The Bayes choice of an experiment in estimating a success probability

Alicja Jokiel-Rokita¹ ; Ryszard Magiera¹

¹Institute of Mathematics Wroc/law University of Technology 50-370 Wroc/law, Poland

Applicationes Mathematicae, Tome 29 (2002) no. 2, pp. 135-144

Résumé

A Bayesian method of estimation of a success probability $p$ is considered in the case when two experiments are available: individual Bernoulli $(p)$ trials—the $p$-experiment—or products of $r$ individual Bernoulli $(p)$ trials—the $p^{r}$-experiment. This problem has its roots in reliability, where one can test either single components or a system of $r$ identical components. One of the problems considered is to find the degree ${\tilde r}$ of the $p^{\tilde r}$-experiment and the size ${\tilde m}$ of the $p$-experiment such that the Bayes estimator based on ${\tilde m}$ observations of the $p$-experiment and $N-{\tilde m}$ observations of the $p^{\tilde r}$-experiment minimizes the Bayes risk among all the Bayes estimators based on $m$ observations of the $p$-experiment and $N-m$ observations of the $p^{r}$-experiment. Another problem is to sequentially select some combination of these two experiments, i.e., to decide, using the additional information resulting from the observation at each stage, which experiment should be carried out at the next stage to achieve a lower posterior expected loss.

Détail

DOI : 10.4064/am29-2-2

Keywords: bayesian method estimation success probability considered experiments available individual bernoulli trials p experiment products individual bernoulli trials experiment problem has its roots reliability where test either single components system identical components problems considered degree tilde tilde experiment size tilde p experiment bayes estimator based tilde observations p experiment n tilde observations tilde experiment minimizes bayes risk among bayes estimators based observations p experiment n m observations experiment another problem sequentially select combination these experiments decide using additional information resulting observation each stage which experiment should carried out stage achieve lower posterior expected loss