# Approximate Bayesian Computation Via the Energy Statistic

@article{Nguyen2020ApproximateBC, title={Approximate Bayesian Computation Via the Energy Statistic}, author={Hien Duy Nguyen and Julyan Arbel and Hongliang L{\"u} and Florence Forbes}, journal={IEEE Access}, year={2020}, volume={8}, pages={131683-131698} }

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of…

## 13 Citations

Approximate Bayesian computation with surrogate posteriors

- Computer Science
- 2021

This work introduces a preliminary learning step in which surrogate posteriors are built from finite Gaussian mixtures using an inverse regression approach and the resulting ABC quasi-posterior distribution is shown to converge to the true one, under standard conditions.

Score Matched Neural Exponential Families for Likelihood-Free Inference

- Computer Science, Mathematics
- 2020

This work introduces a new way to learn ABC statistics: first, parameter-simulation pairs from the model independently on the observation are generated; then, Score Matching is used to train a neural conditional exponential family to approximate the likelihood, the largest class of distributions with fixed-size sufficient statistics.

Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo

- Computer Science
- 2021

The key results are sample complexity bounds which demonstrate that, under smoothness conditions on the generator, QMC can significantly reduce the number of samples required to obtain a given level of accuracy when using three of the most common discrepancies: the maximum mean discrepancy, the Wasserstein distance, and the Sinkhorn divergence.

On the mathematical axiomatization of approximate Bayesian computation. A robust set for estimating mechanistic network models through optimal transport

- Computer Science
- 2021

The idea is to simulate sets of synthetic data from the model with respect to assigned parameters and, rather than comparing prospects of these data with the corresponding observed values as typically ABC requires, to employ just a distance between a chosen distribution associated to the synthetic data and another of the observed values.

A Comparison of Likelihood-Free Methods With and Without Summary Statistics

- Computer Science
- 2021

This article provides a review of full data distance based likelihood-free methods, and conducts the first comprehensive comparison of such methods, both qualitatively and empirically.

Approximating Bayes in the 21st Century

- Computer Science
- 2021

The aim is to help new researchers in particular – and more generally those interested in adopting a Bayesian approach to empirical work – distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways inWhich they can can be combined.

Probabilistic Forecasting with Conditional Generative Networks via Scoring Rule Minimization

- Computer ScienceArXiv
- 2021

This manuscript performs probabilistic forecasting with conditional generative networks trained to minimize scoring rule values on two chaotic models and a global dataset of weather observations; results are satisfactory and better calibrated than what achieved by GANs.

Approximate Bayesian Inference

- Computer ScienceEntropy
- 2020

This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Inference.

Approximate Bayesian Computation via Classification

- Computer Science
- 2021

The theoretical results show that the rate at which ABC posterior distributions concentrate around the true parameter depends on the estimation error of the classiﬁer, and the usefulness of the approach is demonstrated on simulated examples as well as real data in the context of stock volatility estimation.

Generalized Bayesian Likelihood-Free Inference Using Scoring Rules Estimators

- Computer Science
- 2021

A framework for Bayesian Likelihood-Free Inference based on Generalized Bayesian Inference using scoring rules (SRs) is proposed and it is proved finite sample posterior consistency and outlier robustness of the authors' posterior for the Kernel and Energy Scores are proved.

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