beta_binom_post_pred_plot.ipynb

Kernel: Unknown Kernel

# Plots the posterior and plugin predictives for the Beta-Binomial distribution.


import numpy as np
import matplotlib.pyplot as plt

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml

from scipy.special import comb, beta
from scipy.stats import binom


N = 10  # Future sample size M
# Hyperparameters
a = 1
b = 1
N1 = 4
N0 = 1

ind = np.arange(N + 1)
post_a = a + N1
post_b = b + N0

# Compound beta-binomial distribution
distribution = []
for k in range(N + 1):
    distribution.append(comb(N, k) * beta(k + post_a, N - k + post_b) / beta(post_a, post_b))

fig, ax = plt.subplots()
rects = ax.bar(ind, distribution, align="center")
ax.set_title("posterior predictive")
ax.set_xticks(list(range(N + 1)))
ax.set_xticklabels(list(range(N + 1)))
pml.savefig("BBpostpred.pdf")
plt.show()

# Plugin binomial distribution
mu = (post_a - 1) / float(post_a + post_b - 2)  # MAP estimate
distribution = []
rv = binom(N, mu)
for k in range(N + 1):
    distribution.append(rv.pmf(k))

fig, ax = plt.subplots()
rects = ax.bar(ind, distribution, align="center")
ax.set_title("plugin predictive")
ax.set_xticks(list(range(N + 1)))
ax.set_xticklabels(list(range(N + 1)))
pml.savefig("BBpluginpred.pdf")
plt.show()