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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]

Giacomo Zanella develops methods in computational statistics, applied probability theory and machine learning, especially Bayesian computation. His research statement identifies Markov chain Monte Carlo, random measures and variable selection among these interests.^[ref]

With Gareth Roberts, he proposed the Tempered Gibbs sampler. A modified coordinate-selection rule can explore difficult high-dimensional targets more effectively; importance sampling weights then recover averages under the desired probability distribution. Their analysis includes applications to Bayesian variable selection.^[ref]

By Giacomo Zanella, Gareth Roberts. Journal of the Royal Statistical Society, Series B, 81(3), 489–517.

Author preprint: arxiv.org/abs/1805.00541

Section 2, equations (1)–(3), Algorithm TGS and Proposition 1 give the modified conditional ratios, coordinate-selection probabilities, invariant density fZ and importance weights 1/Z.