R中的MLE（多参数功能）

Question

我正在尝试在R中做MLE以模拟标记重获方法。 我正在尝试最大化此功能；

likelihood <- function(N, p){
  likelihood <- 1
  X <- 0
  for (s in 1:S){
    X <- X + M[s]
  }
  likelihood <- likelihood * p^(X) * (1-p)^(N*S-X)
  likelihood <- likelihood * (factorial(N)/factorial((N-length(U))))
  return(likelihood)
}

我正在尝试最大化N，所有其他参数都是已知的或估计的，因此假定已知

调查了nlm和乐观者，但都做不了我想要的...

回应答案； 感谢您提供所有答案，我重新编码了可能性并设法使某些事情起作用，请参见下面的代码。 专门回答问题/答案1.感谢X <- sum(M[1:S])不错的技巧， X在计数“曾经捕获的所有动物（不是唯一捕获的动物）” 2.在下面的代码中生成M ，根据n（捕获），它是每个调查中标记的动物数量的计数，S是调查数量。

 captures <- function(N, S, P){
   P <- replicate(S, P) #Capture Probability (same across animals and surveys)
   captures <- t(replicate(N, rbinom(S, 1, P))) #Generate capture data from N animals with S surveys with capture Probability P 
   return(captures)
 }

 marked <- function(N, S, captures){ #Count numbers that were marked on each survey
   M <- replicate(S, 0) #Initialise the 'marked' variable to zero
   for (s in 1:S){
     for (i in 1:N){
       if (captures[i, s] == 1){
         M[s] <- M[s] + 1
       }
     }
   }
   return(M)
 }

 unseen <- function(N, S, captures){#Count total number of animals that were unseen on any survey
   U <- array()
   seen <- replicate(N, FALSE) #All animals begin as unseen
   for (i in 1:N){
     for (s in 1:S){
       if (captures[i, s] == 1){
         seen[i] = TRUE
       }
     }
     if (seen[i] == FALSE){
       U <- c(U, i)
     }
   }  
   U <- U[-1] #fix the N/A in the first index
   return(U)
 }

 firstcaught <- function(N, S, captures){#Produce a vector containing how many animals were   caught for the first time on each survey
   fc <- 0
   seen <- replicate(N, FALSE)
     for (s in 1:S){
       fc[s] <- 0
       for (i in 1:N){
         if ((seen[i] == FALSE) && (captures[i, s] == 1)){
             fc[s] <- fc[s] + 1
             seen[i] = TRUE
         }
       }
     }
   return(fc)
 }

 ##Generate data using functions
 N <- 200
 S <- 10
 P <- 0.2
 n <- captures(N,S,P)
 M <- marked(N,S,n)
 U <- unseen(N,S,n)
 fc <- firstcaught(N,S,n) 
 Mc <- cumsum(fc) #A running total of animals that have been captured at least once


 ##Define a likelihood for model M_0
 likelihood <- function(N, P){
  likelihood <- 1
   X <- 0
  for (s in 1:S){
   X <- X + M[s]
    likelihood <- likelihood * (1-P)^(N-M[s])
    likelihood <- likelihood * choose(N-M[s],fc[s])
  }
  likelihood <- likelihood * P^(X) * (1-P)^(-X)
  return(-log(likelihood))
}

##Find the MLE
out <- nlm(f = likelihood, p = 200, P = P, check.analyticals = TRUE)