Sam Power

Comparison Theorems for Practical Slice Sampling

Slice sampling is a popular gradient-free MCMC algorithm for approximate sampling from intractable probability distributions, implemented in software packages such as JAGS and TensorFlow Probability. This popularity stems from the intuitive geometric formulation, wide applicability, and general robustness of the algorithm, both in theory and in practice.

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.