# Variational Bayesian Monte Carlo with Noisy Likelihoods

arXiv: https://arxiv.org/abs/2006.08655 · HTML: https://mlsanity.com/paper/2006.08655/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 23 of 23)

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- [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)
- [PyVBMC: Efficient Bayesian inference in Python](https://mlsanity.com/paper/2303.09519/) (2023)
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- [Interpolating between sampling and variational inference with infinite stochastic mixtures](https://mlsanity.com/paper/2110.09618/) (2021)
- [Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature](https://mlsanity.com/paper/2303.05263/) (2023)
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- [Optimality in Noisy Importance Sampling](https://mlsanity.com/paper/2201.02432/) (2022)
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- [Digital twin for virtual sensing of ferry quays via a Gaussian Process Latent Force Model](https://mlsanity.com/paper/2506.14925/) (2025)
- [Score-Based Density Estimation from Pairwise Comparisons](https://mlsanity.com/paper/2510.09146/) (2025)

## Abstract (arXiv)

Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal with noisy log-likelihood evaluations, such as those arising from simulation-based models. We introduce new `global' acquisition functions, such as expected information gain (EIG) and variational interquantile range (VIQR), which are robust to noise and can be efficiently evaluated within the VBMC setting. In a novel, challenging, noisy-inference benchmark comprising of a variety of models with real datasets from computational and cognitive neuroscience, VBMC+VIQR achieves state-of-the-art performance in recovering the ground-truth posteriors and model evidence. In particular, our method vastly outperforms `local' acquisition functions and other surrogate-based inference methods while keeping a small algorithmic cost. Our benchmark corroborates VBMC as a general-purpose technique for sample-efficient black-box Bayesian inference also with noisy models.