### Abstract

An analysis of the relationship between the MDL (Minimum Description Length) estimator and the PBE (projected Bayes estimator) for exponential families is presented. The PBE is obtained by projecting the Bayes estimator, such as posterior mixture, onto the original exponential family and is, under certain conditions, equal to the Bayes estimator. An example of Bernoulli sources is presented according to the formulated theorems. It is implied by a theorem that the PBE can be approximated with Jeffreys prior by deriving an appropriate MDL estimator or a bias-corrected MLE. The arguments presented is restricted to the case in which the class of sources is an i.i.d. exponential family.

Original language | English |
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Number of pages | 1 |

Publication status | Published - Jan 1 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 IEEE International Symposium on Information Theory - Whistler, BC, Can Duration: Sep 17 1995 → Sep 22 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Symposium on Information Theory |
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City | Whistler, BC, Can |

Period | 9/17/95 → 9/22/95 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

### Cite this

*Characterization of the Bayes estimator and the MDL estimator for exponential families*. Paper presented at Proceedings of the 1995 IEEE International Symposium on Information Theory, Whistler, BC, Can, .