Gareth Roberts studies Markov chain Monte Carlo and the mathematical efficiency of Bayesian computation. With Giacomo Zanella, he developed importance tempering for high-dimensional sampling.[ref]
Their Tempered Gibbs sampler changes how coordinates are selected. Its invariant law differs from the intended target, so importance sampling weights correct the averages. This trades easier movement through the state space against the variability of the correcting weights, with explicit theoretical comparisons to ordinary sampling methods.[ref]
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