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Abstract:
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We propose and study various approaches for joint MCMC sampling of multiple dimensions of hierarchical statistical models. Traditional adaptive block sampling, e.g. Metropolis-Hastings (MH) using a multivariate normal proposal, tunes the proposal covariance according to the empirical posterior covariance. Other adaptive sampling strategies for multiple dimensions make use of the Eigen decomposition of the empirical covariance, to apply univariate sampling algorithms (e.g., slice sampling) in a rotated coordinate space. Using several hierarchical modeling examples, we study the advantages and disadvantages of these approaches in a variety of settings, and observe there is no universally best approach. Guided by these lessons, we propose and study hybrid sampling strategies which make use of the strengths of the existing techniques. The performance of these hybrid strategies is evaluated in terms of runtime and posterior effective sample size.
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