Hi there, I interviewed back in early March; I greatly enjoyed discussing MCMC methods with you. One of the things we talked about was sequential site selection vs. random site selection. This was a bit muddied in my head at the time, and it was equally muddied in the first draft of my dissertation as well. :/ Anyway, since then I've resolved these issues to my satisfaction. If you're interested, here's the summary of what I came up with: * For random site selection, the same transition matrix A is used at each Metropolis step. Each Metropolis sweep consists of N steps, so the the transition matrix for sweeps is A^N. At the level of steps or sweeps, the Markov chain is homogeneous. * For sequential site selection, a different transition matrix A_1, A_2, ..., A_N is used at each of the N Metropolis steps. Each of these matrices individually satisfies detailed balance, so their product does as well. The transition matrix for a sweep is the product A_N x ... x A_1. At the level of steps, the Markov chain is not homogeneous; at the level of sweeps, the Markov chain is homogeneous. Details are in chapters 4, 5, and 7 of my dissertation: http://johnkerl.org/rcm/doc/ch4.pdf http://johnkerl.org/rcm/doc/ch5.pdf http://johnkerl.org/rcm/doc/ch7.pdf Please let me know if this makes sense ... I'm eager to hear your thoughts on the matter. Thanks! ---------------------------------------------------------------- John Kerl Graduate student, University of Arizona Department of Mathematics kerl.john.r@gmail.com http://johnkerl.org