  Observed data is 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 lightcurves without spectra. The multi-band lightcurves 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 NP
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.
