Bayes Empirical Bayes Classification of Components Using Masked Data

Abstract

For classification and pattern recognition, it is known that the Bayes decision rule is the best decision rule, which gives the minimum probability of misclassification. The Bayes classifier cannot be immediately applied, since it contains unknown parameters (means, variances, and percentages of k classes). In this study, a set of masked life data is used to establish a Bayes empirical Bayes (BEB) classifier to identify a component in a closed multi-component system whose lifetime is the masked lifetime, such that: (1) it only contains the observations of unclassified masked life data; (2) no other classifier is strictly better than our BEB classifier; and (3) when the number of masked samples increases, the recognition rate of our classifier converges to the rate of the Bayes decision rule. Furthermore, in this article, the BEB estimation leads to a good estimation of each component mean life in the masked system.

Keywords:

• Asymptotic optimality
• Bayes decision rule
• Classification
• Empirical Bayes decision rule
• Failure rates
• Masked system life data
• Maximum likelihood estimation

Mathematics Subject Classification:

• 62C12
• 62C15

Acknowledgment

The authors are grateful to the Editor and referees for their valuable suggestions for the improvement of this article.

Notes

BEB = Bayes empirical Bayes classifier without any parameter.

Bayes =Bayes classifier with known parameters: mean lifetimes (2 and 4).