Weak Poincaré inequality comparisons for ideal and hybrid slice sampling

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• Andi Wang (University of Warwick)
• Tuesday 26 November 2024, 09:15-10:05
• Seminar Room 1, Newton Institute.

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SSDW04 - Monte Carlo sampling: beyond the diffusive regime

Weak Poincaré inequalities are a class of functional inequality that can be used to give L2 convergence guarantees for ergodic Markov chains. Notably, they can be applied in situations where the chain possesses no spectral gap, and the convergence to equilibrium occurs at a subgeometric rate. They can also be used to compare Markov chains and their convergence rates, often when one chain is an “approximate” version of some ideal chain. In this talk I will introduce this comparison framework based on weak Poincaré inequalities, and then apply them to compare convergence rates of Hybrid versions of the popular MCMC algorithm known as Slice Sampling to their ideal counterparts. Joint work with Sam Power, Daniel Rudolf and Björn Sprungk.

This talk is part of the Isaac Newton Institute Seminar Series series.

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