Markov Entropy Rate (2-State)

Problem

For a two-state Markov chain with transition probabilities p01 (0 -> 1) and p10 (1 -> 0), return the entropy rate in bits:

pi0 = p10 / (p01 + p10), pi1 = p01 / (p01 + p10) R = pi0 * H(p01) + pi1 * H(p10)

where H is the binary entropy function in bits.

Hint

The stationary distribution weights each state's transition entropy.

case 1

in: [0.5,0.5]

expected: 1

case 2

in: [0,1]

expected: 0

case 3

in: [0.1,0.2]

expected: 0.5533064273553082

case 4

in: [0.5,0.25]

expected: 0.8741854163060885

Starter codePython

import math
def markov_rate_2state(p01, p10):
    # Your code here
    pass

4 test cases · run your code against them in the editor