simulMk: Simulation of a k-th order Markov chain

In SMM: Simulation and Estimation of Multi-State Discrete-Time Semi-Markov and Markov Models

Description

Simulation of a k-th order Markov chain starting from a transition matrix and an initial distribution.

Usage

simulMk(E, nbSeq, lengthSeq, Ptrans, init, k, File.out = NULL)

Arguments

E	Vector of state space
nbSeq	Number of simulated sequences
lengthSeq	Vector of size nbSeq containing the lengths of each simulated sequence
Ptrans	Matrix of transition probabilities of size (S^(k))xS, with S = length(E)
init	Vector of initial distribution of length S
k	Order of the Markov chain
File.out	Name of the fasta file for saving the sequences. If File.out = NULL, no file is created

Details

The sizes of init and Ptrans depend on S, the length of E. The rows of the transition matrix sums to 1.

For k=1, the transition matrix is defined by Ptrans(i,j) = P(X_{m+1} = j | X_m = i) and the initial distribution is init = P(X_1 = i). For k > 1 we have similar expressions.

The first element of lengthSeq corresponds to the length of the first sequence and so on.

Value

simulMk returns a list of sequences of size lengthSeq simulated with a k-th order Markov chain of parameters init and Ptrans with state space E.

If the parameter File.out is not equal to NULL, a file in fasta format containing the sequence(s) will be created.

Author(s)

Vlad Stefan Barbu, [e-mail]
Caroline Berard, [e-mail]
Dominique Cellier, [e-mail]
Mathilde Sautreuil, [e-mail]
Nicolas Vergne, [e-mail]

See Also

estimMk, simulSM, estimSM

Examples

### Example 1 ###
# Second order model with state space {a,c,g,t}
E <- c("a","c","g","t")
S = length(E)
init.distribution <- c(1/6,1/6,5/12,3/12)
k<-2
p <- matrix(0.25, nrow = S^k, ncol = S)

# We simulate 3 sequences of size 1000, 10000 and 2000 respectively.
simulMk(E = E, nbSeq = 3, lengthSeq = c(1000, 10000, 2000), Ptrans = p, 
init = init.distribution, k = k)

### Example 2 ###
# first order model with state space {1,2,3}
E <- c(1,2,3)
S <- length(E)
init.distr <- rep(1/S, 3)
p <- matrix(c(0.3,0.2,0.5,0.1,0.6,0.3,0.2,0.4,0.4), nrow = 3, byrow = TRUE)

# We simulate one sequence of size 100
simulMk(E = E, nbSeq = 1, lengthSeq = 100, Ptrans = p, init = init.distr, k = 1)

SMM documentation built on Jan. 31, 2020, 5:07 p.m.