Builds all transition probability matrices of an inhomogeneous-HSMM-approximating HMM
Hidden semi-Markov models (HSMMs) are a flexible extension of HMMs. For direct numerical maximum likelhood estimation, HSMMs can be represented as HMMs on an enlarged state space (of size ) and with structured transition probabilities.
This function computes the transition matrices of a periodically inhomogeneos HSMMs.
tpm_ihsmm(omega, dm, eps = 1e-10)
omega: embedded transition probability matrix
Either a matrix of dimension c(N,N) for homogeneous conditional transition probabilities (as computed by tpm_emb), or an array of dimension c(N,N,n) for inhomogeneous conditional transition probabilities (as computed by tpm_emb_g).
dm: state dwell-time distributions arranged in a list of length N
Each list element needs to be a matrix of dimension c(n, N_i), where each row t is the (approximate) probability mass function of state i at time t.
eps: rounding value: If an entry of the transition probabily matrix is smaller, than it is rounded to zero. Usually, this should not be changed.
list of dimension length n - max(sapply(dm, ncol)), containing sparse extended-state-space transition probability matrices for each time point (except the first max(sapply(dm, ncol)) - 1).
N = 2 # time-varying mean dwell times n = 100 z = runif(n) beta = matrix(c(2, 2, 0.1, -0.1), nrow = 2) Lambda = exp(cbind(1, z) %*% t(beta)) sizes = c(15, 15) # approximating chain with 30 states # state dwell-time distributions dm = lapply(1:N, function(i) sapply(1:sizes[i]-1, dpois, lambda = Lambda[,i])) ## homogeneous conditional transition probabilites # diagonal elements are zero, rowsums are one omega = matrix(c(0,1,1,0), nrow = N, byrow = TRUE) # calculating extended-state-space t.p.m.s Gamma = tpm_ihsmm(omega, dm) ## inhomogeneous conditional transition probabilites # omega can be an array omega = array(omega, dim = c(N,N,n)) # calculating extended-state-space t.p.m.s Gamma = tpm_ihsmm(omega, dm)