tpm_thinned: Compute the transition probability matrix of a thinned...

In LaMa: Fast Numerical Maximum Likelihood Estimation for Latent Markov Models

Compute the transition probability matrix of a thinned periodically inhomogeneous Markov chain.

Description

If the transition probability matrix of an inhomogeneous Markov chain varies only periodically (with period length L), it converges to a so-called periodically stationary distribution. This happens, because the thinned Markov chain, which has a full cycle as each time step, has homogeneous transition probability matrix

\Gamma_t = \Gamma^{(t)} \Gamma^{(t+1)} \dots \Gamma^{(t+L-1)}

for all t = 1, \dots, L. This function calculates the matrix above efficiently as a preliminery step to calculating the periodically stationary distribution.

Usage

tpm_thinned(Gamma, t)

Arguments

Gamma	array of transition probability matrices of dimension c(N,N,L).
t	integer index of the time point in the cycle, for which to calculate the thinned transition probility matrix

Value

thinned transition probabilty matrix of dimension c(N,N)

Examples

# setting parameters for trigonometric link
beta = matrix(c(-1, -2, 2, -1, 2, -4), nrow = 2, byrow = TRUE)
# calculating periodically varying t.p.m. array (of length 24 here)
Gamma = tpm_p(beta = beta)
# calculating t.p.m. of thinned Markov chain
tpm_thinned(Gamma, 4)

LaMa documentation built on June 8, 2025, 1:53 p.m.