Computation of Full ML Estimators

Abstract

To compute maximum likelihood estimators we must solve the normal equations which amounts to setting the gradient of the likelihood function to zero. For the full likelihood this is a desperate attempt, since expectations with respect to Gibbs measures are involved, and since in general their partition function is not tractable. A popular alternative are pseudolikelihood methods like those originally proposed by J. BESAG and introduced in the last chapter. In Example 18.2.2 we indicated how pseudolikelihood estimators can be computed. On the other hand, expectations can be approximated by Gibbs or Metropolis samplers which gives us a chance to approximate full likelihood estimators.