Build the transition probability matrix of an 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 \(M\)) and with structured transition probabilities. This function computes the transition matrix of an HSMM.

Usage

tpm_hsmm2(omega, dm, eps = 1e-10)

Arguments

omega: embedded transition probability matrix of dimension c(N,N)
dm: state dwell-time distributions arranged in a list of length(N). Each list element needs to be a vector of length N_i, where N_i is the state aggregate size.
eps: rounding value: If an entry of the transition probabily matrix is smaller, than it is rounded to zero.

Value

extended-state-space transition probability matrix of the approximating HMM

Examples

# building the t.p.m. of the embedded Markov chain
omega = matrix(c(0,1,1,0), nrow = 2, byrow = TRUE)
# defining state aggregate sizes
sizes = c(20, 30)
# defining state dwell-time distributions
lambda = c(5, 11)
dm = list(dpois(1:sizes[1]-1, lambda[1]), dpois(1:sizes[2]-1, lambda[2]))
# calculating extended-state-space t.p.m.
Gamma = tpm_hsmm(omega, dm)