# Multi-fidelity Monte Carlo: a pseudo-marginal approach

arXiv: https://arxiv.org/abs/2210.01534 · HTML: https://mlsanity.com/paper/2210.01534/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 61 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems](https://mlsanity.com/paper/1403.4290/) (2014)
- [Active Multi-Information Source Bayesian Quadrature](https://mlsanity.com/paper/1903.11331/) (2019)
- [On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods](https://mlsanity.com/paper/1306.4032/) (2013)
- [Bayesian Quadrature for Multiple Related Integrals](https://mlsanity.com/paper/1801.04153/) (2018)
- [Bias-Free Scalable Gaussian Processes via Randomized Truncations](https://mlsanity.com/paper/2102.06695/) (2021)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models](https://mlsanity.com/paper/2004.00353/) (2020)
- [Efficient Optimization of Loops and Limits with Randomized Telescoping Sums](https://mlsanity.com/paper/1905.07006/) (2019)
- [Active multi-fidelity Bayesian online changepoint detection](https://mlsanity.com/paper/2103.14224/) (2021)
- [Unbiased Bayesian Inference for Population Markov Jump Processes via Random Truncations](https://mlsanity.com/paper/1509.08327/) (2015)

## Built on by (most cited first, 4 of 4)

- [Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need](https://mlsanity.com/paper/2402.02111/) (2024)
- [Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry](https://mlsanity.com/paper/2301.13749/) (2023)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)
- [FLARE MCMC: Fidelity-based Layer-Adaptive REcursive proposals for MCMC](https://mlsanity.com/paper/2608.13774/) (2026)

## Abstract (arXiv)

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low-fidelity computation, leading to bias in the resulting target density. Multi-fidelity MCMC algorithms combine models of varying fidelities in order to obtain an approximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multi-fidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudo-marginal MCMC approach for multi-fidelity inference that utilizes a cheaper, randomized-fidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the low-fidelity sequence of models. Finally, we discuss and evaluate the proposed multi-fidelity MCMC approach on several applications, including log-Gaussian Cox process modeling, Bayesian ODE system identification, PDE-constrained optimization, and Gaussian process regression parameter inference.