gaussian.py

#This is all from the book. Not my code.

import numpy as np
from numpy.random import randn
import filterpy.stats as stats
import matplotlib.pyplot as plt

from collections import namedtuple
gaussian = namedtuple('Gaussian', ['mean', 'var'])
gaussian.__repr__ = lambda s: '𝒩(μ={:.3f}, 𝜎²={:.3f})'.format(s[0], s[1])

def gaussian_multiply(g1, g2):
    mean = (g1.var * g2.mean + g2.var * g1.mean) / (g1.var + g2.var)
    variance = (g1.var * g2.var) / (g1.var + g2.var)
    return gaussian(mean, variance)

z = gaussian(10., 1.)  # Gaussian N(10, 1)

product = gaussian_multiply(z, z)

xs = np.arange(5, 15, 0.1)
ys = [stats.gaussian(x, z.mean, z.var) for x in xs]
plt.plot(xs, ys, label='$\mathcal{N}(10,1)$')

ys = [stats.gaussian(x, product.mean, product.var) for x in xs]
plt.plot(xs, ys, label='$\mathcal{N}(10,1) \\times \mathcal{N}(10,1)$', ls='--')
plt.legend()
print(product)