tpm_cont {LaMa}

Calculation of continuous time transition probabilities

Description

A continuous-time Markov chain is described by an infinitesimal generator matrix Q. When observing data at time points t_1, \dots, t_n the transition probabilites between t_i and t_{i+1} are caluclated as

\Gamma(\Delta t_i) = \exp(Q \Delta t_i),

where \exp() is the matrix exponential. The mapping \Gamma(\Delta t) is also called the Markov semigroup. This function calculates all transition matrices based on a given generator and time differences.

Usage

tpm_cont(Q, timediff)

Arguments

Q

Infinitesimal generator matrix of the continuous-time Markov chain of dimension c(N,N)

timediff

Time differences between observations of length n-1 when based on n observations

Value

An array of transition matrices of dimension c(N,N,n-1)

Examples

# building a Q matrix for a 3-state cont.-time Markov chain
Q = diag(3)
Q[!Q] = rexp(6)
diag(Q) = 0
diag(Q) = - rowSums(Q)

# draw time differences
timediff = rexp(1000, 10)

Gamma = tpm_cont(Q, timediff)