用锯齿估计dacay常数

我尝试估计数据的衰减。让我解释。想象一下，您观察到事件X，每个事件都有一个效果y，该效果随时间exp（-t / Tau）衰减。您观察时间t和事件x以及预测其作用y的结果。让我向您展示我的JAGS代码。

model{
for( j in 1:N ){
  for(i in 1:p){
    td[j,i] <- exp( - t[j,i] / Tau[i] )
  }

  mu[j] <- inprod( X[j,]*td[j,] ,beta[] )
  Y[j] ~ dnorm( mu[j], sigma )
}

   for(j in 1:p){
     bsigma[j] ~dgamma(0.001,0.001);
     beta[j] ~ dnorm(0,bsigma[j]);
     Tau[j] ~ dgamma(0.001,0.001);
   }
   sigma  ~ dgamma(0.001,0.001)
}

我在R中生成测试数据，如下所示：

N = 1000;

sigma = 0.1;
beta  = c(0.75,0.33)
tau   = c(5.7,1.3)

X<-cbind(rnorm(N,1,1),rnorm(N,2,1))
t<-cbind(rnorm(N,1,1),rnorm(N,2,1))
t = abs(t);
Y<- rnorm(N,(X*exp(- t/tau ) )%*%as.matrix(beta),sigma)

使用我的模型，我可以成功找到beta的值，但是我无法估计Tau的正确值。
这里是完整的代码：

N = 1000;

sigma = 0.1;
beta  = c(0.75,0.33)
tau   = c(5.7,1.3)

X<-cbind(rnorm(N,1,1),rnorm(N,2,1))
t<-cbind(rnorm(N,1,1),rnorm(N,2,1))
t = abs(t);
Y<- rnorm(N,(X*exp(- t/tau ) )%*%as.matrix(beta),sigma)

####JAGS
##################
library(mcmcplots)
library(runjags)
library(rjags)

hmodel_jags<- function(X,Y,t){
  modelstring = "
  model{
    for( j in 1:N ){
      for(i in 1:p){
        td[j,i] <- exp( - t[j,i] / Tau[i] )
      }

     mu[j] <- inprod( X[j,]*td[j,] ,beta[] )
      Y[j] ~ dnorm( mu[j], sigma )
    }

    for(j in 1:p){
      bsigma[j] ~dgamma(0.001,0.001);
      beta[j] ~ dnorm(0,bsigma[j]);
      Tau[j] ~ dgamma(0.001,0.001);
    }
    sigma  ~ dgamma(0.001,0.001)
  }"
  writeLines(modelstring,con="dec.txt")
  ########
  set.seed(123)


  jags_data <- list(Y = Y,
                t = t,
                X = X,
                p = ncol(X),
                N=nrow(X)
                )
  params <- c( "Tau",'sigma','beta') 
  adapt <- 1000
  burn <- 1000
  iterations <- 1000
  inits <- list( )

  sample <- run.jags(model="dec.txt", thin =2, monitor=params,data=jags_data, n.chains=2, inits=inits, adapt=adapt, burnin=burn,      sample=iterations, summarise=T, method="parallel") 

  sample
}
res_jags_het <- hmodel_jags(X,Y,t)