Anderson, E.C., Thompson, E.A., and Williamson, E.G. (1999) "Importance sampling for Monte Carlo evaluation of the likelihood for effective population size," Western North American Region of the International Biometrics Society conference, Seattle, June.

A population's genetically effective size is an important quantity for conservation and management. The effective size may be estimated from the change of allele frequencies observed in temporally-spaced genetic samples taken from the population. Though moment-based estimators exist, a likelihood approach is more flexible. With multi-allelic markers, however, exact evaluation of the likelihood is impossible, requiring an intractable sum over latent variables in a hidden Markov chain. Using a forward-backward algorithm, we generate realizations of the latent variables conditional on the data in order to approximate the sum by Monte Carlo. However, we realize the Monte Carlo samples under a model which differs slightly from the exact likelihood model so that the method is computationally feasible. This importance sampling provides an efficient Monte Carlo approximation to the likelihood.