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

Authors

  • J. Newling,

    Corresponding author
    1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
    2. African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg 7945, South Africa
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  • B. Bassett,

    1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
    2. African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg 7945, South Africa
    3. South African Astronomical Observatory, PO Box 9, Observatory 7935, South Africa
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  • R. Hlozek,

    1. Department of Astrophysics, Oxford University, Oxford OX1 3RH
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  • M. Kunz,

    1. Département de Physique Théorique, Université de Genève, Genève CH1211, Switzerland
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  • M. Smith,

    1. African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg 7945, South Africa
    2. Astrophysics, Cosmology and Gravity Centre, University of Cape Town, Rondebosch 7701, South Africa
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  • M. Varughese

    1. Department of Statistical Sciences, University of Cape Town, Rondebosch 7701, South Africa
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E-mail: james.newling@gmail.com

ABSTRACT

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.

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