A Latent Slice Sampling Algorithm

TL;DR

This paper introduces a new latent slice sampling algorithm that offers a potentially universal replacement for Metropolis--Hastings, capable of efficiently sampling from high-dimensional distributions without accept/reject steps.

Contribution

It presents a novel latent slice sampling method that simplifies sampling from complex distributions, eliminating the need for proposal distributions and accept/reject mechanisms.

Findings

Efficient sampling from high-dimensional distributions.

No need for proposal distributions or accept/reject steps.

Potential to replace Metropolis--Hastings in various applications.

Abstract

In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is applicable to discrete probability distributions %which can be viewed as an alternative to the Metropolis--Hastings algorithm in this setting, which obviates the need for a proposal distribution, in that is has no accept/reject component. This paper looks at the continuous counterpart. A latent variable combined with a slice sampler and a shrinkage procedure applied to uniform density functions creates a highly efficient sampler which can generate random variables from very high dimensional distributions as a single block.