# Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

arXiv: https://arxiv.org/abs/1402.1694 · HTML: https://mlsanity.com/paper/1402.1694/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2014.

## Built on by (most cited first, 17 of 17)

- [Adaptive operator learning for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2310.17844/) (2023)
- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Models](https://mlsanity.com/paper/2108.12657/) (2021)
- [Weak-Form Inference for Hybrid Dynamical Systems in Ecology](https://mlsanity.com/paper/2405.20591/) (2024)
- [Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures](https://mlsanity.com/paper/2302.04518/) (2023)
- [Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2405.13574/) (2024)
- [Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network](https://mlsanity.com/paper/2110.10080/) (2021)
- [Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC](https://mlsanity.com/paper/2104.03942/) (2021)
- [Self-reinforced polynomial approximation methods for concentrated probability densities](https://mlsanity.com/paper/2303.02554/) (2023)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2501.08501/) (2025)
- [Towards fast machine-learning-assisted Bayesian posterior inference of microseismic event location and source mechanism](https://mlsanity.com/paper/2101.04724/) (2021)
- [Fast-Mixing Markov Chains without Gradients](https://mlsanity.com/paper/2606.27564/) (2026)
- [A Bayesian Approach To Graph Partitioning](https://mlsanity.com/paper/2204.12927/) (2022)
- [Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data](https://mlsanity.com/paper/2211.15771/) (2022)
- [FLARE MCMC: Fidelity-based Layer-Adaptive REcursive proposals for MCMC](https://mlsanity.com/paper/2608.13774/) (2026)
- [Heteroscedastic Neural Surrogate Modeling for Robust and Rapid Bayesian Inference in Fusion Plasma Diagnostics](https://mlsanity.com/paper/2608.19377/) (2026)

## Abstract (arXiv)

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some local regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.