Likelihood-Free Cosmological Inference with Type Ia Supernovae: Approximate Bayesian Computation for a Complete Treatment of Uncertainty

TL;DR

This paper demonstrates how Approximate Bayesian Computation (ABC) can be used to perform cosmological inference with Type Ia supernova data, effectively handling complex models and uncertainties without explicit likelihood calculations.

Contribution

It introduces ABC methods into supernova cosmology, enabling accurate posterior estimation despite complex data-generating processes and contamination.

Findings

ABC recovers accurate posterior distributions in supernova cosmology.

ABC remains effective even with contamination from Type IIP supernovae.

The method naturally incorporates priors and marginalizes nuisance parameters.

Abstract

Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state we demonstrate that ABC can recover an accurate posterior distribution. Finally we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.