Composite likelihood-based inferences on genetic data from dependent loci

The structure of dependence between neighboring genetic loci is intractable under some models that treat each locus as a single data-point. Composite likelihood-based methods present a simple approach under such models by treating the data as if they are independent. A maximum composite likelihood estimator (MCLE) is not easy to find numerically, as in most cases we do not have a way of knowing if a maximum is global. We study the local maxima of the composite likelihood (ECLE, the efficient composite likelihood estimators), which is straightforward to compute. We establish desirable properties of the ECLE and provide an estimator of the variance of MCLE and ECLE. We also modify two proper likelihood-based tests to be used with composite likelihood. We modify our methods to make them applicable to datasets where some loci are excluded.