Sample discrete Markov chains

This function draws independent random samples of a discrete Markov chain.

sampleDMC(pInit, Q, n = 1)

Arguments

pInit	an array of length K, containing the marginal distribution of the states for the first variable.
Q	an array of size (p-1,K,K), containing a list of p-1 transition matrices between the K states of the Markov chain.
n	the number of independent samples to be drawn (default: 1).

Value

A matrix of size n-by-p containing the n observed Markov chains of length p.

Details

Each element of the output matrix is an integer value between 0 and K-1. The transition matrices contained in Q are defined such that \(P[X_{j+1}=k|X_{j}=l]=Q[j,l,k]\).

References

Sesia M, Sabatti C, Candès EJ (2019). “Gene hunting with hidden Markov model knockoffs.” Biometrika, 106, 1--18. doi: 10.1093/biomet/asy033 .

See also

Other models: sampleHMM

Examples

p=10; K=5;
pInit = rep(1/K,K)
Q = array(stats::runif((p-1)*K*K),c(p-1,K,K))
for(j in 1:(p-1)) { Q[j,,] = Q[j,,] / rowSums(Q[j,,]) }
X = sampleDMC(pInit, Q, n=20)