#' @importFrom stats dgamma
#'
log_f_post_b <- function( b,
a,
d_0_b,d_1_b,
mu_star_n_r ) {
### Metropolis-Hastings for 'b' ###
# target distribution: log-posterior distribution of 'b' #
n <- sum(mu_star_n_r)
r <- length(mu_star_n_r)
# prior distribution of b
log_prior <- dgamma( b+a, shape=d_0_b, rate=d_1_b, log=T )
# log-prior distribution of 'b' given 'a'
log_lik <- 0
log_lik <- log_lik + ( lgamma(x=b+1)-lgamma(x=b+n) )
if(r>1) {
log_lik <- log_lik + sum( log( b+a*(1:(r-1)) ) )
}
log_post <- log_lik + log_prior
return(log_post)
}
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