stationary_p_sparse function

Sparse version of stationary_p

This is function computes the periodically stationary distribution of a Markov chain given a list of L sparse transition probability matrices. Compatible with automatic differentiation by RTMB

stationary_p_sparse(Gamma, t = NULL)

Arguments

• Gamma: sist of length L containing sparse transition probability matrices for one cycle.
• t: integer index of the time point in the cycle, for which to calculate the stationary distribution If t is not provided, the function calculates all stationary distributions for each time point in the cycle.

Returns

either the periodically stationary distribution at time t or all periodically stationary distributions.

Examples

## periodic HSMM example (here the approximating tpm is sparse)
N = 2 # number of states
L = 24 # cycle length
# time-varying mean dwell times
Z = trigBasisExp(1:L) # trigonometric basis functions design matrix
beta = matrix(c(2, 2, 0.1, -0.1, -0.2, 0.2), nrow = 2)
Lambda = exp(cbind(1, Z) %*% t(beta))
sizes = c(20, 20) # approximating chain with 40 states
# state dwell-time distributions
dm = lapply(1:N, function(i) sapply(1:sizes[i]-1, dpois, lambda = Lambda[,i]))
omega = matrix(c(0,1,1,0), nrow = N, byrow = TRUE) # embedded t.p.m.

# calculating extended-state-space t.p.m.s
Gamma = tpm_phsmm(omega, dm)
# Periodically stationary distribution for specific time point
delta = stationary_p_sparse(Gamma, 4)

# All periodically stationary distributions
Delta = stationary_p_sparse(Gamma)