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March, 1977 Sequential Bayes Estimation of the Difference Between Means
Thomas A. Kelley
Ann. Statist. 5(2): 379-384 (March, 1977). DOI: 10.1214/aos/1176343803


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.


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Thomas A. Kelley. "Sequential Bayes Estimation of the Difference Between Means." Ann. Statist. 5 (2) 379 - 384, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0364.62029
MathSciNet: MR431552
Digital Object Identifier: 10.1214/aos/1176343803

Primary: 62L12
Secondary: 93C40

Keywords: adaptive control process , dynamic programming algorithm , myopic rule , optimal strategy , sequential estimation

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • March, 1977
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