I was looking to code Metropolis-within-Gibbs sampler for a specific model and in that process, stumbled on to an online supplement for a work-in-progress book,``Handbook of Modern Item Response Theory''. The following document summarizes the main points from chapter-15 of the book. The document also contains WinBUGS code to estimate the parameters of 2PL model. Building Metropolis Hastings sampler from scratch

“You never quit on your music. No matter what happens. Cuz anytime something bad happens to you, that’s the one place you can escape to and just let it go. I learned it the hard way” - August Rush

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