{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# State-Space Model\n", "\n", "We may wish to consider another Bayesian setting, but under a markovian setting that evolves over time, namely the latent state space model:\n", "\n", "$$\n", "\\theta \\sim \\mathcal{N}(m, P)\n", "$$\n", "$$\n", "x\\mid \\theta \\;\\sim\\; \\mathcal{N}\\bigl(C\\,\\theta,\\;Q\\bigr)\n", "$$\n", "$$\n", "y\\mid x \\;\\sim\\; \\mathcal{N}\\bigl(A\\,x,\\;R\\bigr)\n", "$$\n", "\n", "Where $y$ is observed data, $x$ is latent, and we wish to infer on $\\theta$\n", "\n", "We first compute the likelihood of y, given by\n", "\n", "$$\n", "p(y\\mid \\theta)\n", "\\;=\\;\\int p(y\\mid x)\\,p(x\\mid \\theta)\\,dx.\n", "$$\n", "\n", "$$\n", "= \\int \\mathcal{N}\\bigl(y; A\\,x,\\;R\\bigr) \\mathcal{N}\\bigl(x; C\\,\\theta,\\;Q\\bigr) dx\n", "$$\n", "\n", "$$\n", "= \\mathcal{N}\\!\\Bigl(\n", "y;\\;A\\,C\\,\\theta,\\;A\\,Q\\,A^\\top + R\n", "\\Bigr)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct the posterior \n", "\n", "$$\n", "p(\\theta\\mid y)\n", "\\propto\n", "p(\\theta) \\; p(y\\mid \\theta)\n", "$$\n", "\n", "$$\n", "\\propto\n", "\\mathcal{N}\\bigl(\\theta; m \\; P )\n", "\\;\n", "\\mathcal{N}\\!\\Bigl(\n", "y;\\;A\\,C\\,\\theta,\\;A\\,Q\\,A^\\top + R\n", "\\Bigr)\n", "$$\n", "\n", "Using established result, we know\n", "\n", "$$\n", "p(\\theta\\mid y) = \\mathcal{N}(y; M, \\Sigma)\n", "$$\n", "\n", "Where the posterior covariance is given by\n", "\n", "$$\n", "\\Sigma \\;=\\;\n", "P - P (AC)^\\top \\Bigl( A\\,Q\\,A^\\top + R + (AC) P (AC) ^\\top \\Bigr)^{-1} (AC) P\n", "$$\n", "\n", "Or equivalently in a more elegant form\n", "\n", "$$\n", "\\Sigma \\;=\\;\n", "\\bigl[P^{-1} + C^\\top A^\\top (A\\,Q\\,A^\\top + R)^{-1} A\\,C\\bigr]^{-1}.\n", "$$ \n", "\n", "And the posterior mean $M$ is given by\n", "\n", "$$\n", "M = m + P (AC)^\\top \\Bigl( A\\,Q\\,A^\\top + R + (AC) P (AC) ^\\top \\Bigr)^{-1} (y - ACm)\n", "$$\n", "\n", "or more elegantly\n", "\n", "$$\n", "M = \\Sigma\\bigl[P^{-1}m + C^\\top A^\\top (A\\,Q\\,A^\\top + R)^{-1}y\\bigr]\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, consider the following parameters:\n", "\n", "$$\n", "m = \\begin{pmatrix}2 \\\\[4pt] 0\\end{pmatrix},\\quad \n", "P = \\begin{pmatrix}1 & 0\\\\[4pt] 0 & 1\\end{pmatrix},\\quad\n", "C = \\begin{pmatrix}1 & 1\\\\[4pt] 1 & 1.01\\end{pmatrix}\n", "$$\n", "\n", "$$\n", "Q = \\begin{pmatrix}0.01 & 0\\\\[4pt] 0 & 0.01\\end{pmatrix}\n", "A = \\begin{pmatrix}1 & 0 \\\\[4pt]\\varepsilon & 0\\end{pmatrix},\\quad \n", "R = \\,\\begin{pmatrix}\\varepsilon & 0\\\\[4pt] 0 & \\varepsilon\\end{pmatrix},\\quad\n", "$$\n", "\n", "And we observed \n", "$\n", "y = \\begin{pmatrix}1\\\\[3pt]1\\end{pmatrix}.\n", "$\n", "\n", "In this case we know the posterior is \n", "$$\n", "p(\\theta\\mid y) = \\mathcal{N}(y; M, \\Sigma)\n", "$$\n", "Where $M, \\Sigma$ depends on $\\epsilon$ and is computed as follow:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EpsilonPosterior MeanPosterior Variance
00.001[1.5032, -0.4968][[0.5027, -0.4973], [-0.4973, 0.5027]]
10.010[1.5099, -0.4901][[0.505, -0.495], [-0.495, 0.505]]
20.100[1.5681, -0.4319][[0.5258, -0.4742], [-0.4742, 0.5258]]
31.000[1.6016, -0.3984][[0.6016, -0.3984], [-0.3984, 0.6016]]
\n", "
" ], "text/plain": [ " Epsilon Posterior Mean Posterior Variance\n", "0 0.001 [1.5032, -0.4968] [[0.5027, -0.4973], [-0.4973, 0.5027]]\n", "1 0.010 [1.5099, -0.4901] [[0.505, -0.495], [-0.495, 0.505]]\n", "2 0.100 [1.5681, -0.4319] [[0.5258, -0.4742], [-0.4742, 0.5258]]\n", "3 1.000 [1.6016, -0.3984] [[0.6016, -0.3984], [-0.3984, 0.6016]]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "m = np.array([[2], [0]])\n", "P = np.eye(2)\n", "C = np.array([[1, 1], [1, 1.01]])\n", "Q = 0.01 * np.eye(2)\n", "y = np.array([[1], [1]])\n", "A_base = np.array([[1, 0], [0, 0]], dtype=float) # Base part of A\n", "R_base = np.array([[1, 0], [0, 1]], dtype=float) # Base part of R\n", "\n", "epsilons = np.logspace(-3, 0, num=4) # 10^-3, 10^-2, 10^-1, 10^0\n", "post_var = []\n", "post_means = []\n", "\n", "for epsilon in epsilons:\n", " A = A_base.copy()\n", " A[1, 0] = epsilon # Update A with the varying epsilon\n", " R = epsilon * R_base # Update R with the varying epsilon\n", " S = A @ Q @ A.T + R\n", "\n", " Sigma = np.linalg.inv(P + C.T @ A.T @ np.linalg.inv(S) @ A @ C)\n", " post_var.append(np.round(Sigma, 4))\n", "\n", " post_mean = Sigma @ (np.linalg.inv(P) @ m + C.T @ A.T @ np.linalg.inv(S) @ y)\n", " post_means.append(np.round(post_mean.flatten(), 4)) # store 4 digits\n", "\n", "# Create a DataFrame for visualization\n", "df_post = pd.DataFrame(\n", " {\"Epsilon\": epsilons, \n", " \"Posterior Mean\": post_means,\n", " \"Posterior Variance\": post_var}\n", " )\n", "df_post" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With $\\epsilon=1$, we have\n", "$$\n", "p(\\theta\\mid y) = \\mathcal{N}(y; \n", "\\begin{pmatrix}1.6 \\\\[4pt] -0.4 \\end{pmatrix}, \n", "\\begin{pmatrix}0.6 & -0.4 \\\\[4pt]-0.4 & 0.6\\end{pmatrix}\n", ")\n", "$$\n", "\n", "And we plot the posterior:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import multivariate_normal\n", "import matplotlib.pyplot as plt\n", "\n", "# Define grid for contour plot\n", "x_bb = np.linspace(-2, 5, 100)\n", "y_bb = np.linspace(-4, 3, 100)\n", "X_bb, Y_bb = np.meshgrid(x_bb, y_bb)\n", "\n", "fig, axes = plt.subplots(1, 4, figsize=(20, 5))\n", "plt.rcParams.update({'font.size': 12}) # Set font size\n", "\n", "for i in df_post.index:\n", " eps = df_post['Epsilon'][i]\n", " post_mean = df_post['Posterior Mean'][i]\n", " post_var = df_post['Posterior Variance'][i]\n", "\n", " rv = multivariate_normal(mean=post_mean, cov=post_var)\n", "\n", " # Evaluate the posterior density on the grid\n", " pos = np.dstack((X_bb, Y_bb))\n", " Z_bb = rv.pdf(pos)\n", "\n", " # Plot the contour\n", " ax = axes[i]\n", " cnt = ax.contourf(X_bb, Y_bb, Z_bb, 100, cmap='RdBu')\n", " ax.set_title(f'$\\\\epsilon = {eps:.3g}$')\n", " ax.set_xlabel('$\\\\theta_1$')\n", " ax.set_ylabel('$\\\\theta_2$')\n", "\n", "fig.colorbar(cnt, ax=axes, orientation='vertical', fraction=0.02, pad=0.04, label='Density')\n", "plt.suptitle('Target Distribution for Posterior $p(\\\\theta | y)$ for Different $\\\\epsilon$ Values')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now consider $\\epsilon=1$. \n", "\n", "We can sample from the posterior if we know the analytical form.\n", "\n", "Assume we don't" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 2 }