markov_chain

Builtin index · Statistics & ML

result = markov_chain(P, [initial_state=0])

Input: P, initial_state · Output: result

What it is

Builds a discrete Markov chain from an (S, S) row-stochastic transition matrix P (every row must sum to 1 — rows that don't are rejected outright, never quietly renormalized) and an integer initial_state (default 0, a state index in 0..S-1).

Overloads

One call shape — this function is not overloaded.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

P = [0.9, 0.5, 0.1, 0.5] as matrix(2, 2)   # column-major: rows [0.9 0.1], [0.5 0.5]

chain = markov_chain(P, 0)
print("stationary: {round(chain.stationary(), 4)}")
print("3-step:     {round(chain.transition ^ 3, 4)}")

trans = [0.7, 0.4, 0.3, 0.6] as matrix(2, 2)
emit  = [0.5, 0.1, 0.4, 0.3, 0.1, 0.6] as matrix(2, 3)
h = hmm(trans, emit, [0.6, 0.4])
print("P(normal, cold, dizzy) = {round(h.forward([0, 1, 2]), 5)}")
print("most likely path       = {h.viterbi([0, 1, 2])}")

stationary: [0.8333, 0.1667]
3-step:     [0.844, 0.156; 0.78, 0.22]
P(normal, cold, dizzy) = 0.03628
most likely path       = [0, 0, 1]

from statistics-ml

How it works

markov_chain(P, [initial_state=0]) — a discrete-time, discrete-state Markov chain over a row-stochastic transition matrix P (row i is state i's outgoing distribution; check_row_stochastic rejects anything else with a clear error rather than silently normalizing). .simulate(n_steps, [seed=]) and .stationary() are separate generic-verb builtins (see their own doc comments, near predict/score) since neither takes an X the way a supervised/clustering model's predict/score do; n-step transition probabilities need no new builtin at all — chain.transition ^ n already works via the existing matrix-power operator (matrix_pow).

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.