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PoissonNPP_MCMC <- function(Data.Cur, Data.Hist,
CompStat = list(n0 = NULL, mean0 = NULL, n1 = NULL, mean1 = NULL),
prior = list(lambda.shape = 1/2, lambda.scale = 100,
delta.alpha = 1, delta.beta = 1),
MCMCmethod = 'IND', rw.logit.delta = 0.1,
ind.delta.alpha= 1, ind.delta.beta= 1, nsample = 5000,
control.mcmc = list(delta.ini = NULL, burnin = 0, thin = 1))
{
# CompStat = list(mean0 = 10, n0 = 20, mean1 = 11, n1 = 30)
# prior = list(lambda.shape = 1/2, lambda.scale = 100,
# delta.alpha = 1, delta.beta = 1)
# ind.delta.alpha= 1; ind.delta.beta= 1;
# nsample = 10000; control.mcmc = list(delta.ini = NULL, burnin = 2000, thin = 1)
if(missing(CompStat)){
n0 <- length(Data.Hist)
n1 <- length(Data.Cur)
sum0 <- sum(Data.Hist)
sum1 <- sum(Data.Cur)
}else{
n0 <- CompStat$n0
n1 <- CompStat$n1
sum0 <- n0*CompStat$mean0
sum1 <- n1*CompStat$mean1
}
prior.lambda.rate <- 1/prior$lambda.scale
#### Normalized Power Prior for Poisson Log Marginal Posterior (unnormalized) of Delta
LogPostPoisDelta <- function(x){
(prior$delta.alpha-1)*log(x)+(prior$delta.beta-1)*log(1-x)+
lgamma(sum1+x*sum0+prior$lambda.shape)-
lgamma(x*sum0+prior$lambda.shape)+
(x*sum0+prior$lambda.shape)*log(n0*x+prior.lambda.rate)-
(x*sum0+sum1+prior$lambda.shape)*log(n0*x+n1+prior.lambda.rate)
}
if(is.null(control.mcmc$delta.ini)) delta.ini = 0.5
delta_cur <- delta.ini
delta <- rep(delta.ini, nsample)
counter <- 0
niter <- nsample*control.mcmc$thin + control.mcmc$burnin
for (i in 1:niter){
### Update delta with RW MH for Logit delta
if(MCMCmethod == 'RW'){
lgdelta_cur <- log(delta_cur/(1-delta_cur))
lgdelta_prop <- rnorm(1, mean = lgdelta_cur, sd = sqrt(rw.logit.delta))
delta_prop <- exp(lgdelta_prop)/(1+exp(lgdelta_prop))
llik.prop <- LogPostPoisDelta(delta_prop)
llik.cur <- LogPostPoisDelta(delta_cur)
logr <- min(0, (llik.prop-llik.cur+log(delta_prop)+log(1-delta_prop)-log(delta_cur)-log(1-delta_cur)))
}
if(MCMCmethod == 'IND'){
delta_prop <- rbeta(1, shape1 = ind.delta.alpha, shape2 = ind.delta.beta)
llik.prop <- LogPostPoisDelta(delta_prop)
llik.cur <- LogPostPoisDelta(delta_cur)
logr <- min(0, (llik.prop-llik.cur+
dbeta(delta_cur, shape1 = ind.delta.alpha, shape2 = ind.delta.beta, log = TRUE) -
dbeta(delta_prop, shape1 = ind.delta.alpha, shape2 = ind.delta.beta, log = TRUE)))
}
if(runif(1) <= exp(logr)){
delta_cur = delta_prop; counter = counter+1
}
if( i > control.mcmc$burnin & (i-control.mcmc$burnin)%%control.mcmc$thin==0) {
delta[(i-control.mcmc$burnin)/control.mcmc$thin] <- delta_cur
}
}
# Generate lambda conditional on delta; vectorized
lambda <- rgamma(nsample, shape = sum1+delta*sum0+prior$lambda.shape,
rate = n1+n0*delta+prior.lambda.rate)
# Calculate DIC
meanlambda <- mean(lambda)
D <- -2*(-n1*lambda + log(lambda)*sum1)
Dlambdabar <- -2*(-n1*meanlambda + log(meanlambda)*sum1)
DIC <- 2*mean(D)-Dlambdabar
return(list(lambda = lambda, delta = delta, acceptrate = counter/niter, DIC = DIC))
}
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