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Abstract:
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The Gibbs sampler is a very useful technique for fitting highly structured hierarchical models that are now prevalent in biological, physical, engineering, and social sciences. Its sometimes slow convergence, however, has been a longstanding complaint especially when complex models are fitted. To alleviate the slow-mixing behavior, we present efficient Gibbs sampling strategies by capitalizing on incompatible conditional distributions derived from different marginal distributions of a target distribution. Until now, such incompatibility has been simply avoided in the construction of Gibbs samplers because the resulting convergence properties were not well understood. However, incompatible Gibbs samplers have known stationary distributions as well as fast convergence. Their applications are illustrated using a highly structured multilevel spectral model in astrophysics.
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