
")\n",
"output = interactive_plot.children[-1]\n",
"output.layout.height = '700px'\n",
"interactive_plot"
]
},
{
"attachments": {
"assets/multilevel-models/models-contrast.png": {
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2VK8zFkYCriJAWeGq7mJlScASAtg/o0qVKvLDDz/oDergXhAsWSkr4A8+e/ZsueOOO6Rc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\n6qm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tIMzEHOY6cT+W++7lhSaDK1vwf/3rXy3hxtixY027Hff2q32FQ4B3FrOJnj17mvMz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\nQ4YM7lMn+Z6Q1KlTu9Niauc6U1k2ccjBK1xHD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}
},
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"id": "887567a8-c79a-4760-9f15-058fc097d531",
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"source": [
"## Models contrasted\n",
"\n",
"\n",
"\n",
"> **Further reading**\n",
">\n",
"> - McElreath (2016, Chapters 1, 13, 14)\n",
"> - Gelman (2014, Chapter 5)\n",
"> - Kruschke (2015, Chapter 9)"
]
}
],
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