Using Ipython Notebook, Bayesian Inference

Using Ipython Notebook, Bayesian Inference

In [8]:

%matplotlib inline

from IPython.core.pylabtools import figsize

import numpy as np

from matplotlib import pyplot as plt

figsize(11, 9)

import scipy.stats as stats

dist = stats.beta

n_trials = [0, 10, 12, 3, 4, 5, 18, 15, 50, 500]

data = stats.bernoulli.rvs(0.5, size=n_trials[-1])

x = np.linspace(0, 1, 100)

# For the already prepared, I'm using Binomial's conj. prior.

for k, N in enumerate(n_trials):

    sx = plt.subplot(len(n_trials) / 2, 2, k + 1)

    plt.xlabel("$p$, probability of heads") \

        if k in [0, len(n_trials) - 1] else None

    plt.setp(sx.get_yticklabels(), visible=False)

    heads = data[:N].sum()

    y = dist.pdf(x, 1 + heads, 1 + N - heads)

    plt.plot(x, y, label="observe %d tosses,\n %d heads" % (N, heads))

    plt.fill_between(x, 0, y, color="#348ABD", alpha=0.4)

    plt.vlines(0.5, 0, 4, color="k", linestyles="--", lw=1)

    leg = plt.legend()

    leg.get_frame().set_alpha(0.4)

    plt.autoscale(tight=True)

plt.suptitle("Bayesian updating of posterior probabilities",

             y=1.02,

             fontsize=14)

plt.tight_layout()

In [ ]: