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@AustinRochford
Created January 10, 2026 21:55
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Decaying Bayesian Updating for Non-stationary Time Series Models
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"cell_type": "markdown",
"id": "d838bfda-a707-40ac-9a6d-ee1812c2f02e",
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"source": [
"In the past, I have both [written](https://austinrochford.com/posts/mab-bias.html) and [spoken](https://austinrochford.com/talks.html#:~:text=Two%20Years%20of%20Bayesian%20Bandits%20for%20E%2DCommerce) about the significant role [multi-armed bandits](https://en.wikipedia.org/wiki/Multi-armed_bandit) have played in my [career](https://monetate.com/). One significant takeaway from my experience so far is the non-[stationarity](https://en.wikipedia.org/wiki/Stationary_process) inherent in the realy world. Human behavior, especially online, is constantly shifting and changing in ways that many naive statistical models are not built to handle. There are, of course, many approaches to modeling non-stationary phenomena. In this post I will share a lesser-known approach that I have found occasionaly useful; in fact, I have never been able to find solid references for this approach.\n",
"\n",
"## Bayesian Models for Sequential Data\n",
"\n",
"I call this approach \"decaying Bayesian updating,\" as it builds on the notion of sequential Bayesian updates as more data arrives over time, while weighting recent data more strongly than older data. Bayesian modeling is theoretically well-suited to modeling sequences of data that arrive over time, as the posterior after time $t$ makes a natural prior for the likelihood of the $(t + 1)$-th observation, whose posterior makes a natural prior for the likelihood of the $(t + 2)$-th observation, and so on.\n",
"\n",
"Throughout most of this post, we will use a simple [beta](https://en.wikipedia.org/wiki/Beta_distribution)-[binomial](https://en.wikipedia.org/wiki/Binomial_distribution) model for the probability of success in independent trials, though we occasionally will work with more general distributions as appropriate.\n",
"\n",
"First we establish some preliminary results in the stationary case where $X_1, X_2, \\ldots, X_T \\sim \\text{Ber}(p)$ are [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) [Bernoulli-distributed](https://en.wikipedia.org/wiki/Bernoulli_trial) random variables with probability of success $p$. Let $\\pi_0(p)$ be the prior distribution of $p$ before any data is collected, and $\\pi_t(p) = \\pi(p\\ |\\ x_1, x_2, \\ldots, x_t)$ be the posterior distribution of $p$ after the first $t$ data points have been collected. There are two plausible methods for calculating $\\pi_T(p)$, the posterior distribution of $p$ after all of the data has been collected. Throughout we assume a uniform prior distribution $\\pi_0(p) = 1$ on $p$ for simplicity. The following analysis does, however, generalize to other, non-uniform beta-distributed priors.\n",
"\n",
"The first method observes that $\\sum_{t = 1}^T X_t \\sim \\text{Bernoulli}(T, p)$, so by Bayes' theorem\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\pi_T(p)\n",
" & \\propto f\\left(\\sum_{t = 1}^T x_t\\ |\\ p\\right) \\cdot \\pi_0(p) \\\\\n",
" & \\propto p^{\\sum_{t = 1}^T x_t} \\cdot (1 - p)^{T - \\sum_{t = 1}^T x_t},\n",
"\\end{align}\n",
"$$\n",
"\n",
"which gives\n",
"\n",
"$$\\pi_T(p) \\sim \\text{Beta}\\left(1 + \\sum_{t = 1}^T x_t, 1 + T - \\sum_{t = 1}^T x_t\\right).$$\n",
"\n",
"The second method uses sequential Bayesian updating, noting that the posterior distribution after the first observation is\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\pi_1(p)\n",
" & \\propto f(x_1\\ |\\ p) \\cdot \\pi_0(p) \\\\\n",
" & = p^{x_1} \\cdot (1 - p)^{1 - x_1}.\n",
"\\end{align}\n",
"$$\n",
"\n",
"Using this posterior as the prior on the second observation, we get\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\pi_2(p)\n",
" & \\propto f(x_2\\ |\\ p) \\cdot \\pi_1(p) \\\\\n",
" & \\propto \\left(p^{x_2} \\cdot (1 - p)^{1 - x_2}\\right) \\cdot \\left(p^{x_1} \\cdot (1 - p)^{1 - x_1}\\right) \\\\\n",
" & = p^{x_1 + x_2} \\cdot (1 - p)^{2 - (x_1 + x_2)}.\n",
"\\end{align}\n",
"$$\n",
"\n",
"It is apparent that repeating this process $T - 2$ more times will yield\n",
"\n",
"$$\\pi_T(p) \\propto p^{\\sum_{t = 1}^T x_t} \\cdot (1 - p)^{T - \\sum_{t = 1}^T x_t},$$\n",
"\n",
"so\n",
"\n",
"$$\\pi_T(p) \\sim \\text{Beta}\\left(1 + \\sum_{t = 1}^T x_t, 1 + T - \\sum_{t = 1}^T x_t\\right),$$\n",
"\n",
"exactly as in the first method.\n",
"\n",
"It is good that these two methods agree in this stationary case; waiting for all of the data to arrive and performing one Bayesian update is equivalent to updating intermediate posterior distributions after each data point arrives. If we were [category theorists](https://en.wikipedia.org/wiki/Category_theory), we might say the following [diagram commutes](https://en.wikipedia.org/wiki/Commutative_diagram)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "294a0f59-2951-412f-b4b2-4ee51371ca66",
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import IFrame"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "54d301b1-caa2-425d-8c72-959bdfe98f9e",
"metadata": {
"jupyter": {
"source_hidden": true
}
},
"outputs": [],
"source": [
"QUIVER_URL = \"https://q.uiver.app/#q=WzAsNixbMCwwLCJcXHBpXzAocCkiXSxbMSwxLCJcXHBpXzEocCkiXSxbMiwxLCJcXHBpXzIocCkiXSxbMywxLCJcXGNkb3RzIl0sWzQsMSwiXFxwaV97VCAtMX0ocCkiXSxbNSwwLCJcXHBpX1QocCkiXSxbMCwxLCJmKHhfMVxcIHxcXCBwKSJdLFsxLDIsImYoeF8yXFwgfFxcIHApIl0sWzIsMywiZih4XzNcXCB8XFwgcCkiXSxbMyw0LCJmKHhfe1QgLSAxfVxcIHxcXCBwKSJdLFs0LDUsImYoeF9UXFwgfFxcIHApIl0sWzAsNSwiZlxcbGVmdChcXHN1bV97dCA9IDF9XlR4X3RcXCB8XFwgcFxccmlnaHQpIiwwLHsiY3VydmUiOi0xfV1d&embed\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cc360365-679e-41ef-b9d8-1e5ef4d7e78c",
"metadata": {},
"outputs": [
{
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"source": [
"IFrame(QUIVER_URL, width=889, height=304)"
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},
{
"cell_type": "markdown",
"id": "74eb0fd7-a164-438c-b520-b0f1d5effc10",
"metadata": {},
"source": [
"Throughout this post, we will supplement theoretical analysis with simulations. First we make the necessary Python imports and do some light configuration."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "36606739-5b0d-4ccc-8091-3396dae3fc36",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "f26cb4c0-1425-43b0-b838-2ba8c600a9e5",
"metadata": {},
"outputs": [],
"source": [
"from warnings import filterwarnings"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c75c2b8b-4a76-46ee-af2e-1ce187f2d090",
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt, ticker\n",
"import numpy as np\n",
"import scipy as sp\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c7dcdb7c-e8dd-41b9-9711-8f0ed5162362",
"metadata": {},
"outputs": [],
"source": [
"filterwarnings(\"ignore\", category=RuntimeWarning)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "253b91cc-ce4d-43bc-84ce-2801d8bcf7db",
"metadata": {},
"outputs": [],
"source": [
"pct_formatter = ticker.StrMethodFormatter(\"{x:.0%}\")\n",
"\n",
"sns.set(color_codes=True)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "cade431d-cc96-48df-88c2-91e64c37735e",
"metadata": {},
"outputs": [],
"source": [
"SEED = 123456789 # for reprodicibility\n",
"rng = np.random.default_rng(SEED)"
]
},
{
"cell_type": "markdown",
"id": "ef4a9c26-7232-483c-ba12-7c7d33e45cda",
"metadata": {},
"source": [
"For now we assume that the probability of success is 30% ($p = 0.3$), and that we will collect $T = 5,000$ samples sequentially."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "12d09733-7278-496d-a44c-5f0e7ea77858",
"metadata": {},
"outputs": [],
"source": [
"P = 0.3\n",
"T = 5_000"
]
},
{
"cell_type": "markdown",
"id": "df02471b-b467-4c9f-9d5e-468f181e80c7",
"metadata": {},
"source": [
"We will conduct 1,001 simulations to understand the avarage behavior in this situation."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "c75f4fee-c0cf-4585-aa22-1b6789c40ac7",
"metadata": {},
"outputs": [],
"source": [
"N_SIM = 1_001"
]
},
{
"cell_type": "markdown",
"id": "4e812334-c243-4a72-9c5a-40638d6a0533",
"metadata": {},
"source": [
"First we generate the $5,000 \\times 1,001$ samples."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "15083358-3cf1-45f6-8fd5-5bec3d36f0b5",
"metadata": {},
"outputs": [],
"source": [
"x = 1 * (rng.uniform(size=(N_SIM, T)) < P)"
]
},
{
"cell_type": "markdown",
"id": "f28e8198-1acc-4326-a022-bd6d32153aa5",
"metadata": {},
"source": [
"Next we calculate and visualize the behavior of the [maximum likelihood estimator](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) for $p$, $\\hat{p}$, in these simulations."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "57a89b0c-60dd-4194-a64c-de448c25e0db",
"metadata": {},
"outputs": [],
"source": [
"t = 1 + np.arange(T)\n",
"p_mle = x.cumsum(axis=1) / t"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6f8bd630-7dac-4879-9f2d-9b46c6aa1aef",
"metadata": {},
"outputs": [],
"source": [
"N_PLOT_TRAJECTORY = 10"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "2ba3471d-a704-4b3d-869c-2dc26d86b8e6",
"metadata": {},
"outputs": [],
"source": [
"def scale_y_axis(ref_val, *, mult=0.1, ax=None):\n",
" if ax is None:\n",
" ax = plt.gca()\n",
"\n",
" ax.set_ylim((1 - mult) * ref_val, (1 + mult) * ref_val)\n",
"\n",
"\n",
"def make_pct_axis(*, ref_val=None, mult=0.1, ax=None):\n",
" if ax is None:\n",
" ax = plt.gca()\n",
"\n",
" ax.yaxis.set_major_formatter(pct_formatter)\n",
"\n",
" if ref_val is not None:\n",
" scale_y_axis(ref_val, mult=mult, ax=ax)\n",
"\n",
" ax.set_ylabel(\"$p$\")\n",
"\n",
"\n",
"def make_time_axis(*, t_max=T, ax=None):\n",
" if ax is None:\n",
" ax = plt.gca()\n",
"\n",
" ax.set_xlim(1, t_max)\n",
" ax.set_xlabel(\"$t$\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e06849f7-678c-4de4-8454-2d4fb0a2c849",
"metadata": {},
"outputs": [
{
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(t, p_mle.mean(axis=0), label=r\"Average MLE\")\n",
"\n",
"ax.plot(t, p_mle[0].T, c=\"C0\", alpha=0.1, label=r\"Simulation MLE\")\n",
"ax.plot(t, p_mle[1:N_PLOT_TRAJECTORY].T, c=\"C0\", alpha=0.2)\n",
"\n",
"ax.axhline(P, c=\"k\", ls=\"--\", label=\"Actual\")\n",
"\n",
"make_time_axis(ax=ax)\n",
"make_pct_axis(ref_val=P, ax=ax)\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "963adfe9-6c4f-4d78-a4d2-b8562beb089a",
"metadata": {},
"source": [
"We see that the average value of $\\hat{p}$ across simulations is quite close to the actual value of $p = 0.3$, and the sample simulations plotted converge to this true value as $t$ increases. The former behavior is due to the [law of large numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers), and the rate at which simulations' $\\hat{p}$s converge is given by the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem).\n",
"\n",
"Next we calculate the parameters of the posterior distributions at each point in time for each simulation assuming a beta-binomial model with a uniform prior on $p$ at $t = 0$, as above."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "a45b3a2f-cf35-4d5b-9ee6-8558e668305c",
"metadata": {},
"outputs": [],
"source": [
"α = 1 + x.cumsum(axis=1)\n",
"β = 1 + t - x.cumsum(axis=1)"
]
},
{
"cell_type": "markdown",
"id": "8c4d7059-fc3f-4a02-99ad-66f32eac5bc6",
"metadata": {},
"source": [
"We calculate the posterior expected values of $p$ as well."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "59717f11-da8b-4b00-95b9-9cbf0092ce14",
"metadata": {},
"outputs": [],
"source": [
"def get_bb_post_mean(α, β):\n",
" return α / (α + β)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "d96aee9f-8237-463e-87a5-616af85729fc",
"metadata": {},
"outputs": [],
"source": [
"p_bb = get_bb_post_mean(α, β)"
]
},
{
"cell_type": "markdown",
"id": "b8d80a36-b08c-480b-a506-4700e79bb65d",
"metadata": {},
"source": [
"We see that this posterior expected value is quite close to the MLE (on average), especially as $t$ increases."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b84115f7-205d-4a73-8629-c6b9cb9df2d0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(t, p_mle.mean(axis=0), label=r\"Average MLE\")\n",
"ax.plot(t, p_bb.mean(axis=0), label=r\"Average posterior EV\")\n",
"\n",
"ax.plot(t, p_bb[0].T, c=\"C1\", alpha=0.1, label=r\"Simulation posterior EV\")\n",
"ax.plot(t, p_bb[1:N_PLOT_TRAJECTORY].T, c=\"C1\", alpha=0.2)\n",
"\n",
"ax.axhline(P, c=\"k\", ls=\"--\", label=\"Actual\")\n",
"\n",
"make_time_axis(ax=ax)\n",
"make_pct_axis(ref_val=P, ax=ax)\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "645b219e-b61a-4493-a7d0-be429a4b607e",
"metadata": {},
"source": [
"## Decaying Bayesian Updating\n",
"\n",
"To motivate decaying Bayesian updating, we consider what happens to the stationary posterior predictions when the probability of success changes over time.\n",
"\n",
"We will use a simple model where\n",
"\n",
"$$\n",
"p_t = \\begin{cases}\n",
" 0.3 & \\text{if } t < T / 2 \\\\\n",
" 0.7 & \\text{if } t \\geq T / 2\n",
"\\end{cases}.\n",
"$$\n",
"\n",
"First we generate $5,000 \\times 1,001$ samples under these assump;tions."
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "500aaba1-3d89-44dd-9481-74f5ef7d5463",
"metadata": {},
"outputs": [],
"source": [
"x_ns = 1 * (rng.uniform(size=(N_SIM, T)) < np.where(t < T // 2, P, 1 - P))"
]
},
{
"cell_type": "markdown",
"id": "2f500645-2333-439f-ba2f-d03d64f64c3c",
"metadata": {},
"source": [
"Here the suffix `ns` indicates non-stationarity.\n",
"\n",
"We visualize the MLE and posterior expected value in this situation."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "0e7567e6-0508-4972-b993-5447f7468fe0",
"metadata": {},
"outputs": [],
"source": [
"p_mle_ns = x_ns.cumsum(axis=1) / t"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "7aeaff88-9f31-42ce-a0e6-44d74ce792aa",
"metadata": {},
"outputs": [],
"source": [
"α_ns = 1 + x_ns.cumsum(axis=1)\n",
"β_ns = 1 + t - x_ns.cumsum(axis=1)\n",
"\n",
"p_bb_ns = get_bb_post_mean(α_ns, β_ns)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "75a0b1f0-4d96-4847-8011-ae439a031a4f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(t, p_mle_ns.mean(axis=0), label=\"Average MLE\")\n",
"ax.plot(t, p_bb_ns.mean(axis=0), label=\"Average posterior EV\")\n",
"\n",
"ax.hlines(P, 1, T // 2, color=\"k\", ls=\"--\", label=\"Actual\")\n",
"ax.hlines(1 - P, T // 2, T, color=\"k\", ls=\"--\")\n",
"\n",
"make_time_axis(ax=ax)\n",
"make_pct_axis(ax=ax)\n",
"\n",
"ax.legend(loc=\"upper left\");"
]
},
{
"cell_type": "markdown",
"id": "3cc4629d-1143-4264-b65e-74d0412131c3",
"metadata": {},
"source": [
"We see that, though these models are not explicitly built to handle nonstationarity, the estimates do start to move towards the later value of $p$ over time, and would continue to do so if we collected more data.\n",
"\n",
"In some situations, however, we might want the estimates to react more quickly to changes in the success probability over time. Decaying Bayesian updates give one method to achieve this, though there are many others. Decaying Bayesian updates can be motivated by writing the standard Bayes' update rule in the somewhat unnatural form\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\pi_t(\\vartheta)\n",
" & \\propto f(x_t\\ |\\ \\vartheta) \\cdot \\pi_{t - 1}(\\vartheta) \\\\\n",
" & = \\left(f(x_t\\ |\\ \\vartheta) \\cdot \\pi_{t - 1}(\\vartheta)\\right)^{1 - 0} \\cdot \\pi_0(\\vartheta)^0.\n",
"\\end{align}\n",
"$$\n",
"\n",
"$\\newcommand{\\eps}{\\varepsilon}$\n",
"\n",
"The following definition and analysis are not specific to the beta-binomial model we have been discussing so far, so we use $\\vartheta$ to denote the set set of parameters of the general model.\n",
"\n",
"If we replace $0$ with a small positive number $0 < \\eps \\ll 1$, we get the decaying Bayesian update rule\n",
"\n",
"$$\\pi_t^{\\eps}(\\vartheta) = \\left(f(x_t\\ |\\ \\vartheta) \\cdot \\pi_{t - 1}^{\\eps}(\\vartheta)\\right)^{1 - \\eps} \\cdot \\pi_0(\\vartheta)^{\\eps}.$$\n",
"\n",
"With this definition, we see that the decayed posterior at time $t$, $\\pi_t^{\\eps}(\\vartheta),$ is proportional to the [weighted geometric mean](https://en.wikipedia.org/wiki/Weighted_geometric_mean) of the (almost) usual joint distribution $f(x_t\\ |\\ \\vartheta) \\cdot \\pi_{t - 1}^{\\eps}(\\vartheta)$\n",
" with weight $1 - \\eps$ and the no data prior $\\pi_0(\\vartheta)$ with weight $\\eps$.\n",
"\n",
"One advantage of this approach over some other methods of accounting for non-stationarity is that, for many model specifications, there is a closed-form, easily computable form for $\\pi_t^{\\eps}(\\vartheta)$. Throughout the rest of this post, we will frequently transition between probabilities and log-probabilities, depending on which is most convenient for the task at hand. In log-space proprotionality will mean equality up to an additive constant that does not depend on the argument(s) of the function on the left hand side.\n",
"\n",
"**Theorem**\n",
"\n",
"$$\\log \\pi_t^{\\eps}(\\vartheta) \\propto \\ell_t^{\\eps}(\\vartheta) + \\log \\pi_0(\\vartheta)$$\n",
"\n",
"where\n",
"\n",
"$$\\ell_t^{\\eps}(\\vartheta) = \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot \\log f(x_s\\ |\\ \\vartheta)$$\n",
"\n",
"is a decaying version of the [log likelihood function](https://en.wikipedia.org/wiki/Likelihood_function#Log-likelihood).\n",
"\n",
"**Proof**\n",
"\n",
"For the first two observations we get\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\log \\pi_1^{\\varepsilon}(\\vartheta)\n",
" & \\propto (1 - \\eps) \\cdot \\log f(x_1\\ |\\ \\vartheta) + (1 - \\eps) \\cdot \\log \\pi_0(\\vartheta) + \\eps \\cdot \\log \\pi_0(\\vartheta) \\\\\n",
" & = (1 - \\eps) \\cdot \\log f(x_1\\ |\\ \\vartheta) + \\log \\pi_0(\\vartheta) \\\\\n",
" \\log \\pi_2^{\\varepsilon}(p)\n",
" & \\propto (1 - \\eps) \\cdot \\log f(x_2\\ |\\ \\vartheta) + (1 - \\eps) \\cdot \\log \\pi_1^{\\eps}(\\vartheta) + \\eps \\cdot \\log \\pi_0(\\vartheta) \\\\\n",
" & \\propto (1 - \\eps)^2 \\cdot \\log f(x_1\\ |\\ \\vartheta) + (1 - \\eps) \\cdot \\log f(x_2\\ |\\ \\vartheta) + \\log \\pi_0(\\vartheta).\n",
"\\end{align}\n",
"$$\n",
"\n",
"The emergence of the form in the theorem for arbitrary time $t$ is clear from here.\n",
"\n",
"**QED**\n",
"\n",
"We see that there is simple, closed-form expression for the contribution of the no data prior to the decayed posterior. For many common distributions, the decayed log likelihood, $\\ell_t^{\\varepsilon}(\\vartheta)$, will also have a relatively simple form. We will return to some specific examples of these distributions throughout this post.\n",
"\n",
"Returning to the beta-binomial case, where\n",
"\n",
"$$\\log f(x\\ |\\ p) = x \\log p + (1 - x) \\cdot \\log(1 - p),$$\n",
"\n",
"we have\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\log \\pi_t^{\\eps}(p)\n",
" & \\propto \\ell_t^{\\eps}(p) + \\log \\pi_0(p) \\\\\n",
" & = \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot \\log f(x_s\\ |\\ p) \\\\\n",
" & = \\left(\\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot x_s\\right) \\cdot \\log p + \\left(\\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot (1 - x_s)\\right) \\cdot \\log (1 - p),\n",
"\\end{align}\n",
"$$\n",
"\n",
"so\n",
"\n",
"$$\\pi_t^{\\eps}(p) \\sim \\text{Beta}\\left(1 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot x_s, 1 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot (1 - x_s)\\right).$$\n",
"\n",
"In my last [post](https://austinrochford.com/posts/cumsum-matmul.html), I showed how to compute sums of this form via matrix multiplication with an upper triangular matrix. We now use this method to calcumate the decayed posterior distributions for a variety of values of $0 < \\eps \\ll 1$."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "7a288823-40d2-44a7-a2d4-cce6e0f9081a",
"metadata": {},
"outputs": [],
"source": [
"def get_decay(T, ε):\n",
" return np.triu((1 - ε) ** sp.linalg.toeplitz(1 + np.arange(T)))"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "f30d95a7-4395-4041-9453-429b8dbd2beb",
"metadata": {},
"outputs": [],
"source": [
"def get_bb_decayed_posterior(x, ε, *, α0=1, β0=1):\n",
" _, T = x.shape\n",
" decay = get_decay(T, ε)\n",
"\n",
" α = α0 + x @ decay\n",
" β = β0 + (1 - x) @ decay\n",
"\n",
" return α, β"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "034cdb02-9d88-478a-987c-bfa7bc7d026d",
"metadata": {},
"outputs": [],
"source": [
"EPSILONS = [0.1, 0.01, 0.001, 0.0001]\n",
"\n",
"bb_decayed_ns = {ε: get_bb_decayed_posterior(x_ns, ε) for ε in EPSILONS}"
]
},
{
"cell_type": "markdown",
"id": "251b9515-eaaf-41e9-95f6-1eb81a120652",
"metadata": {},
"source": [
"We now visualize the posterior expected success rates from these decayed models, along with those of the stationary models calculated previously."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "4680edfc-4d41-4848-b53f-88f5ce427ba8",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(t, p_mle_ns.mean(axis=0), label=\"Average MLE\")\n",
"ax.plot(t, p_bb_ns.mean(axis=0), label=\"Average posterior EV\")\n",
"\n",
"for ε, (α_decayed_ns, β_decayed_ns) in bb_decayed_ns.items():\n",
" ax.plot(\n",
" t,\n",
" get_bb_post_mean(α_decayed_ns, β_decayed_ns).mean(axis=0),\n",
" label=f\"Average posterior EV ($\\\\varepsilon = {ε}$)\",\n",
" )\n",
"\n",
"ax.hlines(P, 1, T // 2, color=\"k\", ls=\"--\", label=\"Actual\")\n",
"ax.hlines(1 - P, T // 2, T, color=\"k\", ls=\"--\")\n",
"\n",
"make_time_axis(ax=ax)\n",
"make_pct_axis(ax=ax)\n",
"\n",
"ax.legend(loc=\"upper right\", bbox_to_anchor=(1.65, 1));"
]
},
{
"cell_type": "markdown",
"id": "979dd1e1-1a40-4e42-bdcc-9b50bb2ffa7c",
"metadata": {},
"source": [
"We see that the decayed models are significantly more responsive to the nonstationarity of the success probability, with exactly how responsive they are depending on the value of $\\eps$.\n",
"\n",
"Inuitively, we expect larger values of $\\eps$ to lead to faster decay, and therefore faster reactions to changes in the success probability. We do see exactly that in this plot, but there is some nuance. The $\\eps = 0.1$ model does indeed react the fastest to the change in success probability, but during the stationary periods, that models does not capture the true sucesss probability well."
]
},
{
"cell_type": "markdown",
"id": "ede556f3-21d3-4e22-a64d-cac12cce568a",
"metadata": {},
"source": [
"### Effective sample size\n",
"\n",
"This observation leads us to consider the effective sample size of each model. One interpretation of decayed updates is that they reduce the model's effective sample size by a factor controlled by $\\eps$ when compared to a stationary model, so that when the true distribution shifts, they have less sample size inertia to overcome when adapting to the change.\n",
"\n",
"We first quantify this phenomenon for the example beta-binomial models we have been working with. In the stationary beta-binomial model, we showed above that $\\pi_t(p) \\sim \\text{Beta}(\\alpha_t, \\beta_t),$ where\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\alpha_t\n",
" & = 1 + \\sum_{s = 1}^t x_s \\text{ and} \\\\\n",
" \\beta_t\n",
" & = 1 + t - \\sum_{ts= 1}^t x_s.\n",
"\\end{align}\n",
"$$\n",
"\n",
"We can recover the sample size, $t$, of this model from these parameters by noting that\n",
"\n",
"$$t = \\alpha_t + \\beta_t - 2.$$\n",
"\n",
"This expression for $t$ motivates the following definition for the effective samples size of a decayed model. If $\\pi_t^{\\eps}(p) \\sim\n",
"\\text{Beta}(\\alpha_t^{\\eps}, \\beta_t^{\\eps}),$ we let\n",
"\n",
"$$n_{\\text{eff}, t}^{\\eps} = \\alpha_t^{\\eps} + \\beta_t^{\\eps} - 2$$\n",
"\n",
"be the effective sample size of the model.\n",
"\n",
"We can simplify this expression to\n",
"\n",
"$$\n",
"\\begin{align}\n",
" n_{\\text{eff}, t}^{\\eps}\n",
" & = \\alpha_t^{\\eps} + \\beta_t^{\\eps} - 2 \\\\\n",
" & = \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\\\\n",
" & = (1 - \\eps)^{t + 1} \\cdot \\left(\\frac{1 - (1 - \\eps)^{-(t + 1)}}{1 - (1 - \\eps)^{-1}} - 1\\right) \\\\\n",
" & = \\frac{1 - (1 - \\eps)^t}{(1 - \\eps)^{-1} - 1} \\\\\n",
" & = \\frac{1 - \\eps}{\\eps} \\cdot \\left(1 - (1 - \\eps)^t\\right).\n",
"\\end{align}\n",
"$$\n",
"\n",
"The following plots show both ways of calculating this effective sample size, confirming our simplification is correct."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "cce70744-10d3-47e5-b3bc-ce867d2f545d",
"metadata": {},
"outputs": [],
"source": [
"def get_ess(t, ε):\n",
" return (1 - ε) / ε * (1 - (1 - ε) ** t)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "09ade4e9-1c0a-4db5-bb15-edd6d863ea81",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (stat_ax, form_ax) = plt.subplots(\n",
" figsize=(10, 5), ncols=2, sharex=True, sharey=True\n",
")\n",
"\n",
"for ε, (α_decayed, β_decayed) in bb_decayed_ns.items():\n",
" stat_ax.plot(\n",
" t, (α_decayed + β_decayed).mean(axis=0) - 2, label=f\"$\\\\varepsilon = {ε}$\"\n",
" )\n",
" form_ax.plot(t, get_ess(t, ε))\n",
"\n",
"stat_ax.plot(t, t, label=r\"$\\varepsilon = 0$ (stationary)\")\n",
"form_ax.plot(t, t)\n",
"\n",
"make_time_axis(ax=stat_ax)\n",
"\n",
"stat_ax.set_yscale(\"log\")\n",
"stat_ax.set_ylabel(\"Effective sample size\")\n",
"\n",
"stat_ax.set_title(\n",
" r\"Average $n_{\\text{eff}, t}^{\\varepsilon} = \\alpha_t^{\\varepsilon} + \\beta_t^{\\varepsilon} - 2$\"\n",
")\n",
"stat_ax.legend(loc=\"upper left\")\n",
"\n",
"make_time_axis(ax=form_ax)\n",
"form_ax.set_title(\n",
" r\"$n_{\\text{eff}, t}^{\\varepsilon} = \\frac{1 - \\varepsilon}{\\varepsilon} \\cdot (1 - (1 - \\varepsilon)^t)$\"\n",
")\n",
"\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "2f0b4f7d-09d9-47ed-a0e8-309b6b071205",
"metadata": {},
"source": [
"The most striking feature of these plots is that the decayed models have an asymptotic maximum sample size. In fact,\n",
"\n",
"$$n_{\\text{eff}, \\infty}^\\eps = \\lim_{t \\to \\infty} n_{\\text{eff}, t}^{\\eps} = \\frac{1 - \\eps}{\\eps},$$\n",
"\n",
"so we see that a choice of $0 < \\eps \\ll 1$ is equivalent to choosing an asymptotic maximum sample size. This relationship between these quantities is visualized below."
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "adaaf121-81f1-4f01-bcac-ca684f8f4162",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"plot_ε = np.logspace(-5, 0, 10_000)\n",
"\n",
"ax.plot(plot_ε, (1 - plot_ε) / plot_ε)\n",
"\n",
"ax.set_xscale(\"log\")\n",
"ax.set_xlabel(r\"$\\varepsilon$\")\n",
"\n",
"ax.set_yscale(\"log\")\n",
"ax.set_ylabel(\n",
" r\"$n_{\\text{eff}, \\infty}^{\\varepsilon} = \\frac{1 - \\varepsilon}{\\varepsilon}$\"\n",
")\n",
"\n",
"ax.set_title(\"Asymptotic maximum effective sample size\");"
]
},
{
"cell_type": "markdown",
"id": "54099747-9af2-4567-beb4-3081ac22b209",
"metadata": {},
"source": [
"So far we have not addressed methods for choosing the decay parameter, $\\eps$, but this analysis of asymptotic maximum effective sample size provides some intuition. If we have an intuition for the rough time scale (in terms of number of samples) over which we expect the parameters of interest to meaningfully vary, we can choose $\\eps$ to produce the corresponding asymptotic maximum effective sample size. We will discuss another perspective on choosing $\\eps$ later in this post.\n",
"\n",
"So far our analysis of effective sample size has been theoretical. We now turn to the practical implications of reduced effective sample size. When our (effective) sample size is relatively smaller, we expect more uncertainy in our estimates, corresponding to relatively larger credible intervals. We return to the stationary case to visualize this behavior."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "1f53b724-a202-4cad-a78b-e1cdcaa386ef",
"metadata": {},
"outputs": [],
"source": [
"bb_decayed = {ε: get_bb_decayed_posterior(x, ε) for ε in EPSILONS}"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "8ce1b92a-5346-4579-95cc-95e72fa783d2",
"metadata": {},
"outputs": [],
"source": [
"CI_WIDTH = 0.95"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "998d9dd7-066f-460b-87e0-e9d9824a5702",
"metadata": {},
"outputs": [],
"source": [
"def get_bb_ci_width(α, β):\n",
" dist = sp.stats.beta(α, β)\n",
"\n",
" low = dist.ppf((1 - CI_WIDTH) / 2)\n",
" high = dist.isf((1 - CI_WIDTH) / 2)\n",
"\n",
" return high - low"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "83ff3092-0c6c-4cde-a36c-9efafb90732e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"for ε, (α_decayed, β_decayed) in bb_decayed.items():\n",
" ax.plot(\n",
" t,\n",
" get_bb_ci_width(α_decayed.mean(axis=0), β_decayed.mean(axis=0)),\n",
" label=f\"$\\\\varepsilon = {ε}$\",\n",
" )\n",
"\n",
"ax.plot(t, get_bb_ci_width(α.mean(axis=0), β.mean(axis=0)), label=r\"$\\varepsilon = 0$\")\n",
"\n",
"make_time_axis(ax=ax)\n",
"\n",
"ax.set_yscale(\"log\")\n",
"ax.set_ylabel(f\"{CI_WIDTH:.0%}-credible interval width\")\n",
"\n",
"ax.legend()\n",
"ax.set_title(f\"Stationary case ($p = {P:0.1f}$),\\naverage posterior parameters\");"
]
},
{
"cell_type": "markdown",
"id": "90644372-250a-4a45-ba8f-e10dbe0c1ac7",
"metadata": {},
"source": [
"This plot confirms that as $\\eps$ increases and the effective sample size decreases, the width of the credible interval increases. This relationship makes clear a fundamental tradeoff at the heart of model decay; to increase the speed at which the models react to changes in the true parameters, we are introducing uncertainty that makes them less confident in the stationary case."
]
},
{
"cell_type": "markdown",
"id": "ba038aa4-0f6e-4c54-8d47-03e51c5144d6",
"metadata": {},
"source": [
"### No data updates, sample time versus clock time\n",
"\n",
"Throughout this post so far, we have been implicitly defining the progression of time by the arrival of another piece of data. That is, if we have collected samples $x_1, x_2, \\ldots, x_t$, we say that we have reached time $t + 1$ when the next piece of data, $x_{t + 1}$ arrives. We call this definition of time _sample time_. Depending on the data generating process, the clock time between sample times $t$ and $t + 1$ may be constant or could vary.\n",
"\n",
"While this sample time approach is convenient in many cases, others call for defining the the progression of time independently of data arrival. For simplicity, we will assume data arrives (or not, more about that shortly) at even spaced intervals according to the progression of _clock time_. If we are guaranteed to have data arrive at even clock time intervals, there is no real difference between samplem time and clock time as we have described them here. It is when data is not guaranteed to arrive at every clock time interval that the difference between these definitions becomes interesting. This sort of situation arrives, for instance, when we are updating models on a regular interval based on visits to certain parts of a website. If the update interval is short (single digit minutes), some portions of a website may not get visited during every time interval.\n",
"\n",
"Assume we are operating by clock time. If no data arrives between time $t$ and $t+1$, we define the decayed posterior at time $t + 1$ as\n",
"\n",
"$$\\pi_{t + 1}^{\\eps}(\\vartheta) \\propto \\pi_t^{\\eps}(\\vartheta)^{1 - \\eps} \\cdot \\pi_0(\\vartheta)^{\\eps}.$$\n",
"\n",
"Note that this is equivalent to assuming the likelihood of no data is one, together with the standard definition of the decayed posterior. Intuitively, when no data arrives, we shrink the posterior back towards the $t = 0$ prior.\n",
"\n",
"Returning to the beta-binomial model for simplicity, assume that at time $t$, $\\pi_t^{\\eps}(p) \\sim \\text{Beta}(\\alpha_t, \\beta_t).$ Assume that no data arrives after time $t$. We will now explore the behavior of the decayed posterior as time goes on.\n",
"\n",
"At time $t + 1$,\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\log \\pi_{t + 1}^{\\eps}(p)\n",
" & \\propto (1 - \\eps) \\cdot \\log \\pi_t^{\\eps}(p) + \\eps \\cdot \\log \\pi_0(p) \\\\\n",
" & \\propto (1 - \\eps) \\cdot \\left((\\alpha_t - 1) \\cdot \\log p + (\\beta_t - 1) \\cdot \\log(1 - p)\\right) \\\\\n",
" & = (1 - \\eps) \\cdot (\\alpha_t - 1) \\cdot \\log p + (1 - \\eps) \\cdot (\\beta_t - 1) \\cdot \\log(1 - p).\n",
"\\end{align}\n",
"$$\n",
"\n",
"At time $t + 2$,\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\log \\pi_{t + 2}^{\\eps}(p)\n",
" & \\propto (1 - \\eps) \\cdot \\log \\pi_{t + 1}^{\\eps}(p) + \\eps \\cdot \\log \\pi_0(p) \\\\\n",
" & \\propto (1 - \\eps)^2 \\cdot (\\alpha_t - 1) \\cdot \\log p + (1 - \\eps)^2 \\cdot (\\beta_t - 1) \\cdot \\log(1 - p).\n",
"\\end{align}\n",
"$$\n",
"\n",
"The pattern is apparent, so at time $t + s$, we have\n",
"\n",
"$$\\log \\pi_{t + s}^{\\eps}(p) \\propto (1 - \\eps)^s \\cdot (\\alpha_t - 1) \\cdot \\log p + (1 - \\eps)^s \\cdot (\\beta_t - 1) \\cdot \\log(1 - p),$$\n",
"\n",
"so\n",
"\n",
"$$\\pi_{t + s}^{\\eps}(p) \\sim \\text{Beta}\\left(1 + (1 - \\eps)^s \\cdot (\\alpha_t - 1), 1 + (1 - \\eps)^s \\cdot (\\beta_t - 1)\\right).$$\n",
"\n",
"We see that\n",
"\n",
"$$\\lim_{s \\to \\infty} \\pi_{t + s}^{\\eps}(p) \\sim \\text{Beta}(1, 1) = \\pi_0(p),$$\n",
"\n",
"so as longer periods of time go without any data arriving, the decayed posterior approaches the $t = 0$ posterior.\n",
"\n",
"Calculating the effective sample size at time $t + s$ we get\n",
"\n",
"$$\n",
"\\begin{align}\n",
" n_{\\text{eff}, t + s}^{\\eps}\n",
" & = (1 - \\eps)^s \\cdot (\\alpha_t + \\beta_t - 2).\n",
"\\end{align}\n",
"$$\n",
"\n",
"We can get another heuristic for helping to choose $\\eps$ by calculating the half-life of information, which is how long it takes the effective sample size to be cut in half after an extended period of no data. We get\n",
"\n",
"$$\n",
"\\begin{align}\n",
" n_{\\text{eff}, t_{\\textonehalf}^{\\eps}}^{\\eps}\n",
" & = \\frac{1}{2} n_{\\text{eff}, t}^{\\eps} \\\\\n",
" (1 - \\eps)^{t_{\\textonehalf}^{\\eps}} \\cdot (\\alpha_t + \\beta_t - 2)\n",
" & = \\frac{1}{2} \\cdot (\\alpha_t + \\beta_t - 2) \\\\\n",
" t_{\\textonehalf}^{\\eps}\n",
" & = -\\frac{\\log 2}{\\log(1 - \\eps)}.\n",
"\\end{align}\n",
"$$\n",
"\n",
"We visualize how thisn quantity changes with $\\eps$ below."
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "bc281d84-27e3-458d-95a6-62a9bae562e3",
"metadata": {},
"outputs": [],
"source": [
"def get_bb_half_life(ε):\n",
" return -np.log(2) / np.log(1 - ε)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "8a23a076-ba0b-4b3c-9053-2c63664b9c6a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(plot_ε, get_bb_half_life(plot_ε))\n",
"\n",
"ax.set_xscale(\"log\")\n",
"ax.set_xlabel(r\"$\\varepsilon$\")\n",
"\n",
"ax.set_yscale(\"log\")\n",
"ax.set_ylabel(r\"$t_{1/2}^{\\varepsilon} = -\\frac{\\log 2}{\\log(1 - \\varepsilon)}$\")\n",
"\n",
"ax.set_title(\"Half life of information\");"
]
},
{
"cell_type": "markdown",
"id": "d4f53f6a-96d5-4410-98e1-3b5f6ede525c",
"metadata": {},
"source": [
"There may be some situations where we have stronger intuition around the half life of information than the time scale over which we expect changes to occur. In this case the above quantity may be used to choose an appropriate value of $\\eps$."
]
},
{
"cell_type": "markdown",
"id": "100043bc-2228-4571-897b-bdf53c184221",
"metadata": {},
"source": [
"### Decayed posteriors for exponential family distributions\n",
"\n",
"So far we have focused our concrete analysis of decayed Bayesian updated on the simple beta-binomial model. Analogous closed-form expressions exist for the decayed posterior many different distributions. In this section, we will show that this is the case for distributions in the [exponential family](https://en.wikipedia.org/wiki/Exponential_family), a class which includes many common distributions (normal, exponential, $\\chi^2$, etc.).\n",
"\n",
"Recall that a distribution is in the exponential family if its probability density function is of the form\n",
"\n",
"$$f(x\\ |\\ \\eta) \\propto \\exp(\\eta \\cdot T(x) - A(\\eta)),$$\n",
"\n",
"where $T$ is a [sufficient statistic](https://en.wikipedia.org/wiki/Sufficient_statistic) of the distribution and $A$ is its [log-partition function](https://en.wikipedia.org/wiki/Partition_function_(mathematics)).\n",
"\n",
"A pleasant property of exponential family distributions for Bayesian statistics is that they have conjugate priors given by\n",
"\n",
"$$\\pi(\\eta\\ |\\ \\chi, \\nu) \\propto \\exp(\\eta \\cdot \\chi - \\nu \\cdot A(\\eta)).$$\n",
"\n",
"We can quickly verify that the posterior for observation $x$ is\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\pi(\\eta\\ |\\ x, \\chi, \\nu)\n",
" & \\propto f(x\\ |\\ \\eta) \\cdot \\pi(\\eta\\ |\\ \\chi, \\nu) \\\\\n",
" & \\propto \\exp(\\eta \\cdot T(x) - A(\\eta)) \\cdot \\exp(\\eta \\cdot \\chi - \\nu \\cdot A(\\eta)) \\\\\n",
" & = \\exp(\\eta \\cdot (\\chi + T(x)) - (\\nu + 1) \\cdot A(\\eta)),\n",
"\\end{align}$$\n",
"\n",
"so $\\pi(\\eta\\ |\\ x, \\chi, \\nu) = \\pi(\\eta\\ |\\ \\chi + T(x), \\nu + 1),$ and therefore the prior is conjugate.\n",
"\n",
"**Theorem**\n",
"\n",
"For a distribution in the exponential family with sufficient statistic $T(x)$, log-partition function $A(\\eta)$, and conjugate prior $\\pi(\\eta\\ |\\ \\chi_0, \\nu_0)$,\n",
"\n",
"$$\\pi_t^{\\varepsilon}(\\eta\\ |\\ \\chi, \\nu) = \\pi(\\eta\\ |\\ \\chi_t^{\\varepsilon}, \\nu_t^{\\varepsilon}),$$\n",
"\n",
"where\n",
"\n",
"$$\\chi_t^{\\varepsilon} = \\chi_0 + \\sum_{s = 1}^t (1 - \\varepsilon)^{t - s + 1} \\cdot T(x_s),$$\n",
"\n",
"and\n",
"\n",
"$$\\nu_t^{\\varepsilon} = \\nu_0 + \\frac{1 - \\eps}{\\eps} \\cdot \\left(1 - (1 - \\eps)^t\\right).$$\n",
"\n",
"**Proof**\n",
"\n",
"Recall from our first theorem that\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\log \\pi_t^{\\eps}(\\eta)\n",
" & \\propto \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot \\log f(x_s\\ |\\ \\vartheta) + \\log \\pi(\\eta\\ |\\ \\chi_0, \\eta_0) \\\\\n",
" & \\propto \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot (\\eta \\cdot T(x_s) - A(\\eta)) + (\\eta \\cdot \\chi_0 - \\nu_0 \\cdot A(\\eta)) \\\\\n",
" & = \\eta \\cdot(\\chi_0 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\cdot T(x_s)) + (\\nu_0 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1}) \\cdot A(\\eta) \\\\\n",
" & = \\eta \\cdot \\chi_t^{\\varepsilon} - \\left(\\nu_0 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1}\\right) \\cdot A(\\eta).\n",
"\\end{align} \n",
"$$\n",
"\n",
"We already summed the geometric series present here during our derivation of effective sample size for the beta-binomial model, so we have that\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\nu_t^{\\varepsilon}\n",
" & = \\nu_0 + \\sum_{s = 1}^t (1 - \\eps)^{t - s + 1} \\\\\n",
" & = \\nu_0 + \\frac{1 - \\eps}{\\eps} \\cdot \\left(1 - (1 - \\eps)^t\\right).\n",
"\\end{align}\n",
"$$\n",
"\n",
"**QED**\n",
"\n",
"Many of the other calculations we performed for the beta-binomial model above can also be worked out for arbitrary distributions in the exponential family."
]
},
{
"cell_type": "markdown",
"id": "4f1e0696-8b4d-4de3-a132-843471ef7aba",
"metadata": {},
"source": [
"This post is available as a Jupyter notebooks [here]()."
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "7e48188a-43a0-41b5-b85b-a6b41aae07d5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Last updated: Sat Jan 10 2026\n",
"\n",
"Python implementation: CPython\n",
"Python version : 3.12.5\n",
"IPython version : 8.29.0\n",
"\n",
"matplotlib: 3.9.2\n",
"seaborn : 0.13.2\n",
"numpy : 2.0.2\n",
"IPython : 8.29.0\n",
"scipy : 1.14.1\n",
"\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -n -u -v -iv"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.12.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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