Some references for Markov chain Monte Carlo methods

  • Robert, Christian P. and Casella, George (2006), "Monte Carlo statistical methods", Second Edition, Springer-Verlag Inc (Berlin; New York).
    Note: comprehensive treatment of Monte Carlo methods (including MCMC, Importance Sampling and recently developed techniques) with plenty of related theoretical details. The level of the text is generally more advanced than the other two references below (notation is sometimes measure-theoretic). The book is an excellent reference with a view towards a lot of the latest research on advanced MCMC techniques.

  • Gilks, W. R. (ed), Richardson, S. (ed), and Spiegelhalter, D. J.(ed) (1996), ``Markov chain Monte Carlo in practice'', Chapman & Hall Ltd (London; New York)
    Note: well written chapters by several different experts on a variety of topics from MCMC basics to specialized applications of MCMC. Useful practical advice for first time MCMC users although the information is somewhat dated.

  • Liu, Jun S. (2001), "Monte Carlo strategies in scientific computing", Springer-Verlag Inc (Berlin; New York).
    Note: this book has descriptions about a few advanced MCMC strategies along with a thorough treatment of Importance Sampling and Sequential Importance Sampling. It is hence a bit more specialized than the other two references.

    Other references for Monte Carlo and Statistical Computing:
  • Givens and Hoeting (2005) "Computational Statistics" (Wiley): Chapters 6,7 and 8 (Ch.8 is on more advanced topics)

    Some references for the idea of using estimated standard errors to stop an MCMC run: Markov chain Monte Carlo: Can we trust the third significant figure? and a more technical reference: Fixed Width Output Analysis for Markov chain Monte Carlo (2006), Journal of the American Statistical Association.