# Efficient MCMC Sampling with Expensive-to-Compute and Irregular Likelihoods

arXiv: https://arxiv.org/abs/2505.10448 · HTML: https://mlsanity.com/paper/2505.10448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 10 of 10)

- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget](https://mlsanity.com/paper/1304.5299/) (2013)
- [Firefly Monte Carlo: Exact MCMC with Subsets of Data](https://mlsanity.com/paper/1403.5693/) (2014)
- [Speeding Up MCMC by Efficient Data Subsampling](https://mlsanity.com/paper/1404.4178/) (2014)
- [Asymptotically Optimal Exact Minibatch Metropolis-Hastings](https://mlsanity.com/paper/2006.11677/) (2020)
- [Multilevel Delayed Acceptance MCMC](https://mlsanity.com/paper/2202.03876/) (2022)
- [Coreset Markov Chain Monte Carlo](https://mlsanity.com/paper/2310.17063/) (2023)
- [Scalable Metropolis-Hastings for Exact Bayesian Inference with Large Datasets](https://mlsanity.com/paper/1901.09881/) (2019)
- [Delayed acceptance ABC-SMC](https://mlsanity.com/paper/1708.02230/) (2017)
- [Metropolis--Hastings with Scalable Subsampling](https://mlsanity.com/paper/2407.19602/) (2024)

## Abstract (arXiv)

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.