Understanding Markov Chain source code in R

Question

The following source code is from a book. Comments are written by me to understand the code better.

#==================================================================
# markov(init,mat,n,states) = Simulates n steps of a Markov chain 
#------------------------------------------------------------------
# init = initial distribution 
# mat = transition matrix 
# labels = a character vector of states used as label of data-frame; 
#           default is 1, .... k
#-------------------------------------------------------------------
markov <- function(init,mat,n,labels) 
{ 
    if (missing(labels)) # check if 'labels' argument is missing
    {
        labels <- 1:length(init) # obtain the length of init-vecor, and number them accordingly.
    }

    simlist <- numeric(n+1) # create an empty vector of 0's
    states <- 1:length(init)# ???? use the length of initial distribution to generate states.
    simlist[1] <- sample(states,1,prob=init) # sample function returns a random permutation of a vector.
                        # select one value from the 'states' based on 'init' probabilities.

    for (i in 2:(n+1))
    { 
        simlist[i] <- sample(states, 1, prob = mat[simlist[i-1],]) # simlist is a vector.
                                                    # so, it is selecting all the columns 
                                                    # of a specific row from 'mat'
    }

    labels[simlist]
}
#==================================================================

I have a few confusions regarding this source code.

Why is states <- 1:length(init) used to generate states? What if states are like S ={-1, 0, 1, 2,...} ?

Answer 1

Names of the states don't really need to have any statistical meaning as long as they are different. So, while simulating transitions between states, it's perfectly fine to choose states <- 1:length(init) or any other names for them. Ultimately, though, for practical purposes we often have in mind some labels in mind, such as -1, 0, ..., n, as in your example. You can provide those names as the labels parameter and then labels[simlist] will rename 1:length(init) to labels , element by element. Ie, if initially we had c(1, 2, 3) and you provided labels as c(5, 10, 12) , then the output will be in terms of the latter vector. For instance,

(states <- sample(1:3, 10, replace = TRUE))
# [1] 1 3 3 2 2 1 2 1 3 3
labels <- c(5, 10, 12)
labels[states]
# [1]  5 12 12 10 10  5 10  5 12 12