Closed sequential procedures for selecting the multinomial events which have the largest probabilities

System comparison procedures for automatic target recognition systems

“…They do discuss the preceding R&S method along with others based on odds ratios rather than differences. One particularly interesting technique due to Bechhofer and Kulkarni [2] supposes that a maximum common number of observations per system, n, are available. This bound established, the systems are then sampled one at a time.…”

“…A third method for comparing the probabilities of success for different systems that generally requires fewer samples than confidence or difference intervals would be to use a ranking and selection (R&S) procedure. The goal of this technique is to "select the population with the largest p value" from a set of k binomial populations with ordered p-values such that p [1] Յ p [2] Յ . .…”

“…Likewise, a difference interval would be expected to require half as many observations (1791) before it did not contain zero. Using a ranking and selection procedure, we need to test n ϭ (1 Ϫ ␦* 2 )( s / 2␦*) 2 images from each system, where s is the number of systems being compared and s is a value tabulated by Gibbons, Olkin, and Sobel [4]. For the current case where s ϭ 2, 2 ϭ 2.3262 and thus n ϭ (1 Ϫ 0.03 2 )(2.3262/0.06) 2 ϭ 1502, providing some savings over both the confidence and difference interval techniques.…”

Truncated selection procedures for the most probable event and the least probable event

“…There is no possibility of a tie for the first place. Bechhofer and Kulkarni (1984) studied the performance of the curtailment of the fixed sample size procedure considered in Bechhofer et al (1959). The curtailed procedure stops sampling once the frequency of any cell is large enough to guarantee the selection of a particular cell.…”

Parametric Empirical Bayes Rules for Selecting the Most Probable Multinomial Event

“…Gupta and Nagel (1967), Panchapakesan (1971) and, Gupta and Huang (1975) have studied this selection problem using a subset selection approach. Cacoullos and Sobel (1966), Alam (1971), Alam, Seo and Thompson (1971), Alam (1979, 1980) and Bechhofer and Kulkarni (1984) have considered sequential selection procedures.…”