Bayesian Online Changepoint Step

Problem

Perform one Bayesian online changepoint detection update. Given current run-length probabilities, a constant hazard rate, and the predictive probability of the new observation, form the changepoint term hazard * predictive and the growth terms run_prob * (1 - hazard) * predictive, then normalize.

Return the new run-length probability vector (one element longer). Return an empty list for empty input.

Hint

Index 0 is the probability that a changepoint just happened.

Test cases

case 1

in: [[0.8,0.2],0.1,0.5]

expected: [0.1,0.7200000000000001,0.18000000000000002]

case 2

in: [[1],0.05,1]

expected: [0.05,0.95]

case 3

in: [[0.5,0.3,0.2],0,1]

expected: [0,0.5,0.3,0.2]

case 4

in: [[0.5,0.5],1,0.5]

expected: [1,0,0]

Starter codePython

def bayesian_online_changepoint_step(run_probs, hazard, predictive_prob):
    # Your code here
    pass

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