Chapter 3 of Mackay's ITILA

itila_chp3.py

import numpy as np
from scipy.stats import binom
import matplotlib.pyplot as plt
import numpy
from math import factorial as fac
from collections import Counter
from scipy.stats import norm

# P(ph | s=hth, N =3)

def coin_likelihood(ph, X) :
	return ph**X["h"] * (1-ph)**X["t"]

def coin_bias_posterior(X, ph) :
	N = len(X)
	X = Counter(X)

	z = fac(X["h"]) * fac(X["t"]) / (fac(X["h"]+ X["t"] + 1))
	return coin_likelihood(ph, X) / z


def plot_and_summarise_posterior(data) :
	x = np.arange(0,1, 0.005)
	y = [coin_bias_posterior(data, i) for i in x ]
	plt.plot(x,y)
	plt.show()
	print(data)
	print( "ph:", mean(x, y)  )
	print( "ph:", mode(x, y)  )


def mode(x,y) :
	i = max(zip(y, range(len(y))))[1]
	return x[i]


def mean(x, y) :
	ev = sum(p * v for p,v in zip(x,y))
	return ev / len(x)

# Ex 3.5
data = ["h", "t", "h"]
plot_and_summarise_posterior(data)
data = ["t", "t", "t"]
plot_and_summarise_posterior(data)