Accelerating Approximate Bayesian Computation with Quantile Regression: Application to Cosmological Redshift Distributions

TL;DR

The paper introduces qABC, a novel method that accelerates Approximate Bayesian Computation by using Quantile Regression to predict promising regions of parameter space, significantly reducing the number of simulations needed.

Contribution

The authors propose qABC, a new approach that integrates Quantile Regression into ABC to improve convergence speed and reduce computational cost in cosmological parameter estimation.

Findings

qABC achieves a fivefold reduction in simulations needed.

It converges to a posterior similar to basic ABC.

Performance depends on prior proximity to the posterior.

Abstract

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20\% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method.