# An automatic adaptive method to combine summary statistics in approximate Bayesian computation

## TL;DR

This paper introduces an automatic, adaptive weighting algorithm for summary statistics in approximate Bayesian computation, improving parameter inference especially for high-dimensional data by maximizing the distance between prior and posterior.

## Contribution

The paper presents a novel algorithm that automatically adjusts weights for summary statistics in ABC, enhancing inference accuracy without manual tuning.

## Key findings

- The adaptive algorithm outperforms existing methods in test problems.
- It effectively handles high-dimensional data like biological imaging.
- Theoretical justification supports its reliability.

## Abstract

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms.