hmmProcess function

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

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.

Returns

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

Details

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

The calculation is based on the following formula:

c("$P(Z_{i} = k) = \\sum_{l} P(Z_{i} = k, Z_{i-1} = l) = \\sum_{l}\n$", "$P(Z_{i} = k | Z_{i-1} = l) x P(Z_{i-1} = l) = \\sum_{l} A_{lk} x P(Z_{i-1})$")