## Annals of Statistics

- Ann. Statist.
- Volume 5, Number 2 (1977), 379-384.

### Sequential Bayes Estimation of the Difference Between Means

#### Abstract

It is desired to estimate the difference between the means of two independent normal distributions as accurately as possible and in a sequential manner when the total number of observations is fixed. The problem is posed in a Bayesian framework with conjugate prior distributions and squared error loss function. It is shown that the optimal sequential design depends on the ratio of the posterior variances of the two means. There exist constants (dependent on the prior parameters, the number of observations taken from each distribution, and the number of observations remaining) such that when the above-mentioned ratio exceeds this constant it is optimal to select the next observation from one distribution; otherwise it is optimal to select it from the other distribution.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 2 (1977), 379-384.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343803

**Digital Object Identifier**

doi:10.1214/aos/1176343803

**Mathematical Reviews number (MathSciNet)**

MR431552

**Zentralblatt MATH identifier**

0364.62029

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L12: Sequential estimation

Secondary: 93C40: Adaptive control

**Keywords**

Sequential estimation adaptive control process dynamic programming algorithm optimal strategy myopic rule

#### Citation

Kelley, Thomas A. Sequential Bayes Estimation of the Difference Between Means. Ann. Statist. 5 (1977), no. 2, 379--384. doi:10.1214/aos/1176343803. https://projecteuclid.org/euclid.aos/1176343803