A Level-Set Hit-and-Run Sampler for Quasi-Concave Distributions

TL;DR

This paper introduces a novel level-set hit-and-run sampling method tailored for quasi-concave distributions, demonstrating effectiveness in high-dimensional, multi-modal, and complex Bayesian models.

Contribution

The authors develop a versatile sampling algorithm that extends to exponentially-tilted quasi-concave densities, improving sampling efficiency in complex Bayesian models.

Findings

Performs well in high-dimensional settings

Effective for multi-modal posterior distributions

Handles high dependence between parameters

Abstract

We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of the target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Our sampler performs well in high-dimensional settings, which we illustrate with a comparison to Gibbs sampling on a spike-and-slab mixture model. We also extend our method to exponentially-tilted quasi-concave densities, which arise often in Bayesian models consisting of a log-concave likelihood and quasi-concave prior density. Within this class of models, our method is effective at sampling from posterior distributions with high dependence between parameters, which we illustrate with a simple multivariate normal example. We also implement our level-set sampler on a Cauchy-normal model where we demonstrate the ability of our level set sampler to handle multi-modal posterior distributions.