Extending pseudo-likelihood for Potts models

We propose a conditional composite likelihood based on conditional probabilities of parts of the data given the rest for spatial lattice processes, in particular for Potts models, which generalizes the pseudo-likelihood of Besag. Instead of using conditional probabilities of single pixels given the rest (like Besag), we use conditional probabilities of multiple pixels given the rest. We find that our maximum composite likelihood estimates (MCLE) are more efficient than maximum pseudolikelihood 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 MCLE and MPLE can be calculated exactly, whereas MLE cannot, only approximated by Markov chain Monte Carlo.