Journal Article

Parameter estimation with Bayesian estimation applied to multiple species in the presence of biases and correlations

J. Newling, B. Bassett, R. Hlozek, M. Kunz, M. Smith and M. Varughese

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 421, issue 2, pages 913-925
Published in print April 2012 | ISSN: 0035-8711
Published online March 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.20147.x
Parameter estimation with Bayesian estimation applied to multiple species in the presence of biases and correlations

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The original formulation of Bayesian estimation applied to multiple species (BEAMS) showed how to use a data set 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 per cent 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.

Keywords: methods: data analysis; methods: statistical; supernovae: general; cosmological parameters

Journal Article.  9669 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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