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@tatsy
Last active January 4, 2022 02:22
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Gibbs sampling
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Parameters\n",
"n_mutate = 50000"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def inv_dist_fun(x):\n",
" x_, y_ = np.split(x, 2, axis=-1)\n",
" return np.exp(-0.5 *\n",
" (x_ * x_ - x_ * y_ + y_ * y_)) / (4.0 * np.pi / np.sqrt(3.0))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"class Gibbs(object):\n",
" def __init__(self, x, inv_dist_fun, sigma, seed=0):\n",
" self.x = np.asarray(x, dtype='float64')\n",
" self.inv_dist_fun = inv_dist_fun\n",
" self.sigma = sigma\n",
" self.rng = np.random.RandomState(seed)\n",
"\n",
" def sample(self):\n",
" i = self.rng.randint(0, 2)\n",
" j = 1 - i\n",
" self.x[i] = self.rng.normal(0.5 * self.x[j], 1.0)\n",
" return self.x.copy()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"sampler = Gibbs((0.0, 0.0), inv_dist_fun, 1.0)\n",
"n_burnin = max(n_mutate // 100, 100)\n",
"for i in range(n_burnin):\n",
" sampler.sample()\n",
"\n",
"samples = []\n",
"for i in range(n_mutate):\n",
" samples.append(sampler.sample())\n",
"samples = np.stack(samples)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1152x576 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bins = 50\n",
"v_min = -5.0\n",
"v_max = 5.0\n",
"\n",
"fig = plt.figure(figsize=(16, 8))\n",
"ax = fig.add_subplot(121)\n",
"ax.hist2d(samples[:, 0],\n",
" samples[:, 1],\n",
" bins=bins,\n",
" range=((v_min, v_max), (v_min, v_max)),\n",
" cmin=0.0,\n",
" cmax=0.15,\n",
" density=True)\n",
"ax.set_title(\"samples\")\n",
"ax.set_aspect(1)\n",
"\n",
"xs = np.linspace(v_min, v_max, bins)\n",
"ys = np.linspace(v_min, v_max, bins)\n",
"ys, xs = np.meshgrid(ys, xs)\n",
"vals = inv_dist_fun(np.stack([xs, ys], axis=-1))\n",
"ax = fig.add_subplot(122)\n",
"ax.pcolormesh(xs, ys, vals.squeeze(), vmin=0.0, vmax=0.15, shading=\"gouraud\")\n",
"ax.set_title(\"target\")\n",
"ax.set_aspect(1)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"interpreter": {
"hash": "02d3c230780613a338b307efe1c8520401457e802ba0c889aabda605c4f627d4"
},
"kernelspec": {
"display_name": "Python 3.8.11 64-bit ('base': conda)",
"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": "3.8.11"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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