# A Metropolis-class sampler for targets with non-convex support

## TL;DR

This paper introduces a new Metropolis-class sampler that reuses rejected proposals in non-convex support regions, improving exploration efficiency for complex target distributions.

## Contribution

It proposes a novel sampler that enhances exploration in non-convex supports by reusing proposals, with theoretical guarantees and practical applications.

## Key findings

- The new sampler satisfies a strong law of large numbers.
- Numerical experiments show improved performance over standard Metropolis.
- Applications include global optimization and rare event sampling.

## Abstract

We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support $A \subset \mathbb{R}^d$, by reusing proposals in $A^c$ which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.