# Efficient acquisition rules for model-based approximate Bayesian computation

## TL;DR

This paper introduces an efficient method for selecting simulation points in model-based approximate Bayesian computation, reducing computational costs while improving posterior estimation accuracy.

## Contribution

It proposes a novel acquisition rule that minimizes uncertainty in the ABC posterior, addressing a gap in existing Bayesian optimisation strategies.

## Key findings

- Proposed method outperforms common BO strategies in accuracy
- Reduces the number of simulations needed for reliable posterior estimates
- Demonstrates effectiveness through experimental comparisons

## Abstract

Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.