## The Annals of Statistics

- Ann. Statist.
- Volume 8, Number 4 (1980), 840-844.

### Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach

#### Abstract

This paper provides explicit solutions to the problem of estimating the arrival rate $\lambda$ of a Poisson process using a Bayes sequential approach. The loss associated with estimating $\lambda$ by $d$ is assumed to be of the form $(\lambda - d)^2\lambda^{-p}$ and the cost of observation includes both a time cost and an event cost. A discrete time approach is taken in which decisions are made at the end of time intervals having length $t$. Limits of the procedures as $t$ approaches zero are discussed and related to the continuous time Bayes sequential procedure.

#### Article information

**Source**

Ann. Statist., Volume 8, Number 4 (1980), 840-844.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345076

**Digital Object Identifier**

doi:10.1214/aos/1176345076

**Mathematical Reviews number (MathSciNet)**

MR572627

**Zentralblatt MATH identifier**

0463.62072

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L12: Sequential estimation

Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 62C10: Bayesian problems; characterization of Bayes procedures

**Keywords**

Bayes sequential estimation sequential decision procedure optimal stopping Poisson process

#### Citation

Novic, Bradley. Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach. Ann. Statist. 8 (1980), no. 4, 840--844. doi:10.1214/aos/1176345076. https://projecteuclid.org/euclid.aos/1176345076