prob140.MarkovChain.prob_of_path

MarkovChain.prob_of_path(starting_condition, path)

Finds the probability of a path given a starting condition.

Parameters:

starting_condition : state or Distribution

If a state, finds the probability of the path starting at that state. If a Distribution, finds the probability of the path with the first element sampled from the Distribution.

path : ndarray

Array of states

Returns:

float

probability

Examples

>>> states = ['A', 'B']
>>> transition_matrix = np.array([[0.1, 0.9],
...                               [0.8, 0.2]])
>>> mc = MarkovChain.from_matrix(states, transition_matrix)
>>> mc.prob_of_path('A', ['A', 'B', 'A'])
0.072
>>> 0.1 * 0.9 * 0.8
0.072
>>> start = Table().states(['A', 'B']).probability([0.8, 0.2])
>>> mc.prob_of_path(start, ['A', 'B', 'A'])
0.576
>>> 0.8 * 0.9 * 0.8
0.576