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Paper No. 13-21

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H Ogden

A sequential reduction method for inference in generalized linear mixed models

Abstract: The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information available on each random effect. The sequential reduction method described in this paper exploits the dependence structure of the posterior distribution of the random effects to reduce the cost of finding a good approximation to the likelihood in models with sparse structure.

Keywords: Graphical model, Intractable likelihood, Laplace approximation, Pairwise comparisons, Sparse grid interpolation.