Adapting the ABC distance function

TL;DR

This paper introduces two adaptive ABC algorithms that dynamically update weights for summary statistics, improving inference accuracy in iterative approximate Bayesian computation where data scales change.

Contribution

It proposes novel iterative ABC algorithms that adaptively update weights for summary statistics, addressing a key challenge in sequential ABC methods.

Findings

Improved inference results on test applications.

Adaptive weighting enhances ABC performance.

Algorithms effectively handle changing data scales.

Abstract

Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are close enough to the observations. There has been much progress on deciding which summary statistics of the data should be used to judge closeness, but less work on how to weight them. Typically weights are chosen at the start of the algorithm which normalise the summary statistics to vary on similar scales. However these may not be appropriate in iterative ABC algorithms, where the distribution from which the parameters are proposed is updated. This can substantially alter the resulting distribution of summary statistics, so that different weights are needed for normalisation. This paper presents two iterative ABC algorithms which adaptively update their weights and demonstrates improved results on test applications.