Parameter Estimation with BEAMS in the presence of biases and correlations

TL;DR

This paper extends the BEAMS method for unbiased parameter estimation to account for correlations between data and type probabilities, significantly improving accuracy in contaminated datasets like supernova surveys.

Contribution

It introduces a formal extension of BEAMS to handle correlations, demonstrating a 50% reduction in variance and analyzing bias effects in supernova data.

Findings

Extended BEAMS reduces estimation variance by 50% with correlations.

Bias in type probabilities impacts parameter estimates.

Recommendations for future supernova surveys are provided.

Abstract

The original formulation of BEAMS - Bayesian Estimation Applied to Multiple Species - showed how to use a dataset contaminated by points of multiple underlying types to perform unbiased parameter estimation. An example is cosmological parameter estimation from a photometric supernova sample contaminated by unknown Type Ibc and II supernovae. Where other methods require data cuts to increase purity, BEAMS uses all of the data points in conjunction with their probabilities of being each type. Here we extend the BEAMS formalism to allow for correlations between the data and the type probabilities of the objects as can occur in realistic cases. We show with simple simulations that this extension can be crucial, providing a 50% reduction in parameter estimation variance when such correlations do exist. We then go on to perform tests to quantify the importance of the type probabilities, one of which illustrates the effect of biasing the probabilities in various ways. Finally, a general presentation of the selection bias problem is given, and discussed in the context of future photometric supernova surveys and BEAMS, which lead to specific recommendations for future supernova surveys.