Notebook for mcmc transforms

notebooks/user/rragonnet/mcmc_transform.ipynb

@@ -0,0 +1,107 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from matplotlib import pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Prior bounds"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a, b = 0, 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Default transformation (standard with pymc, stan...)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_default_transform():\n",
+    "    default_transform = lambda x: np.log(x - a) - np.log(b - x)\n",
+    "\n",
+    "    x = np.linspace(a, b, num=1000)[1:-1] \n",
+    "    y = default_transform(x)\n",
+    "    plt.plot(x, y, label=\"Default transform\")\n",
+    "    plt.xlim((a - .5 * (b-a), b + .5 * (b-a)))\n",
+    "    plt.xlabel(\"Original parameter\")\n",
+    "    plt.ylabel(\"Transformed parameter\")\n",
+    "    plt.vlines(x=[a, b], ymin=plt.gca().get_ylim()[0], ymax=plt.gca().get_ylim()[1], linestyles=[\"--\", \"--\"], color='black')\n",
+    "\n",
+    "\n",
+    "plot_default_transform()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tweaked transformation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_tweaked_transform(eps=.1):\n",
+    "    a_prime = a - eps * (b - a)\n",
+    "    b_prime = b + eps * (b - a)\n",
+    "    tweaked_transform = lambda x: np.log(x - a_prime) - np.log(b_prime - x)\n",
+    "\n",
+    "    x = np.linspace(a_prime, b_prime, num=1000)[1:-1] \n",
+    "    y = tweaked_transform(x)\n",
+    "    plot_default_transform()\n",
+    "    plt.plot(x, y, label=\"Tweaked transform\")\n",
+    "    plt.legend()\n",
+    "\n",
+    "plot_tweaked_transform(.1)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "summer2",
+   "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": "3.10.11"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}