# Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach

arXiv: https://arxiv.org/abs/2006.14126 · HTML: https://mlsanity.com/paper/2006.14126/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

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

- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Pseudo-Likelihood Inference](https://mlsanity.com/paper/2311.16656/) (2023)
- [Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operators](https://mlsanity.com/paper/2507.06055/) (2025)

## Abstract (arXiv)

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately yields inefficient inference; 2) a possible lack of robustness to deviations from the underlying model structure. Motivated by these efficiency and robustness concerns, we construct a new Bayesian method that can deliver efficient estimators when the underlying model is well-specified, and which is simultaneously robust to certain forms of model misspecification. This new approach bypasses the calculation of summaries by considering a norm between empirical and simulated probability measures. For specific choices of the norm, we demonstrate that this approach can deliver point estimators that are as efficient as those obtained using exact Bayesian inference, while also simultaneously displaying robustness to deviations from the underlying model assumptions.