# Batch simulations and uncertainty quantification in Gaussian process surrogate approximate Bayesian computation

arXiv: https://arxiv.org/abs/1910.06121 · HTML: https://mlsanity.com/paper/1910.06121/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Generative Bayesian Inference with GANs](https://mlsanity.com/paper/2208.12113/) (2022)
- [Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC](https://mlsanity.com/paper/2104.03942/) (2021)
- [Active Nearest Neighbor Regression Through Delaunay Refinement](https://mlsanity.com/paper/2206.08061/) (2022)
- [Toward Robust Uncertainty Estimation with Random Activation Functions](https://mlsanity.com/paper/2302.14552/) (2023)
- [Computationally-Efficient Climate Predictions using Multi-Fidelity Surrogate Modelling](https://mlsanity.com/paper/2109.07468/) (2021)

## Abstract (arXiv)

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is modelled with a GP which is further used to form a model-based estimator for the intractable posterior. In this article we improve this approach in several ways. We develop batch-sequential Bayesian experimental design strategies to parallellise the expensive simulations. In earlier work only sequential strategies have been used. Current surrogate-based ABC methods also do not fully account the uncertainty due to the limited budget of simulations as they output only a point estimate of the ABC posterior. We propose a numerical method to fully quantify the uncertainty in, for example, ABC posterior moments. We also provide some new analysis on the GP modelling assumptions in the resulting improved framework called Bayesian ABC and discuss its connection to Bayesian quadrature (BQ) and Bayesian optimisation (BO). Experiments with toy and real-world simulation models demonstrate advantages of the proposed techniques.