Comparison Theorems for Slice Sampling
Probability Seminar
15th November 2024, 3:30 pm – 4:30 pm
Fry Building, 2.04
It is a classical fact that sampling uniformly under the graph of a probability density is tantamount to sampling from the corresponding probability distribution itself. Taking this equivalence seriously, one can then attempt to solve the general sampling problem by defining a dynamical system which “explores the area beneath the graph” in a suitable sense. One method which results from this perspective is Neal's "Slice Sampling", a Markov chain Monte Carlo simulation method of great popularity, applicability, and practical robustness.
An outstanding theoretical challenge has been that while the “ideal" slice sampler admits an elegant quantitative convergence theory, practical implementations typically involve additional approximations, which prevent the existing theory from applying as-is. In recent work, we advance a mathematical framework for the analysis of such “hybrid” slice samplers, facilitating novel convergence results for slice sampling as implemented in practice.
We provide a number of concrete examples to illustrate the flexibility and practicality of our approach. No prior knowledge of the slice sampling algorithm will be assumed, and relevant theoretical concepts will be recalled as appropriate in the talk.
This is joint work with Daniel Rudolf, Björn Sprungk, and Andi Wang.
Comments are closed.