Sample hidden Markov models

This function draws independent random samples of an hidden Markov model.

sampleHMM(pInit, Q, pEmit, 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.
pEmit	an array of size (p,M,K), containing the emission probabilities for each of the M possible emission states, from each of the K hidden states and the p variables.
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 with the same convention as in sampleDMC. The emission propability matrices contained in pEmit are defined such that \(P[X_{j}=k|H_{j}=l]=\mathrm{pEmit}[j,k,l]\), where \(H_j\) is the latent variable associated to \(X_j\).

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: sampleDMC

Examples

p=10; K=5; M=3;
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,,]) }
pEmit = array(stats::runif(p*M*K),c(p,M,K))
for(j in 1:p) { pEmit[j,,] = pEmit[j,,] / rowSums(pEmit[j,,]) }
X = sampleHMM(pInit, Q, pEmit, n=20)