用於離散馬爾可夫鏈模擬的R庫

Question

我正在尋找'msm'包，但是用於離散馬爾可夫鏈。例如，如果我有定義爲這樣

Pi <- matrix(c(1/3,1/3,1/3, 
0,2/3,1/6, 
2/3,0,1/2)) 

對於狀態A，B，C的過渡矩陣。如何根據該轉換矩陣模擬馬爾可夫鏈？

感謝，

Answer 1

後來我寫了一組用於模擬和估計離散馬爾可夫鏈概率矩陣的函數：http://www.feferraz.net/files/lista/DTMC.R。你在問什麼

相關代碼：

simula <- function(trans,N) { 
     transita <- function(char,trans) { 
       sample(colnames(trans),1,prob=trans[char,]) 
     } 

sim <- character(N) 
sim[1] <- sample(colnames(trans),1) 
for (i in 2:N) { 
    sim[i] <- transita(sim[i-1],trans) 
} 

sim 
} 

#example 
#Obs: works for N >= 2 only. For higher order matrices just define an 
#appropriate mattrans 
mattrans <- matrix(c(0.97,0.03,0.01,0.99),ncol=2,byrow=TRUE) 
colnames(mattrans) <- c('0','1') 
row.names(mattrans) <- c('0','1') 
instancia <- simula(mattrans,255) # simulates 255 steps in the process 

Answer 2

哎呀，你找到了解決辦法，而我在寫它給你的。這裏有一個簡單的例子，我想出了：

run = function() 
{ 
    # The probability transition matrix 
    trans = matrix(c(1/3,1/3,1/3, 
       0,2/3,1/3, 
       2/3,0,1/3), ncol=3, byrow=TRUE); 

    # The state that we're starting in 
    state = ceiling(3 * runif(1, 0, 1)); 
    cat("Starting state:", state, "\n"); 

    # Make twenty steps through the markov chain 
    for (i in 1:20) 
    { 
     p = 0; 
     u = runif(1, 0, 1); 

     cat("> Dist:", paste(round(c(trans[state,]), 2)), "\n"); 
     cat("> Prob:", u, "\n"); 

     newState = state; 
     for (j in 1:ncol(trans)) 
     { 
      p = p + trans[state, j]; 
      if (p >= u) 
      { 
       newState = j; 
       break; 
      } 
     } 

     cat("*", state, "->", newState, "\n"); 
     state = newState; 
    } 
} 

run(); 

請注意，您的概率轉移矩陣不每一行，它應該做的總和爲1。我的例子有一個稍微改變的概率轉換矩陣，它遵守這個規則。

Answer 3

您現在可以使用在CRAN可用markovchain包。用戶manual。很不錯，有幾個例子。