Abstract
Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean mu and variance sigma(2). Marginal prior distributions on logit(p) and mu were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for mu; hence minimally informative. Marginal prior distribution on sigma(2) was placed on tau(2) = 1/sigma(2) as a gamma distribution with alpha = beta = 0.001. The study design has 432 points spread over 5 factors: occasions (t), new releases per occasion (u), p, mu, and sigma. At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n = 10, 000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on mu, and sigma based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter mu, but under the conditions used here, MCMC inference performance for sigma was mixed: poor for sparse data (i.e., only 7 occasions) or sigma = 0, but good when there were sufficient data and not small sigma.