BOUNDED STOPPING TIME OF SOME BAYES SEQUENTIAL TESTS FOR
THE -TEST MODEL
Abstract: For the -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 ;
(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: -