R 为什么使用jags对我的贝塔二项模型的参数估计不同于最大似然估计

我有一个这样的贝塔二项模型

其中，$B$是beta函数

我想估计参数$\theta\u 1、\theta\u 2、\ldots、\theta\u 5$

我使用了最大似然法：

BBlikelihood = function(theta){
    k = theta[1]/(1+exp(theta[2]*x+theta[3]))+theta[4]
    mu = exp(k)/(1+exp(k))
    if(theta[5]<0) theta[5]=0
    return(-sum(lchoose(n,y)+
                   lbeta(y+mu*theta[5],n-y+(1-mu)*theta[5]) -
                   lbeta(mu*theta[5],(1-mu)*theta[5])))
}

theta.init = c(8,100,-3,-6,1)
BBtheta = optim(theta.init,BBlikelihood,control=list(maxit=1000))  
BBtheta$par

bb似然=函数（θ）{
k=theta[1]/（1+exp（theta[2]*x+theta[3]））+theta[4]
mu=exp（k）/（1+exp（k））
如果（theta[5]@Jthorp:你好，你发现错误了吗？
HastingsBBlikelihood = function(theta,theta.prime){
    k = theta[1]/(1+exp(theta[2]*x+theta[3]))+theta[4]
    mu = exp(k)/(1+exp(k))
    k.prime = theta.prime[1]/(1+exp(theta.prime[2]*x+theta.prime[3]))+theta.prime[4]
    mu.prime = exp(k.prime)/(1+exp(k.prime))
    if(theta.prime[5]<0) 
        return(-Inf) 
    sum( ( lbeta(y+mu.prime*theta.prime[5],n-y+(1-mu.prime)*theta.prime[5])
          - lbeta(mu.prime*theta.prime[5],(1-mu.prime)*theta.prime[5]))
        - ( lbeta(y+mu*theta[5],n-y+(1-mu)*theta[5])
           lbeta(mu*theta[5],(1-mu)*theta[5])))
}

SigmaBB = list(0.1*diag(5))
Sigma.i = 1
thetaBB.mcmc = matrix(c(8,100,-3,-6,1),1,5)
for(i in 2:25000){
    if((i %% 1000)==0){ 
        Sigma.i <- Sigma.i + 1; 
        SigmaBB[[Sigma.i]] <- 2.38^2*var(thetaBB.mcmc)/5
    }
    thetaBB.mcmc = rbind(thetaBB.mcmc,
                            mvrnorm(n=1,
                                       thetaBB.mcmc[i-1,],
                                       Sigma=SigmaBB[[Sigma.i]]))
    if(log(runif(1))>HastingsBBlikelihood(thetaBB.mcmc[i-1,],thetaBB.mcmc[i,]))
        thetaBB.mcmc[i,] <- thetaBB.mcmc[i-1,]
}

  cat("model {

    # Parameters
    theta[1] ~ dunif(-1.e10, 1.e10)   
    theta[2] ~ dunif(-1.e10, 1.e10)
    theta[3] ~ dunif(-1.e10, 1.e10)
    theta[4] ~ dunif(-1.e10, 1.e10)
    theta[5] ~ dunif(0, 1.e10)

    # Observations
    for (i in 1:TT){

    k[i] <- theta[1]/(1+exp(theta[2]*x[i]+theta[3]))+theta[4]
    mu[i] <- exp(k[i])/(1+exp(k[i]))

    p[i] ~ dbeta(mu[i]*theta[5],(1-mu[i])*theta[5])     

    y[i] ~ dbin(p[i],n[i])

  }
    }",
    file="BetaBinom.bug")    

library("rjags")
TT<-length(y)
jags <- jags.model('BetaBinom.bug', data = list('x'=x, 'y'=y, 'n'=n , TT=TT ))

res <- coda.samples(jags,c('theta'),1000)
res.median = apply(res[[1]],2,median)
res.median
res.mean = apply(res[[1]],2,mean)
res.mean
res.sd = apply(res[[1]],2,sd)
res.sd