# GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

arXiv: https://arxiv.org/abs/1401.2838 · HTML: https://mlsanity.com/paper/1401.2838/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2014.

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

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
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- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC](https://mlsanity.com/paper/2104.03942/) (2021)
- [Tree Bandits for Generative Bayes](https://mlsanity.com/paper/2404.10436/) (2024)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [Approximate Bayesian Computation for Physical Inverse Modeling](https://mlsanity.com/paper/2111.13296/) (2021)
- [Sampling as Bandits: Evaluation-Efficient Design for Black-Box Densities](https://mlsanity.com/paper/2509.01437/) (2025)
- [Neural-Inspired Posterior Approximation (NIPA)](https://mlsanity.com/paper/2601.22539/) (2026)
- [A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems](https://mlsanity.com/paper/2607.06252/) (2026)

## Abstract (arXiv)

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms.