Simulate from a homogeneous or non-homogeneous Markov chain

Simulates trajectories of a homogeneous Markov chain (a markovchain object) or of a non-homogeneous one (a markovchainList object, whose \(k\)-th matrix gives the transition from time \(k - 1\) to time \(k\)).

Usage

rmarkovchain(
  n,
  object,
  what = "data.frame",
  useRCpp = TRUE,
  parallel = FALSE,
  num.cores = NULL,
  ...
)

Arguments

n

For a markovchain, the number of steps of the trajectory; for a markovchainList, the number of trajectories, each as long as the list.

object

A markovchain or markovchainList object.

what

Form of the output for a markovchainList: "data.frame" (default; columns iteration and values, one row per simulated state), "matrix" (one row per trajectory) or "list" (one character vector per trajectory). Ignored for a markovchain.

useRCpp

Logical: use the C++ implementation (default)?

parallel

Logical: simulate the trajectories of a markovchainList in parallel (default FALSE)?

num.cores

Number of threads used when parallel = TRUE. If NULL (the default) the thread count is read from getOption("RcppParallel.numThreads"), then getOption("Ncpus"), then the environment variables RCPP_PARALLEL_NUM_THREADS and OMP_NUM_THREADS, falling back to min(2, cores) as CRAN policy requires.

...

Further arguments: t0 (initial state) and include.t0 (include it in the output), as in markovchainSequence().

Value

For a markovchain, a character vector of states. For a markovchainList, a data frame, matrix or list, according to what.

Details

For a markovchain the function calls markovchainSequence(). For a markovchainList each trajectory starts from t0 (by default a state drawn at random) and moves once with each matrix of the list.

References

Ross, S. (2010). A First Course in Probability (8th edition). Prentice Hall.

See also

markovchainFit() and markovchainListFit() for the reverse operation.

Other simulation: markovchainSequence()

Author

Giorgio Spedicato

Examples

statesNames <- c("a", "b", "c")
mcA <- new("markovchain", states = statesNames, transitionMatrix =
  matrix(c(0.2, 0.5, 0.3, 0, 0.2, 0.8, 0.1, 0.8, 0.1), nrow = 3,
  byrow = TRUE, dimnames = list(statesNames, statesNames)))
rmarkovchain(n = 20, object = mcA, t0 = "a")
#>  [1] "b" "b" "c" "b" "c" "b" "c" "b" "c" "b" "c" "b" "c" "b" "b" "c" "b" "b" "b"
#> [20] "c"

# a non-homogeneous chain: a different matrix at each of three steps
mcB <- new("markovchain", states = statesNames, transitionMatrix =
  matrix(c(0.5, 0.5, 0, 0.1, 0.8, 0.1, 0, 0.5, 0.5), nrow = 3,
  byrow = TRUE, dimnames = list(statesNames, statesNames)))
mclist <- new("markovchainList", markovchains = list(mcA, mcB, mcA))
rmarkovchain(5, mclist, what = "matrix")
#>      [,1] [,2] [,3]
#> [1,] "c"  "b"  "c" 
#> [2,] "b"  "b"  "b" 
#> [3,] "c"  "b"  "c" 
#> [4,] "b"  "b"  "c" 
#> [5,] "c"  "c"  "b" 
rmarkovchain(2, mclist, what = "list", t0 = "a", include.t0 = TRUE)
#> [[1]]
#> [1] "a" "c" "b" "c"
#> 
#> [[2]]
#> [1] "a" "b" "b" "b"
#>