# Diagnostic tools of approximate Bayesian computation using the coverage property

arXiv: https://arxiv.org/abs/1301.3166 · HTML: https://mlsanity.com/paper/1301.3166/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2013.

## Built on by (most cited first, 10 of 10)

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference](https://mlsanity.com/paper/2203.03353/) (2022)
- [Bayesian score calibration for approximate models](https://mlsanity.com/paper/2211.05357/) (2022)
- [Discriminative calibration: Check Bayesian computation from simulations and flexible classifier](https://mlsanity.com/paper/2305.14593/) (2023)
- [Model-Free Local Recalibration of Neural Networks](https://mlsanity.com/paper/2403.05756/) (2024)
- [SoftCVI: Contrastive variational inference with self-generated soft labels](https://mlsanity.com/paper/2407.15687/) (2024)

## Abstract (arXiv)

Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples, (m,θ,y), from the prior, and then accepting as samples from the approximate posterior, those pairs (m,θ) for which y, or a summary of y, is "close" to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter, ε. Appropriate choice of ε is important to producing a good quality approximation. This paper proposes diagnostic tools for the choice of ε based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re-analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. R code implementing the proposed methodology is freely available in the package "abc."