Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

摘要

Performing model selection between Gibbs random fields is a very challengingtask. Indeed, due to the Markovian dependence structure, the normalizingconstant of the fields cannot be computed using standard analytical ornumerical methods. Furthermore, such unobserved fields cannot be integrated outand the likelihood evaluztion is a doubly intractable problem. This forms acentral issue to pick the model that best fits an observed data. We introduce anew approximate version of the Bayesian Information Criterion. We partition thelattice into continuous rectangular blocks and we approximate the probabilitymeasure of the hidden Gibbs field by the product of some Gibbs distributionsover the blocks. On that basis, we estimate the likelihood and derive the BlockLikelihood Information Criterion (BLIC) that answers model choice questionssuch as the selection of the dependency structure or the number of latentstates. We study the performances of BLIC for those questions. In addition, wepresent a comparison with ABC algorithms to point out that the novel criterionoffers a better trade-off between time efficiency and reliable results.