R/simulate_markov_chain.R

In oeli: Utilities for Developing Data Science Software

#' Simulate Markov chain
#'
#' @description
#' This function simulates a Markov chain.
#'
#' @param Gamma \[`matrix()`\]\cr
#' A transition probability matrix.
#'
#' @param T \[`integer(1)`\]\cr
#' The length of the Markov chain.
#'
#' @param delta \[`numeric()`\]\cr
#' A probability vector, the initial distribution.
#'
#' By default, \code{delta} is the stationary distribution of \code{Gamma}.
#'
#' @return
#' A \code{numeric} vector of length \code{T} with states.
#'
#' @keywords simulation
#' @family simulation helpers
#' @export
#'
#' @examples
#' Gamma <- sample_transition_probability_matrix(dim = 3)
#' simulate_markov_chain(Gamma = Gamma, T = 10)

simulate_markov_chain <- function(
    Gamma, T, delta = oeli::stationary_distribution(Gamma)
  ) {
  assert_transition_probability_matrix(Gamma)
  checkmate::assert_int(T, lower = 1)
  assert_probability_vector(delta, len = nrow(Gamma))
  N <- length(delta)
  markov_chain <- numeric(T)
  markov_chain[1] <- sample(1:N, 1, prob = delta)
  for (t in 2:T) {
    markov_chain[t] <- sample(1:N, 1, prob = Gamma[markov_chain[t - 1], ])
  }
  markov_chain
}