模型是泊松似然和高斯先验。我计算了模型的后验，我认为我已经正确编码但是我在尝试实现算法时遇到了很多麻烦。我知道这不是一个简单的问题，我没有正确定义我的变量，但我没有看到问题所在。我到目前为止的代码是：
# Poisson model
#
#
# Log of the unnormalized posterior density:
log.post.dens = function( theta, n, sum.y, mu0, sig0 )
{
alpha = (log.dpois(x, lamda=exp(theta)))*dnorm(x, mu0, sig0)
}
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++
rw.sim = function( M, mu0, sig0, n, sum.y, sd.pd, theta.start )
{
# create theta array and initialize theta[1]
#
theta = rep( 0, M )
theta[1] = theta.start
acc.cnt = 0
for( ii in 2:M ) {
# Normal proposal distribution is centered at the current theta
#
theta.new = rnorm( 1, theta[ii-1], sd.pd )
log.alpha = log.post.dens( theta.new, n, sum.y, mu0, sig0 ) -
log.post.dens( theta[ii-1], n, sum.y, mu0, sig0 )
if( log.alpha > 0 || exp( log.alpha ) > runif( 1, 0, 1 ) )
{
theta[ii] = theta.new
acc.cnt = acc.cnt + 1
}
else
theta[ii] = theta[ii-1]
}
list( ac = acc.cnt, theta = theta )
}
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++
n = 200
mu0 = log(10)
sig0 = 3
yy = rpois( n, exp( mu0 ))
sd.pd = 1
theta.start = mu0
M = 100000
print( paste("M =", M, " mu0 =", mu0, " sig0 =", sig0, "sd.pd =", sd.pd,
"start", theta.start ))
res = rw.sim( M, mu0, sig0, length(yy), sum( yy ), sd.pd, theta.start )
theta = res$theta
acc.rate = res$ac / M
corr = cor( theta[1:(M-1)], theta[2:M])
print( paste("acceptance rate =", acc.rate ))
print( paste("correlation =", corr ))
3
m = 1
if( m )
{
theta0 = theta
thin.const = 40
theta = theta[ seq( .1*length(theta), length(theta), thin.const )]
}
par( mfrow=c(2,2))
hist( theta, prob=T, breaks=32 )
x = seq( min( theta ), max( theta ), len=200 )
lines( x, dnorm( x, mu0, sig0 ), col = 2)
plot( theta, type=’l’ )
acf( theta )
##pacf( theta )
#++++++++++++++++++++++++++++
#
# Posterior predictive density for data on a grid
#
hist( yy, prob=T)
lim1 = max(yy) + 2
xx = 0:lim1
ppd = rep( 0, lim1+1 )
for( ii in 1:(lim1+1) )
{
ppd[ii] = (1/M)*sum(yy)*((log.dpois(x, lamda=exp(theta)))*dnorm(x, mu0, sig0))
}
points( xx+.5, ppd, col=2 )
lines( xx+.5, ppd, col=2 )
正如我所说，这是我对参数的定义，但我不确定如何修复它。