MCMC for estimating negative binomial distribution
Change dnorm
in loglikelihood
to dnbinom
and fix the proposal for prob
so it doesn't go outside (0,1):
set.seed(42)
y <- rnbinom(20, size = 3, prob = 0.2)
prior_r <- function(r) {
return(dpois(r, lambda = 2, log = T))
}
prior_prob <- function(prob) {
return(dunif(prob, min = 0, max = 1, log = TRUE))
}
loglikelihood <- function(data, r, prob) {
loglikelihoodValue <- sum(dnbinom(data, size = r, prob = prob, log = TRUE))
return(loglikelihoodValue)
}
joint <- function(r, prob) {
return(loglikelihood(y, r, prob) + prior_r(r) + prior_prob(prob))
}
run_mcmc <- function(startvalue, iterations) {
chain <- array(dim = c(iterations + 1, 2))
chain[1, ] <- startvalue
for (i in 1:iterations) {
proposal_r <- rpois(1, lambda = chain[i, 1])
proposal_prob <- chain[i, 2] + runif(1, min = max(-0.2, -chain[i,2]), max = min(0.2, 1 - chain[i,2]))
quotient <- joint(proposal_r, proposal_prob) - joint(chain[i, 1], chain[i, 2])
if (runif(1, 0, 1) < min(1, exp(quotient))) {
chain[i + 1, ] <- c(proposal_r, proposal_prob)
} else {
chain[i + 1, ] <- chain[i, ]
}
}
return(chain)
}
iterations <- 2000
startvalue <- c(4, 0.25)
res <- run_mcmc(startvalue, iterations)
colMeans(res)
#> [1] 3.1009495 0.1988177