如何在JAGS中定义截断的泊松模型？

Question

我想对具有不同较低测量阈值的计数数据使用相同的模型。截短的泊松模型使我可以做到这一点。

可以在R中成功定义模型。但是我无法将同一模型转换为JAGS。问题似乎在于，在定义可能性时，不可能用CDF划分PDF。

这是我尝试过的：

数据

set.seed(42)
N <- 10000
x1 <- runif(N, -1, 1)
lower_limit = 7
upper_limit = Inf
b0 <- 0.5
b1 <- 1.3
b2 <- 0.1
true_lambda <- exp(b0 + b1 * x1 + b2 * x1^2)
# extraDistr::dtpois behaves exactly like the truncated poisson defined below
y <- extraDistr::rtpois(N, lambda = true_lambda, a = lower_limit, b = upper_limit)
summary(y)

Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
8.000   8.000   8.000   8.354   8.000  16.000 

hist(y)

histogram of data

对于模型，我使用了可以通过以下方式用基数R定义的截断的泊松分布：

trunc <- function(x,s, lambda, log){
  out <- dpois(x, lambda)/(1-ppois(s, lambda))
  if(log){
    out <- log(out)
  }
  return(out)
}


optfun <- function(data, par){
  b0 <- par[1]
  b1 <- par[2]
  b2 <- par[3]
  loglikelihood <- sum(trunc(
    x = data,
    lambda = exp(b0 + b1 * x1 + b2 * x1^2),
    s = lower_limit,
    log = T
  ))
  return(-loglikelihood)
}

output <- optim(par = rep(0, 3),
                fn = optfun2,
                data = y)
output$par

[1] 0.4808197 1.3141579 0.1097217

但是，我想在JAGS中定义相同的模型：

Model.Data <- list(
  y = y,
  N = N,
  s = rep(lower_limit,N),
  x1 = x1
)

sink("trunc_pois.txt")
cat(
  "
  model{

    # Likelihood data model:
    for (i in 1:N) {
      # truncated poisson in JAGS:
      y[i] ~ dpois(lambda_fit[i])/(1-ppois(s[i],lambda_fit[i]))
      log(lambda_fit[i]) <- b0 + b1 * x1[i] + b2 * pow(x1[i],2)
    }

    # Priors:
    b0 ~ dnorm(0, 0.0001) # mean, precision = N(0, 10^4)
    b1 ~ dnorm(0, 0.0001)
    b2 ~ dnorm(0, 0.0001)
  }
"
  )

sink()


inits.fn <- function() list(
  b0 = rnorm(1),
  b1 = rnorm(1),
  b2 = rnorm(1)
)

jagsModel <- rjags::jags.model(file = "trunc_pois.txt", data = Model.Data,
                        inits = inits.fn,n.chains = 3, n.adapt = 100)

这会给我以下错误消息：

Error in rjags::jags.model(file = "trunc_pois.txt", data = Model.Data,  : 

Error parsing model file:
syntax error on line 7 near "/"

有没有办法在JAGS中定义截短的泊松模型？我应该使用T（）以某种方式截断泊松模型吗？