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Abstract:
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Statistical models with a hierarchical structure, such as generalized linear mixed models, can, in the absence of conjugacy, give rise to analytically intractable likelihood functions. Monte Carlo methods, such as Monte Carlo versions of EM or Newton-Raphson, or the Monte Carlo Likelihood Approximation of Geyer (1994), provide an appealing approach to likelihood-based inference in such cases. The empirical performance of these algorithms is highly dependent upon efficient simulation from the conditional distribution of the random effects. In this talk we consider a number of approaches to this simulation problem, including rejection sampling, importance sampling, and Markov chain Monte Carlo (MCMC). Empirical performance in realistic examples and theoretical properties, such as rate of convergence of MCMC algorithms, will be discussed.
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