# Bayesian estimation applied to multiple species

## Abstract

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.

- Authors:

- Departement de Physique Theorique, Universite de Geneve, 24 quai Ernest Ansermet, CH-1211 Geneva 4 (Switzerland)
- (South Africa)

- Publication Date:

- OSTI Identifier:
- 20935250

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.103508; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSIFICATION; DISTRIBUTION; MATHEMATICAL MODELS; MAXIMUM-LIKELIHOOD FIT; PROBABILITY; SPECTRA; VISIBLE RADIATION

### Citation Formats

```
Kunz, Martin, Bassett, Bruce A., Hlozek, Renee A., South African Astronomical Observatory, Observatory, Cape Town, South Africa and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, Cape Town, and National Astrophysics and Space Science Programme, University of Cape Town, Rondebosch, 7700, Cape Town.
```*Bayesian estimation applied to multiple species*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.103508.

```
Kunz, Martin, Bassett, Bruce A., Hlozek, Renee A., South African Astronomical Observatory, Observatory, Cape Town, South Africa and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, Cape Town, & National Astrophysics and Space Science Programme, University of Cape Town, Rondebosch, 7700, Cape Town.
```*Bayesian estimation applied to multiple species*. United States. doi:10.1103/PHYSREVD.75.103508.

```
Kunz, Martin, Bassett, Bruce A., Hlozek, Renee A., South African Astronomical Observatory, Observatory, Cape Town, South Africa and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, Cape Town, and National Astrophysics and Space Science Programme, University of Cape Town, Rondebosch, 7700, Cape Town. Tue .
"Bayesian estimation applied to multiple species". United States.
doi:10.1103/PHYSREVD.75.103508.
```

```
@article{osti_20935250,
```

title = {Bayesian estimation applied to multiple species},

author = {Kunz, Martin and Bassett, Bruce A. and Hlozek, Renee A. and South African Astronomical Observatory, Observatory, Cape Town, South Africa and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, Cape Town and National Astrophysics and Space Science Programme, University of Cape Town, Rondebosch, 7700, Cape Town},

abstractNote = {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.},

doi = {10.1103/PHYSREVD.75.103508},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}