diff --git a/nb01-box-loop.ipynb b/nb01-box-loop.ipynb index e57959d..d74b08a 100755 --- a/nb01-box-loop.ipynb +++ b/nb01-box-loop.ipynb @@ -25,46 +25,146 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 9, "metadata": { "tags": [] }, "outputs": [], "source": [ - "# Generative model\n" + "import numpy as np\n", + "\n", + "# Generative model\n", + "def simulate(v, alpha, dt=0.001, G=9.81):\n", + " v_x = v * np.cos(alpha)\n", + " v_y = v * np.sin(alpha)\n", + "\n", + " x = 0\n", + " y = 1.5\n", + "\n", + " trajectory = [(x, y)]\n", + "\n", + " while y > 0:\n", + " v_y += dt * -G\n", + " x += dt * v_x\n", + " y += dt * v_y \n", + " trajectory.append((x, y))\n", + "\n", + " return np.array(trajectory)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt \n", + "\n", + "v = 5.0\n", + "alpha = np.pi / 4 \n", + "\n", + "trajectory = simulate(v, alpha, dt=0.001)\n", + "plt.plot(trajectory[:, 0], trajectory[:, 1])\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 23, "metadata": { "tags": [] }, "outputs": [], "source": [ - "# Probabilistic model\n" + "# Probabilistic model\n", + "from scipy.stats import norm, uniform\n", + "\n", + "def likelihood(v, alpha):\n", + " trajectory = simulate(v, alpha)\n", + " x = trajectory[-1, 0]\n", + " return norm(loc=x, scale=0.1)\n", + "\n", + "p_v = uniform(0, 10.)\n", + "p_alpha = uniform(0, np.pi / 2)" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 21, "metadata": { "tags": [] }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# p(x | v, alpha)\n" + "# p(x | v, alpha)\n", + "v = 5.0\n", + "alpha = np.pi / 4\n", + "\n", + "trajectory = simulate(v, alpha)\n", + "plt.plot(trajectory[:, 0], trajectory[:, 1])\n", + "\n", + "lk = likelihood(v, alpha)\n", + "xs = lk.rvs(10000)\n", + "plt.hist(xs, density=True, bins=30, color=\"orange\")\n", + "\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 25, "metadata": { "tags": [] }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# p(x)\n" + "# p(x)\n", + "xs = []\n", + "\n", + "for i in range(1000):\n", + " v = p_v.rvs()\n", + " alpha = p_alpha.rvs()\n", + "\n", + " trajectory = simulate(v, alpha)\n", + " plt.plot(trajectory[:, 0], trajectory[:, 1], color=\"b\", alpha=0.05)\n", + " x = likelihood(v, alpha).rvs()\n", + " xs.append(x)\n", + "\n", + "plt.hist(xs, density=True, bins=30, color=\"orange\")\n", + "plt.show()" ] }, { @@ -76,12 +176,43 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 39, "metadata": { "tags": [] }, "outputs": [], - "source": [] + "source": [ + "v_true = 5.0\n", + "alpha_true = np.pi / 4.\n", + "x_obs = likelihood(v_true, alpha_true).rvs()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trajectory = simulate(v_true, alpha_true)\n", + "plt.plot(trajectory[:, 0], trajectory[:, 1])\n", + "\n", + "lk = likelihood(v_true, alpha_true)\n", + "xs = lk.rvs(10000)\n", + "plt.hist(xs, density=True, bins=30)\n", + "plt.scatter([x_obs], [0.])\n", + "plt.show()" + ] }, { "cell_type": "markdown", @@ -92,24 +223,166 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 42, "metadata": { "tags": [] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + " message: Optimization terminated successfully.\n", + " success: True\n", + " status: 0\n", + " fun: -1.3836465597888634\n", + " x: [ 5.738e+00 1.674e-01]\n", + " nit: 4\n", + " jac: [ 6.869e-06 -6.065e-06]\n", + " hess_inv: [[ 2.362e-02 6.349e-04]\n", + " [ 6.349e-04 1.395e-03]]\n", + " nfev: 18\n", + " njev: 6" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Point-valued estimate\n", + "from scipy.optimize import minimize\n", + "\n", + "def log_likelihood(theta, x):\n", + " v, alpha = theta\n", + " lk = likelihood(v, alpha)\n", + " return lk.logpdf(x)\n", + "\n", + "nll = lambda *args: -log_likelihood(*args)\n", + "initial = np.array([p_v.rvs(), p_alpha.rvs()])\n", + "soln = minimize(nll, initial, args=(x_obs,))\n", + "soln" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Point-valued estimate\n" + "v_sol, alpha_sol = soln.x \n", + "\n", + "trajectory = simulate(v_sol, alpha_sol)\n", + "plt.plot(trajectory[:, 0], trajectory[:, 1])\n", + "plt.scatter([x_obs], [0.])\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 44, "metadata": { "tags": [] }, "outputs": [], "source": [ - "# Uncertainty estimation\n" + "# Uncertainty estimation\n", + "def log_prior(theta):\n", + " v, alpha = theta \n", + " return p_v.logpdf(v) + p_alpha.logpdf(alpha)\n", + "\n", + "def log_posterior(theta, x):\n", + " lp = log_prior(theta)\n", + " if not np.isfinite(lp):\n", + " return -np.inf \n", + " return lp + log_likelihood(theta, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/10000 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(2, figsize=(10, 7), sharex=True)\n", + "samples = sampler.get_chain()\n", + "labels = [\"v\", \"alpha\"]\n", + "\n", + "for i in range(ndim):\n", + " ax = axes[i]\n", + " ax.plot(samples[:, :, i], \"k\", alpha=0.2)\n", + " ax.set_xlim(0, len(samples))\n", + " ax.set_ylabel(labels[i])\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import corner\n", + "thetas = sampler.get_chain(flat=True)\n", + "fig = corner.corner(thetas, labels=labels, truths=[v_true, alpha_true])" ] }, { @@ -121,25 +394,105 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 49, "metadata": { "tags": [] }, - "outputs": [], + "outputs": [ + { + "ename": "AutocorrError", + "evalue": "The chain is shorter than 50 times the integrated autocorrelation time for 2 parameter(s). Use this estimate with caution and run a longer chain!\nN/50 = 200;\ntau: [563.19026509 735.90346359]", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAutocorrError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[49], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Computational diagnostics \u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m tau \u001b[38;5;241m=\u001b[39m \u001b[43msampler\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_autocorr_time\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28mprint\u001b[39m(tau)\n", + "File \u001b[0;32m~/anaconda3/envs/dats0001/lib/python3.9/site-packages/emcee/ensemble.py:605\u001b[0m, in \u001b[0;36mEnsembleSampler.get_autocorr_time\u001b[0;34m(self, **kwargs)\u001b[0m\n\u001b[1;32m 604\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mget_autocorr_time\u001b[39m(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m--> 605\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackend\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_autocorr_time\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/anaconda3/envs/dats0001/lib/python3.9/site-packages/emcee/backends/backend.py:150\u001b[0m, in \u001b[0;36mBackend.get_autocorr_time\u001b[0;34m(self, discard, thin, **kwargs)\u001b[0m\n\u001b[1;32m 131\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Compute an estimate of the autocorrelation time for each parameter\u001b[39;00m\n\u001b[1;32m 132\u001b[0m \n\u001b[1;32m 133\u001b[0m \u001b[38;5;124;03mArgs:\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 147\u001b[0m \n\u001b[1;32m 148\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 149\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_chain(discard\u001b[38;5;241m=\u001b[39mdiscard, thin\u001b[38;5;241m=\u001b[39mthin)\n\u001b[0;32m--> 150\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m thin \u001b[38;5;241m*\u001b[39m \u001b[43mautocorr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mintegrated_time\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/anaconda3/envs/dats0001/lib/python3.9/site-packages/emcee/autocorr.py:112\u001b[0m, in \u001b[0;36mintegrated_time\u001b[0;34m(x, c, tol, quiet)\u001b[0m\n\u001b[1;32m 110\u001b[0m msg \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mN/\u001b[39m\u001b[38;5;132;01m{0}\u001b[39;00m\u001b[38;5;124m = \u001b[39m\u001b[38;5;132;01m{1:.0f}\u001b[39;00m\u001b[38;5;124m;\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124mtau: \u001b[39m\u001b[38;5;132;01m{2}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(tol, n_t \u001b[38;5;241m/\u001b[39m tol, tau_est)\n\u001b[1;32m 111\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m quiet:\n\u001b[0;32m--> 112\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m AutocorrError(tau_est, msg)\n\u001b[1;32m 113\u001b[0m logger\u001b[38;5;241m.\u001b[39mwarning(msg)\n\u001b[1;32m 115\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m tau_est\n", + "\u001b[0;31mAutocorrError\u001b[0m: The chain is shorter than 50 times the integrated autocorrelation time for 2 parameter(s). Use this estimate with caution and run a longer chain!\nN/50 = 200;\ntau: [563.19026509 735.90346359]" + ] + } + ], + "source": [ + "# Computational diagnostics \n", + "tau = sampler.get_autocorr_time()\n", + "print(tau)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2000, 2)" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "thetas = sampler.get_chain(flat=True, thin=50)\n", + "thetas.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Computational diagnostics \n" + "fig = corner.corner(thetas, labels=labels, truths=[v_true, alpha_true])" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 53, "metadata": { "tags": [] }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Posterior predictive checks\n", - "# p(x | x_obs)\n" + "# p(x | x_obs)\n", + "xs = []\n", + "\n", + "for v, alpha in thetas:\n", + " trajectory = simulate(v, alpha)\n", + " plt.plot(trajectory[:, 0], trajectory[:, 1], color=\"b\", alpha=0.05)\n", + " x = likelihood(v, alpha).rvs()\n", + " xs.append(x)\n", + "\n", + "plt.hist(xs, density=True, bins=30, color=\"orange\")\n", + "plt.scatter([x_obs], [0.], c=\"r\")\n", + "plt.show()" ] }, {