Bayesian estimation applied to multiple species

Observed data are often contaminated by undiscovered interlopers, leading to biased parameter estimation. Here we present BEAMS (Bayesian estimation applied to multiple species) which significantly improves on the standard maximum likelihood approach in the case where the probability for each data point being ``pure'' is known. We discuss the application of BEAMS to future type-Ia supernovae (SNIa) surveys, such as LSST, which are projected to deliver over a million supernovae light curves without spectra. The multiband light curves for each candidate will provide a probability of being Ia (pure) but the full sample will be significantly contaminated with other types of supernovae and transients. Given a sample of N supernovae with mean probability, ⟨P⟩, of being Ia, BEAMS delivers parameter constraints equal to N⟨P⟩ spectroscopically confirmed SNIa. In addition BEAMS can be simultaneously used to tease apart different families of data and to recover properties of the underlying distributions of those families (e. g. the type-Ibc and II distributions). Hence BEAMS provides a unified classification and parameter estimation methodology which may be useful in a diverse range of problems such as photometric redshift estimation or, indeed, any parameter estimation problem where contamination is an issue.