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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 7, Fasc. 1,
pages 1 - 5
 

BOUNDED STOPPING TIME OF SOME BAYES SEQUENTIAL TESTS FOR THE t -TEST MODEL

Arthur Cohen

Abstract: For the t -test model the problem is to sequentially test whether the sign of the mean is negative or positive. Consider normal-gamma priors and the following three loss functions:

(i) linear combination of cost and 0- 1 ;

(ii) linear combination of cost and absolute error;

(iii) linear combination of cost and absolute error divided by the standard deviation.

For losses (i) and (iii) the Bayes test is shown to have bounded stopping time and a bound on the maximum sample size is obtainable. For loss (ii) the Bayes test does not have bounded stopping time. Intuitive explanations for these somewhat surprising results are offered.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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