## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 41, Number 3 (1970), 894-906.

### Consistency a Posteriori

#### Abstract

Conditions are given under which a sequence of posterior distributions converges weakly to a degenerate distribution. It is not assumed that the model being used actually governs the data. Exponential models are studied in particular and are shown to be well behaved under mild assumptions. Large-deviation results for $U$-statistics and posterior odds are also given.

#### Article information

**Source**

Ann. Math. Statist., Volume 41, Number 3 (1970), 894-906.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177696967

**Digital Object Identifier**

doi:10.1214/aoms/1177696967

**Mathematical Reviews number (MathSciNet)**

MR266356

**Zentralblatt MATH identifier**

0214.45703

**JSTOR**

links.jstor.org

#### Citation

Berk, Robert H. Consistency a Posteriori. Ann. Math. Statist. 41 (1970), no. 3, 894--906. doi:10.1214/aoms/1177696967. https://projecteuclid.org/euclid.aoms/1177696967