# Continuously-Tempered PDMP Samplers

arXiv: https://arxiv.org/abs/2205.09559 · HTML: https://mlsanity.com/paper/2205.09559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 8 of 8)

- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [The Boomerang Sampler](https://mlsanity.com/paper/2006.13777/) (2020)
- [PDMP Monte Carlo methods for piecewise-smooth densities](https://mlsanity.com/paper/2111.05859/) (2021)
- [Pseudo-extended Markov chain Monte Carlo](https://mlsanity.com/paper/1708.05239/) (2017)
- [Adaptive Path Sampling in Metastable Posterior Distributions](https://mlsanity.com/paper/2009.00471/) (2020)
- [Reversible Jump PDMP Samplers for Variable Selection](https://mlsanity.com/paper/2010.11771/) (2020)
- [Concave-Convex PDMP-based sampling](https://mlsanity.com/paper/2112.12897/) (2021)

## Abstract (arXiv)

New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or heavy-tailed distributions. We show how tempering ideas can improve the mixing of PDMPs in such cases. We introduce an extended distribution defined over the state of the posterior distribution and an inverse temperature, which interpolates between a tractable distribution when the inverse temperature is 0 and the posterior when the inverse temperature is 1. The marginal distribution of the inverse temperature is a mixture of a continuous distribution on [0,1) and a point mass at 1: which means that we obtain samples when the inverse temperature is 1, and these are draws from the posterior, but sampling algorithms will also explore distributions at lower temperatures which will improve mixing. We show how PDMPs, and particularly the Zig-Zag sampler, can be implemented to sample from such an extended distribution. The resulting algorithm is easy to implement and we show empirically that it can outperform existing PDMP-based samplers on challenging multimodal posteriors.