[英]Manual simulation of Markov Chain in R (3)
I have tried to improve my previous code so that I can incorporate conditional probability . 我已尝试改进以前的代码,以便可以合并条件概率 。
Source Code 源代码
states <- c(1, 2)
alpha <- c(1, 1)/2
mat <- matrix(c(0.5, 0.5,
0, 1), nrow = 2, ncol = 2, byrow = TRUE)
# this function calculates the next state, if present state is given.
# X = present states
# pMat = probability matrix
nextX <- function(X, pMat)
{
#set.seed(1)
probVec <- vector() # initialize vector
if(X == states[1]) # if the present state is 1
{
probVec <- pMat[1,] # take the 1st row
}
if(X==states[2]) # if the prsent state is 2
{
probVec <- pMat[2,] # take the 2nd row
}
return(sample(states, 1, replace=TRUE, prob=probVec)) # calculate the next state
}
# this function simulates 5 steps
steps <- function(alpha1, mat1, n1)
{
vec <- vector(mode="numeric", length = n1+1) # initialize an empty vector
X <- sample(states, 1, replace=TRUE, prob=alpha1) # initial state
vec[1] <- X
for (i in 2:(n1+1))
{
X <- nextX(X, mat1)
vec[i] <- X
}
return (vec)
}
# this function repeats the simulation n1 times.
# steps(alpha1=alpha, mat1=mat, n1=5)
simulate <- function(alpha1, mat1, n1)
{
mattt <- matrix(nrow=n1, ncol=6, byrow=T);
for (i in 1:(n1))
{
temp <- steps(alpha1, mat1, 5)
mattt[i,] <- temp
}
return (mattt)
}
Execution 执行
I created this function so that it can handle any conditional probability: 我创建了此函数,以便它可以处理任何条件概率:
prob <- function(simMat, fromStep, toStep, fromState, toState)
{
mean(simMat[toStep+1, simMat[fromStep+1, ]==fromState]==toState)
}
sim <- simulate(alpha, mat, 10)
p <- prob(sim, 0,1,1,1) # P(X1=1|X0=1)
p
Output 产量
NaN
Why is this source code giving NaN
? 为什么此源代码提供NaN
?
How can I correct it? 我该如何纠正?
I didn't inspect the rest of your code, but it seems that only prob
has a mistake; 我没有检查其余的代码,但似乎只有prob
有错误; you are mixing up rows with columns and instead it should be 您将行与列混合在一起,而是
prob <- function(simMat, fromStep, toStep, fromState, toState)
mean(simMat[simMat[, fromStep + 1] == fromState, toStep + 1] == toState)
Then NaN
still remains a valid possibility for the following reason. 然后,由于以下原因, NaN
仍然是有效的可能性。 We are looking at a conditional probability P(X 1 =1|X 0 =1) which, by definition, is well defined only when P(X 0 =1)>0. 我们正在研究一个条件概率P(X 1 = 1 | X 0 = 1),根据定义,只有当P(X 0 = 1)> 0时才可以很好地定义它。 The same holds with sample estimates: if there are no cases where X 0 =1, then the "denominator" in the mean inside of prob
is zero. 样本估计值也是如此:如果没有X 0 = 1的情况,则prob
内均值的“分母”为零。 Thus, it cannot and should not be fixed (ie, returning 0 in those cases would be wrong). 因此,它不能也不应该被修复(即,在这些情况下返回0将是错误的)。
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