I gave a short seminar at National Marine Fisheries Services NMFS in Honolulu, Hawaii, entitled "Bayesian Mark-Recapture for Small Sample Sizes"
Mark-recapture methods are often used to estimate the abundance of rare or elusive populations but produce highly uncertain results when sample sizes are small. We develop a new estimator for a single-release, single-recapture experiment based on Bayesian methodology to handle this situation. The number of marked recaptures is assumed to have a binomial likelihood that is a function of the marked proportion of the population. The prior distribution for this proportion is chosen to be a beta distribution, the conjugate prior of the binomial, so that the posterior distribution of the marked proportion is simply an updated beta distribution. The probability density function for population abundance is derived from this posterior distribution, from which a closed-form estimator of abundance emerges, providing ease of use and general applicability. A Bayesian credible interval is found by numerically integrating the posterior density. This method is then extended to a multiple-release, multiple-recapture experiment. A sensitivity analysis showed that estimation is relatively insensitive to the choice of prior parameters. A simulation study showed that as sample sizes become smaller, the Bayesian estimator has relative bias less than 3%. The Bayesian credible interval had narrower width than the Schnabel profile likelihood interval. The method is illustrated with data from sperm whales off Alaska.
KEY WORDS Bayesian methods; mark-recapture; Petersen method; rare populations; Schnabel method; small samples; sperm whales;