postDensityIntervals.ipynb

Kernel: Unknown Kernel

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


def logdet(Sigma):
    return np.log2(Sigma)


def gaussProb(X, mu, Sigma):
    d = 1
    X = X.reshape(X.shape[0], d)
    X = X - np.transpose(mu)
    logp = -0.5 * np.sum(np.multiply((X / (Sigma)), X), 1)
    logZ = (d / 2) * np.log(2 * np.pi) + 0.5 * logdet(Sigma)
    logp = logp - logZ
    p = np.exp(logp)
    return p


def f(x):
    return gaussProb(x, 0, 1) + gaussProb(x, 6, 1)


domain = np.arange(-4, 10.001, 0.001)
plt.plot(domain, f(domain), "-r", linewidth=3)
plt.fill_between(domain, f(domain), color="gray", alpha=0.2)
plt.fill_between(np.arange(-4, -1.999, 0.001), f(np.arange(-4, -1.999, 0.001)), color="white")
plt.fill_between(np.arange(8, 10.001, 0.001), f(np.arange(8, 10.001, 0.001)), color="white")
plt.annotate(r"$\alpha /2$", xytext=(-3.5, 0.11), xy=(-2.3, 0.015), arrowprops=dict(facecolor="black"), fontsize=14)
plt.annotate(r"$\alpha /2$", xytext=(9.5, 0.11), xy=(8.3, 0.015), arrowprops=dict(facecolor="black"), fontsize=14)
plt.ylim(0, 0.5)
pml.savefig("centralInterval.pdf")
plt.show()

plt.plot(domain, f(domain), "-r", linewidth=3)
plt.fill_between(domain, f(domain), color="gray", alpha=0.2)
plt.fill_between(np.arange(-4, -1.43992, 0.001), f(np.arange(-4, -1.43992, 0.001)), color="white")
plt.fill_between(np.arange(7.37782, 10.001, 0.001), f(np.arange(7.37782, 10.001, 0.001)), color="white")
plt.plot(domain, [0.15 for i in range(0, 14001)], "b-")
plt.fill_between(np.arange(1.3544, 4.5837, 0.001), f(np.arange(1.3544, 4.5837, 0.001)), color="white")
plt.yticks([0.15], ["pMIN"], fontsize=14)
plt.ylim(0, 0.5)
pml.savefig("HPD.pdf")

plt.show()