Mostly Markov Chains Working Group

Fall 2009

October 6 from 2:00--3:00 in Ford 300:

Charlie, Sai and Leif
A Composite Likelihood Extending Pseudo-Likelihood for Potts Models
We propose a composite likelihood based on conditional probabilities of parts of the data given the rest for spatial lattice processes, in particular for Potts models. These composite likelihoods generalize the pseudo-likelihood of Besag. The generalization is that, instead of using conditional probabilities of single pixels given the rest (like Besag), we use conditional probabilities of multiple pixels (called a window) given the rest. We find that our maximum conditional likelihood estimates (MCLE) are more efficient than maximum pseudo-likelihood estimates (MPLE) when the true parameter value of the Potts model is the phase transition parameter value. Our MCLE are not as efficient as maximum likelihood estimates (MLE), but unlike the true likelihood, which cannot be calculated exactly, only approximated by Markov chain Monte Carlo, our composite likelihoods can be calculated exactly (as can Besag pseudo-likelihoods) so MCLE can also be calculated exactly.

November 3 from 2:00--3:00 in Ford 300:

Charlie

November 24 from 2:00--3:00 in Ford 300:

Galin: "Hybrid MCMC algorithms"

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