Composite Likelihood Methods

Abstract

Composite likelihood methods are extensions of the Fisherian likelihood theory, one of the most influential approaches in statistics. Such extensions are generally motivated by the issue of computational feasibility arising in the application of the likelihood method in high-dimensional data analysis. Complex dependence presents substantial challenges in statistical modelling and methods and in substantive applications. The idea of projecting high-dimensional complicated likelihood functions to low-dimensional computationally feasible likelihood objects is methodologically appealing. Composite likelihood inherits many of the good properties of inference based on the full likelihood function, but is more easily implemented with high-dimensional data sets. This methodology is, to some extent, an alternative to the Markov Chain Monte Carlo method, and its impact is unbounded. The literature on both theoretical and practical issues for inference based on composite likelihood continues to expand quickly; the field of extremal processes for spatial data, of particular importance for climate modelling, is one of the most recent examples of an area where composite likelihood inference is both practical and efficient. The first international workshop on composite likelihood methods was held at the University of Warwick in April 2008. It attracted participants from all over the world and was widely viewed as very successful. Following the workshop, a special issue of the journal Statistica Sinica devoted to composite likelihood was announced; it was published in January 2011. This issue includes two long overview papers, one of which is devoted to applications in statistical genetics; several papers developing new theory for inference based on composite likelihood; new results in the application of composite likelihood to time series, spatial processes, longitudinal data and missing data. The methodology has drawn considerable attention in a broad range of applied disciplines in which complex data structures arise. Some notable application areas include, statistical genetics, genetic epidemiology, finance, panel surveys, computer experiments, geostatistics and biostatistics.