### Abstract

Bayesian estimators are defined in terms of the posterior distribution. Typically, this is written as the product of the likelihood function and a prior probability density, both of which are assumed to be known. But in many situations, the prior density is not known, and is difficult to learn from data since one does not have access to uncorrupted samples of the variable being estimated. We show that for a wide variety of observation models, the Bayes least squares (BLS) estimator may be formulated without explicit reference to the prior. Specifically, we derive a direct expression for the estimator, and a related expression for the mean squared estimation error, both in terms of the density of the observed measurements. Each of these prior-free formulations allows us to approximate the estimator given a sufficient amount of observed data. We use the first form to develop practical nonparametric approximations of BLS estimators for several different observation processes, and the second form to develop a parametric family of estimators for use in the additive Gaussian noise case. We examine the empirical performance of these estimators as a function of the amount of observed data.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference |

Pages | 1145-1152 |

Number of pages | 8 |

State | Published - Dec 1 2007 |

Event | 20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada Duration: Dec 4 2006 → Dec 7 2006 |

### Publication series

Name | Advances in Neural Information Processing Systems |
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ISSN (Print) | 1049-5258 |

### Other

Other | 20th Annual Conference on Neural Information Processing Systems, NIPS 2006 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/4/06 → 12/7/06 |

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

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## Cite this

*Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference*(pp. 1145-1152). (Advances in Neural Information Processing Systems).