了解R中的马尔可夫链源代码 [英] Understanding Markov Chain source code in R

问题描述

以下源代码来自一本书.我写评论是为了更好地理解代码.

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]
}
#==================================================================

我对这个源代码有些困惑.

I have a few confusions regarding this source code.

为什么使用states <- 1:length(init)生成状态?如果状态如 S = {-1，0，1，2，...} 该怎么办?

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

推荐答案

状态名称实际上不需要具有任何统计意义，只要它们不同即可.因此，在模拟状态之间的转换时，最好为它们选择states <- 1:length(init)或任何其他名称.最终，尽管如此，出于实际目的，我们通常会想到一些标签，例如-1、0，...，n，如您的示例所示.您可以提供这些名称作为labels参数，然后labels[simlist]会逐元素将1:length(init)重命名为labels.即，如果最初我们有c(1, 2, 3)并且您将labels提供为c(5, 10, 12)，则输出将基于后一个向量.例如，

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. I.e., 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

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