[PYTHON] How to use PyMC3 (Bayesian inference)

I will forget it when I try to use it for the first time in a long time, so make a note of it.

What is PyMC3?

--Probabilistic programming library for Python --Can be used for Bayesian inference

Installation

pip install pymc3

Basic writing


import numpy as np
from matplotlib import pyplot as plt

#Number of trials and observation results(Number of times)
N = 100
a = 5

with pm.Model() as model:
  #Prior distribution
  #Uniform distribution with a range of 0 to 1
  theta = pm.Uniform('theta', lower=0, upper=1)

  #Likelihood function
  #Set the binomial distribution as the distribution followed by the number of observations a when the Bernoulli trial is performed N times.
  obs = pm.Binomial('a', p=theta, n=N, observed=a)

  #Perform inference and from posterior distribution 5000*2 Get a sample
  trace = pm.sample(5000, chains=2)

--In pm.sample, the sample is obtained by MCMC and the result is stored in trace.

Visualization of sample (posterior distribution)

with model:
  pm.traceplot(trace)

--The figure on the left shows the estimated posterior distribution for the random variable of interest. --On the right side, the trajectory of the sample obtained after burn-in is displayed. --Burn-in: The period during which the sample is discarded to remove the effect of the initial value of the search.

Displaying summary statistics

with model:
  # HDI(highest density interval)As 95%Set HDI
  print(pm.summary(trace, hdi_prob=0.95)

Visualize sample (posterior distribution) with summary statistics

with model:
  pm.plot_posterior(trace, hdi_prob=0.95)

Reference material

PyMC3 Documentation