Modeling Capture-Recapture Data via Bayes involves specifying the likelihood of the survival + encounter probabilities and the priors on the parameters. A natural extension of a plain vanilla model is to make the survival probabilities time dependent. The paper titled, “Autoregressive models for capture–recapture data: A Bayesian approach”, is about modeling the survival probabilities by taking various covariates such as time and random effects. The following document contains a brief summary of the paper :

AR(2) estimation in Bayes from first principles involves writing an M-H sampler as full conditional distributions for some of the parameters does not belong to any standard form. However softwares like WinBUGS and JAGS make the life easy for a modeler. The following document contains some basic code to do Bayesian inference for AR(2) process using WinBUGS and JAGS AR(2) parameter estimation in WinBUGS and JAGS

The paper, “Understanding the Metropolis-Hastings Algorithm” by Chib and Greenberg is a vintage paper that illustrates the nuts and bolts of the algorithm. The following is a link to the document that summarizes the paper. Summary of Metropolis Hastings Algorithm

Summary of the main points from the paper

[youtube https://www.youtube.com/watch?v=fZB2vVHmiug?rel=0]