Parsimonious and Efficient Likelihood Composition by Gibbs Sampling

Abstract

The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full likelihood specification by combining a number of partial likelihood objects depending on small data subsets, thus enabling inference for complex data. A fundamental difficulty in making the McLE approach practicable is the selection from numerous candidate likelihood objects for constructing the composite likelihood function. In this article, we propose a flexible Gibbs sampling scheme for optimal selection of sub-likelihood components. The sampled composite like..