Asymptotic Validity of the Bayes-Inspired Indifference Zone Procedure: The Non-Normal Known Variance Case

TL;DR

This paper proves that a modified Bayes-inspired indifference zone procedure remains valid asymptotically for selecting the best alternative in ranking and selection problems with known, finite variances, even when samples are not normally distributed.

Contribution

It extends the validity of the BIZ procedure to non-normal distributions with known variances, under asymptotic conditions.

Findings

Asymptotic validity of the modified BIZ procedure is established.

The procedure is effective for non-normal, known-variance cases.

The proof relaxes the normality assumption required in previous work.

Abstract

We consider the indifference-zone (IZ) formulation of the ranking and selection problem in which the goal is to choose an alternative with the largest mean with guaranteed probability, as long as the difference between this mean and the second largest exceeds a threshold. Conservatism leads classical IZ procedures to take too many samples in problems with many alternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed in Frazier (2014), is less conservative than previous procedures, but its proof of validity requires strong assumptions, specifically that samples are normal, and variances are known with an integer multiple structure. In this paper, we show asymptotic validity of a slight modification of the original BIZ procedure as the difference between the best alternative and the second best goes to zero,when the variances are known and finite, and samples are independent and identically distributed, but not necessarily normal.