diff --git a/examples/howto/hypothesis_testing.ipynb b/examples/howto/hypothesis_testing.ipynb new file mode 100644 index 00000000..34c17a1e --- /dev/null +++ b/examples/howto/hypothesis_testing.ipynb @@ -0,0 +1,659 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9b22c91b-aa50-4807-a2c4-5d4ec91b7747", + "metadata": { + "tags": [] + }, + "source": [ + "(hypothesis-testing)=\n", + "# Bayesian Hypothesis Testing - an introduction\n", + "\n", + ":::{post} December 2024\n", + ":tags: hypothesis testing, bayesian decision theory\n", + ":category: beginner \n", + ":author: Benjamin T. Vincent\n", + ":::" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a71c0158", + "metadata": {}, + "outputs": [], + "source": [ + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pymc as pm" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e8c93da2", + "metadata": {}, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = 'retina'\n", + "az.style.use(\"arviz-darkgrid\")\n", + "plt.rcParams.update({\"font.size\": 14, \"figure.constrained_layout.use\": False})\n", + "SEED = 42\n", + "rng = np.random.default_rng(SEED)" + ] + }, + { + "cell_type": "markdown", + "id": "a551c9b3", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "Bayesian hypothesis testing provides a flexible and intuitive way to assess whether parameters differ from specified values. Unlike classical methods focusing on p-values, Bayesian methods let us directly compute probabilities of hypotheses and quantify the strength of evidence in various ways.\n", + "\n", + "In this tutorial, we'll use PyMC to:\n", + "\n", + "* Fit a simple model to synthetic data and obtain samples from the prior and posterior distributions.\n", + "* Demonstrate the following Bayesian hypothesis testing methods:\n", + " * Posterior probability statements\n", + " * Highest Density Intervals (HDIs)\n", + " * Regions of Practical Equivalence (ROPE)\n", + " * Bayes Factors using ArviZ's `plot_bf` function\n", + "\n", + "We'll work through a scenario where we want to know if the mean of some metric (e.g., sales) is different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "5c268654", + "metadata": {}, + "source": [ + "## Setting up the example\n", + "\n", + "Rather than focus on a complex example, we'll pick a trivial one were we are simply estimating the mean of a single variable. This will allow us to focus on the hypothesis testing. The important thing is what we do with our MCMC samples, not the particulars of the model." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3f9fabda", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 171, + "width": 1105 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "true_mu = 2.0\n", + "true_sigma = 3.0\n", + "n = 12\n", + "\n", + "x = rng.normal(loc=true_mu, scale=true_sigma, size=n)\n", + "\n", + "fig, ax = plt.subplots(figsize=(14, 1))\n", + "ax.plot(x, np.zeros_like(x), \"ro\")\n", + "ax.set(yticklabels=[], yticks=[], xlabel=\"x\", title=\"Observations\");" + ] + }, + { + "cell_type": "markdown", + "id": "159213a0", + "metadata": {}, + "source": [ + "## Sampling from the prior and posterior\n", + "\n", + "Now we'll build our simple model. Again, the focus here is not on the model of the data as such, but simply obtaining a meaningful prior and posterior distribution. We'll ask for more MCMC samples than we normally do, so that we can get a more accurate approximation of the prior and posterior distributions." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bfaed521", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [mu, sigma, y]\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [mu, sigma]\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "14efb8f02a424c809a90b180accd5120", + "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 10_000 draw iterations (4_000 + 40_000 draws total) took 2 seconds.\n"
+     ]
+    }
+   ],
+   "source": [
+    "with pm.Model() as model:\n",
+    "    # priors\n",
+    "    mu = pm.Normal(\"mu\", mu=0, sigma=2)\n",
+    "    sigma = pm.Gamma(\"sigma\", alpha=2, beta=1)\n",
+    "    # likelihood\n",
+    "    pm.Normal(\"y\", mu=mu, sigma=sigma, observed=x)\n",
+    "    # sample\n",
+    "    idata = pm.sample_prior_predictive(samples=10_000)\n",
+    "    idata.extend(pm.sample(draws=10_000))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "790c4959",
+   "metadata": {},
+   "source": [
+    "We didn't get any warnings from the sampling processes.\n",
+    "\n",
+    "It is good practice to visualise the posterior distribution, so below we'll look at the joint posterior over $\\mu$ and $\\sigma$ parameters. Everything looks fine here."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "59a1800f",
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
" + ] + }, + "metadata": { + "image/png": { + "height": 439, + "width": 620 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_pair(idata, var_names=[\"mu\", \"sigma\"], marginals=True, point_estimate=\"mean\");" + ] + }, + { + "cell_type": "markdown", + "id": "e55dda73", + "metadata": {}, + "source": [ + "Finally, seeing as $\\mu$ is the core parameter of interest, we'll visualise both the prior and posterior distributions for $\\mu$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c4d2dc2d", + "metadata": { + "tags": [ + "hide-input" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 301, + "width": 1140 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = az.plot_dist(idata.prior[\"mu\"], label=\"Prior\", color=\"C0\", figsize=(14, 3))\n", + "az.plot_dist(idata.posterior[\"mu\"], label=\"Posterior\", color=\"C1\", ax=ax)\n", + "ax.set(title=r\"Prior and posterior distributions of $\\mu$\");" + ] + }, + { + "cell_type": "markdown", + "id": "d200233f", + "metadata": {}, + "source": [ + "## Bayesian Hypothesis Testing Methods\n", + "\n", + "### Posterior probability statements\n", + "\n", + "The simplest form of hypothesis testing is to ask whether the mean is greater than zero. This is equivalent to asking whether the probability that $\\mu$ is greater than zero is greater than 0.5. We can compute this directly from the samples. So computing compute $P(\\mu>0 | x)$ is as simple as counting the number of samples where $\\mu>0$ and dividing by the total number of samples - equivalent to computing the mean of the samples where $\\mu>0$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "18369e50", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.95345" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mu_samples = idata.posterior[\"mu\"].values\n", + "p_mu_greater_0 = np.mean(mu_samples > 0)\n", + "p_mu_greater_0" + ] + }, + { + "cell_type": "markdown", + "id": "52913dbd", + "metadata": {}, + "source": [ + "It could also be that we have some kind of minimum meaningful threshold that we care about. For example, we might care about whether the mean is greater than 0.1. We can compute this in the same way." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "3790c7e8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.940775" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p_mu_greater = np.mean(mu_samples > 0.1)\n", + "p_mu_greater" + ] + }, + { + "cell_type": "markdown", + "id": "7cea999e", + "metadata": {}, + "source": [ + "We can also include such information in a visual plot using `az.plot_posterior`." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "d1d2997d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 308, + "width": 1105 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_posterior(idata, var_names=[\"mu\"], ref_val=0, hdi_prob=\"hide\", figsize=(14, 3));" + ] + }, + { + "cell_type": "markdown", + "id": "6511a148", + "metadata": {}, + "source": [ + "### Highest Density Intervals (HDIs)\n", + "\n", + "The HDI gives an interval of highest probability density. If zero is outside the HDI, it’s unlikely the parameter is near zero." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "8aed0b24", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.12833959, 2.84289526])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hdi_mu = az.hdi(idata, var_names=[\"mu\"])[\"mu\"].data\n", + "hdi_mu" + ] + }, + { + "cell_type": "markdown", + "id": "c05274a2", + "metadata": {}, + "source": [ + "In this case, zero is within the HDI, so based on this measure, we can't express much confidence that the mean is different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "f3365bc1", + "metadata": {}, + "source": [ + "Again, we can use `az.plot_posterior` to visualize the HDIs." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "4c67ca02", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 308, + "width": 1105 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_posterior(idata, var_names=[\"mu\"], figsize=(14, 3));" + ] + }, + { + "cell_type": "markdown", + "id": "2bc616ec", + "metadata": {}, + "source": [ + "### Region of Practical Equivalence (ROPE)\n", + "\n", + "If the probability that the parameter is within a certain range is high, we can say that the parameter is practically equivalent to that value. This is a useful way to express that we don't care about small differences. \n", + "\n", + "One proposal is that we now examine the HDI's but compare them to the ROPE and not zero." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "48b6496f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.022825" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rope = [-0.1, 0.1]\n", + "p_in_rope = np.mean((mu_samples > rope[0]) & (mu_samples < rope[1]))\n", + "p_in_rope" + ] + }, + { + "cell_type": "markdown", + "id": "5a623e4a", + "metadata": {}, + "source": [ + "Third time in a row, `arviz` has our back and can plot the ROPE and HDIs." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "1cdea94a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 308, + "width": 1105 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_posterior(idata, var_names=[\"mu\"], rope=rope, figsize=(14, 3));" + ] + }, + { + "cell_type": "markdown", + "id": "f2d486d2", + "metadata": {}, + "source": [ + "This shows that there is only a 2.6% chance that the mean is within the chosen ROPE." + ] + }, + { + "cell_type": "markdown", + "id": "0524af06", + "metadata": {}, + "source": [ + "### Bayes Factors\n", + "\n", + "Bayes Factors provide a Bayesian alternative to classical hypothesis tests, allowing you to weigh evidence for one hypothesis relative to another. In the simplest case—testing whether $\\mu=0$ versus $\\mu \\neq 0$ — the Bayes Factor (BF) tells you how much more (or less) likely your observed data are under the model where $\\mu=0$ than under the model where $\\mu$ is free to vary.\n", + "\n", + "Intuitively, the Bayes Factor can be understood by comparing the density of $\\mu$ at zero before and after observing the data. Before collecting data, you have a prior belief about $\\mu$. This prior density at $\\mu=0$ represents how plausible zero was considered initially. After seeing the data, you update these beliefs to get the posterior distribution. The posterior density at $\\mu=0$ indicates how plausible zero remains given the evidence. The ratio of these densities—the Savage-Dickey ratio—is closely related to the Bayes Factor. If the data make \n", + "$\\mu=0$ more plausible relative to your initial belief, the Bayes Factor will favor $\\mu=0$. If the data diminish the credibility of $\\mu=0$, the Bayes Factor will favor $\\mu\\neq0$\n", + "\n", + "Because the Bayes Factor directly compares how the data update the prior odds of each hypothesis, the choice of prior is crucial. A strong prior concentration at $\\mu=0$ could make it harder for data to move the posterior density away from zero, influencing the resulting Bayes Factor. On the other hand, a diffuse prior might make it easier for data to shift your beliefs about $\\mu$. Thus, specifying a reasonable and justifiable prior distribution is essential when using Bayes Factors for hypothesis testing." + ] + }, + { + "cell_type": "markdown", + "id": "645e7fb3", + "metadata": {}, + "source": [ + "Yet again, `arviz` has a function to help us here. We can use `plot_bf` to compute the Bayes Factor for the hypothesis that $\\mu=0$ versus $\\mu\\neq0$." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "16003a42", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 351, + "width": 1166 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_bf(idata, var_name=\"mu\", ref_val=0, figsize=(14, 3));" + ] + }, + { + "cell_type": "markdown", + "id": "f10d77d2", + "metadata": {}, + "source": [ + "We can see that the probability of $\\mu=0$ has gone _down_ after observing the data. This is reflected in the value of $BF_{01}=0.66$ in that it is less than 1." + ] + }, + { + "cell_type": "markdown", + "id": "650f409c", + "metadata": {}, + "source": [ + "## Summary" + ] + }, + { + "cell_type": "markdown", + "id": "763e2a54", + "metadata": {}, + "source": [ + "## Authors\n", + "* Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in December, 2024." + ] + }, + { + "cell_type": "markdown", + "id": "1aec5c13", + "metadata": {}, + "source": [ + "## Watermark" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "1f25d6b6-f0a1-4ca3-96f5-9a5a858bb461", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last updated: Mon Dec 09 2024\n", + "\n", + "Python implementation: CPython\n", + "Python version : 3.12.8\n", + "IPython version : 8.30.0\n", + "\n", + "pytensor: 2.26.4\n", + "xarray : 2024.11.0\n", + "\n", + "arviz : 0.20.0\n", + "numpy : 1.26.4\n", + "pymc : 5.19.1\n", + "matplotlib: 3.9.3\n", + "\n", + "Watermark: 2.5.0\n", + "\n" + ] + } + ], + "source": [ + "%load_ext watermark\n", + "%watermark -n -u -v -iv -w -p pytensor,xarray" + ] + }, + { + "cell_type": "markdown", + "id": "818c2750-89d5-4310-8df2-91b1e531afe7", + "metadata": {}, + "source": [ + ":::{include} ../page_footer.md\n", + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pymc_env", + "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": "3.12.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/howto/hypothesis_testing.myst.md b/examples/howto/hypothesis_testing.myst.md new file mode 100644 index 00000000..6746c561 --- /dev/null +++ b/examples/howto/hypothesis_testing.myst.md @@ -0,0 +1,210 @@ +--- +jupytext: + text_representation: + extension: .md + format_name: myst + format_version: 0.13 +kernelspec: + display_name: pymc_env + language: python + name: python3 +--- + +(hypothesis-testing)= +# Bayesian Hypothesis Testing - an introduction + +:::{post} December 2024 +:tags: hypothesis testing, bayesian decision theory +:category: beginner +:author: Benjamin T. Vincent +::: + +```{code-cell} ipython3 +import arviz as az +import matplotlib.pyplot as plt +import numpy as np +import pymc as pm +``` + +```{code-cell} ipython3 +%config InlineBackend.figure_format = 'retina' +az.style.use("arviz-darkgrid") +plt.rcParams.update({"font.size": 14, "figure.constrained_layout.use": False}) +SEED = 42 +rng = np.random.default_rng(SEED) +``` + +## Introduction + +Bayesian hypothesis testing provides a flexible and intuitive way to assess whether parameters differ from specified values. Unlike classical methods focusing on p-values, Bayesian methods let us directly compute probabilities of hypotheses and quantify the strength of evidence in various ways. + +In this tutorial, we'll use PyMC to: + +* Fit a simple model to synthetic data and obtain samples from the prior and posterior distributions. +* Demonstrate the following Bayesian hypothesis testing methods: + * Posterior probability statements + * Highest Density Intervals (HDIs) + * Regions of Practical Equivalence (ROPE) + * Bayes Factors using ArviZ's `plot_bf` function + +We'll work through a scenario where we want to know if the mean of some metric (e.g., sales) is different from zero. + ++++ + +## Setting up the example + +Rather than focus on a complex example, we'll pick a trivial one were we are simply estimating the mean of a single variable. This will allow us to focus on the hypothesis testing. The important thing is what we do with our MCMC samples, not the particulars of the model. + +```{code-cell} ipython3 +true_mu = 2.0 +true_sigma = 3.0 +n = 12 + +x = rng.normal(loc=true_mu, scale=true_sigma, size=n) + +fig, ax = plt.subplots(figsize=(14, 1)) +ax.plot(x, np.zeros_like(x), "ro") +ax.set(yticklabels=[], yticks=[], xlabel="x", title="Observations"); +``` + +## Sampling from the prior and posterior + +Now we'll build our simple model. Again, the focus here is not on the model of the data as such, but simply obtaining a meaningful prior and posterior distribution. We'll ask for more MCMC samples than we normally do, so that we can get a more accurate approximation of the prior and posterior distributions. + +```{code-cell} ipython3 +with pm.Model() as model: + # priors + mu = pm.Normal("mu", mu=0, sigma=2) + sigma = pm.Gamma("sigma", alpha=2, beta=1) + # likelihood + pm.Normal("y", mu=mu, sigma=sigma, observed=x) + # sample + idata = pm.sample_prior_predictive(samples=10_000) + idata.extend(pm.sample(draws=10_000)) +``` + +We didn't get any warnings from the sampling processes. + +It is good practice to visualise the posterior distribution, so below we'll look at the joint posterior over $\mu$ and $\sigma$ parameters. Everything looks fine here. + +```{code-cell} ipython3 +:tags: [hide-input] + +az.plot_pair(idata, var_names=["mu", "sigma"], marginals=True, point_estimate="mean"); +``` + +Finally, seeing as $\mu$ is the core parameter of interest, we'll visualise both the prior and posterior distributions for $\mu$. + +```{code-cell} ipython3 +:tags: [hide-input] + +ax = az.plot_dist(idata.prior["mu"], label="Prior", color="C0", figsize=(14, 3)) +az.plot_dist(idata.posterior["mu"], label="Posterior", color="C1", ax=ax) +ax.set(title=r"Prior and posterior distributions of $\mu$"); +``` + +## Bayesian Hypothesis Testing Methods + +### Posterior probability statements + +The simplest form of hypothesis testing is to ask whether the mean is greater than zero. This is equivalent to asking whether the probability that $\mu$ is greater than zero is greater than 0.5. We can compute this directly from the samples. So computing compute $P(\mu>0 | x)$ is as simple as counting the number of samples where $\mu>0$ and dividing by the total number of samples - equivalent to computing the mean of the samples where $\mu>0$. + +```{code-cell} ipython3 +mu_samples = idata.posterior["mu"].values +p_mu_greater_0 = np.mean(mu_samples > 0) +p_mu_greater_0 +``` + +It could also be that we have some kind of minimum meaningful threshold that we care about. For example, we might care about whether the mean is greater than 0.1. We can compute this in the same way. + +```{code-cell} ipython3 +p_mu_greater = np.mean(mu_samples > 0.1) +p_mu_greater +``` + +We can also include such information in a visual plot using `az.plot_posterior`. + +```{code-cell} ipython3 +az.plot_posterior(idata, var_names=["mu"], ref_val=0, hdi_prob="hide", figsize=(14, 3)); +``` + +### Highest Density Intervals (HDIs) + +The HDI gives an interval of highest probability density. If zero is outside the HDI, it’s unlikely the parameter is near zero. + +```{code-cell} ipython3 +hdi_mu = az.hdi(idata, var_names=["mu"])["mu"].data +hdi_mu +``` + +In this case, zero is within the HDI, so based on this measure, we can't express much confidence that the mean is different from zero. + ++++ + +Again, we can use `az.plot_posterior` to visualize the HDIs. + +```{code-cell} ipython3 +az.plot_posterior(idata, var_names=["mu"], figsize=(14, 3)); +``` + +### Region of Practical Equivalence (ROPE) + +If the probability that the parameter is within a certain range is high, we can say that the parameter is practically equivalent to that value. This is a useful way to express that we don't care about small differences. + +One proposal is that we now examine the HDI's but compare them to the ROPE and not zero. + +```{code-cell} ipython3 +rope = [-0.1, 0.1] +p_in_rope = np.mean((mu_samples > rope[0]) & (mu_samples < rope[1])) +p_in_rope +``` + +Third time in a row, `arviz` has our back and can plot the ROPE and HDIs. + +```{code-cell} ipython3 +az.plot_posterior(idata, var_names=["mu"], rope=rope, figsize=(14, 3)); +``` + +This shows that there is only a 2.6% chance that the mean is within the chosen ROPE. + ++++ + +### Bayes Factors + +Bayes Factors provide a Bayesian alternative to classical hypothesis tests, allowing you to weigh evidence for one hypothesis relative to another. In the simplest case—testing whether $\mu=0$ versus $\mu \neq 0$ — the Bayes Factor (BF) tells you how much more (or less) likely your observed data are under the model where $\mu=0$ than under the model where $\mu$ is free to vary. + +Intuitively, the Bayes Factor can be understood by comparing the density of $\mu$ at zero before and after observing the data. Before collecting data, you have a prior belief about $\mu$. This prior density at $\mu=0$ represents how plausible zero was considered initially. After seeing the data, you update these beliefs to get the posterior distribution. The posterior density at $\mu=0$ indicates how plausible zero remains given the evidence. The ratio of these densities—the Savage-Dickey ratio—is closely related to the Bayes Factor. If the data make +$\mu=0$ more plausible relative to your initial belief, the Bayes Factor will favor $\mu=0$. If the data diminish the credibility of $\mu=0$, the Bayes Factor will favor $\mu\neq0$ + +Because the Bayes Factor directly compares how the data update the prior odds of each hypothesis, the choice of prior is crucial. A strong prior concentration at $\mu=0$ could make it harder for data to move the posterior density away from zero, influencing the resulting Bayes Factor. On the other hand, a diffuse prior might make it easier for data to shift your beliefs about $\mu$. Thus, specifying a reasonable and justifiable prior distribution is essential when using Bayes Factors for hypothesis testing. + ++++ + +Yet again, `arviz` has a function to help us here. We can use `plot_bf` to compute the Bayes Factor for the hypothesis that $\mu=0$ versus $\mu\neq0$. + +```{code-cell} ipython3 +az.plot_bf(idata, var_name="mu", ref_val=0, figsize=(14, 3)); +``` + +We can see that the probability of $\mu=0$ has gone _down_ after observing the data. This is reflected in the value of $BF_{01}=0.66$ in that it is less than 1. + ++++ + +## Summary + ++++ + +## Authors +* Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in December, 2024. + ++++ + +## Watermark + +```{code-cell} ipython3 +%load_ext watermark +%watermark -n -u -v -iv -w -p pytensor,xarray +``` + +:::{include} ../page_footer.md +:::