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@drbenvincent
Last active December 29, 2021 02:42
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Plotting univariate distributions in PyMC3
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "4c4de0ec-d9e9-4a72-ba36-64297d501bda",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'3.11.2'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pymc3 as pm\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%config InlineBackend.figure_format = 'retina'\n",
"%matplotlib inline\n",
"pm.__version__"
]
},
{
"cell_type": "markdown",
"id": "fc2fde22-f093-48c5-a610-25ced92c01f9",
"metadata": {},
"source": [
"## Plotting pdf of continuous distributions"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "44813e80-62c0-44e2-a7f0-0f371b634fca",
"metadata": {},
"outputs": [],
"source": [
"def plot_cont(self, ax=None):\n",
" if ax is None:\n",
" _, ax = plt.subplots()\n",
" samples = self.random(size=1000)\n",
" x = np.linspace(np.min(samples), np.max(samples), 1000)\n",
" ax.plot(x, np.exp(self.logp(x)).eval())\n",
" return ax\n",
"\n",
"# Assign this distribution to the abstract class Continuous\n",
"pm.Continuous.plot = plot_cont"
]
},
{
"cell_type": "markdown",
"id": "ceb5e4a2-6294-4c9f-a84c-44bb59f0c767",
"metadata": {},
"source": [
"Example use"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ec3a8e31-cb48-4a45-955d-05b3bc60c966",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 248,
"width": 384
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = pm.Normal.dist(mu=0, sd=2).plot()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5387a639-d98d-4529-9c32-60a2753466cc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 248,
"width": 372
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = pm.Normal.dist(mu=0, sd=2).plot()\n",
"pm.Laplace.dist(mu=3, b=1).plot(ax);"
]
},
{
"cell_type": "markdown",
"id": "8a90dc85-5215-41cb-a79b-b42578eafcc9",
"metadata": {},
"source": [
"## Plotting pdf of discrete distributions"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d1e3b3c8-ead8-4da3-9c5f-8dea672f9568",
"metadata": {},
"outputs": [],
"source": [
"def plot_disc(self, ax=None):\n",
" if ax is None:\n",
" _, ax = plt.subplots()\n",
" samples = self.random(size=1000)\n",
" x = np.arange(np.min(samples), np.max(samples)+1)\n",
" plt.plot(x, np.exp(self.logp(x)).eval(), \"-o\")\n",
" return ax\n",
"\n",
"# add plot method to abstract class Discrete\n",
"pm.Discrete.plot = plot_disc"
]
},
{
"cell_type": "markdown",
"id": "8641b110-15fa-4709-aa0d-473e8399e7ed",
"metadata": {},
"source": [
"Example use"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9270698f-d91c-4532-837a-25c7d4e6b603",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 248,
"width": 378
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = pm.Binomial.dist(n=10, p=0.2).plot()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "72d27c7a-906f-45a2-a52b-d898c57b2c6a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 248,
"width": 372
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = pm.Binomial.dist(n=10, p=0.2).plot()\n",
"pm.Geometric.dist(p=0.5).plot(ax);"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "beaa4c0f-3354-48b0-8539-ad82fb42d66d",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "pymc3_stable",
"language": "python",
"name": "pymc3_stable"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
@harcel
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harcel commented Dec 24, 2021

Awesome, thanks!
The comment line before "pm.Discrete.plot = plot_disc" should probably say that this adds it to the Discrete abstract class, but that's just details.
Really cool. I have often been doing things like this by hand, and it never occurred to me to assign it to that class so easily. Thanks again and happy to follow along with the new youtube channel!

@drbenvincent
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Author

Thanks @harcel, I've made that edit. Hope to have more videos like it soon.

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