hmmProcess: hmmProcess calculates the probability distribution of a...

In samurais: Statistical Models for the Unsupervised Segmentation of Time-Series ('SaMUraiS')

Description

hmmProcess calculates the probability distribution of a random process following a Markov chain

Usage

hmmProcess(prior, trans_mat, n)

Arguments

prior	Numeric vector or a one row matrix of length K representing the prior probabilities of the Markov chain.
trans_mat	Matrix of size (K, K) representing the transition matrix of the Markov chain.
n	Numeric. Number of variables of the Markov chain.

Details

hmmProcess calculates the distribution P(Z_{1},…,Z_{n};π,A) of a Markov chain (Z_{1},…,Z_{n}) with prior probability π and transition matrix A.

The calculation is based on the following formula:

P(Z_{i} = k) = ∑_{l} P(Z_{i} = k, Z_{i-1} = l) = ∑_{l} P(Z_{i} = k | Z_{i-1} = l) x P(Z_{i-1} = l) = ∑_{l} A_{lk} x P(Z_{i-1})

Value

Matrix of size (n, K) giving the distribution of process given the K-state Markov chain parameters.

samurais documentation built on July 28, 2019, 5:02 p.m.