The Best Two Independent Measurements Are Not the Two Best

Abstract

Consider an item that belongs to one of two classes, θ = 0 or θ = 1, with equal probability. Suppose also that there are two measurement experiments E 1 and E 2 that can be performed, and suppose that the outcomes are independent (given θ). Let E í denote an independent performance of experiment E I . Let P e (E) denote the probability of error resulting from the performance of experiment E. Elashoff [1] gives an example of three experiments E 1 ,E 2 ,E 3 such that P e (E 1 ) e (E 2 ) e (E 3 ), but P e (E 1 ,E 3 ) e (E 1 ,E 2 ). Toussaint [2] exhibits binary valued experiments satisfying P e (E 1 ) e (E 2 ) e (E 3 ), such that P e (E 2 ,E 3 ) e (E 1 ,E 3 ) e (E 1 ,E 2 ). We shall give an example of binary valued experiments E 1 and E 2 such that P e (E 1 ) e (E 2 ), but P e (E 2 ,E 2 ') < P, e (E 1 ,E 2 ) < P, e (E 1 ,E 1 '). Thus if one observation is allowed, E 1 is the best experiment. If two observations are allowed, then two independent copies of the ''worst'' experiment E 2 are preferred. This is true despite the conditional independence of the observations.

Keywords

Computer scienceArtificial intelligenceAlgorithm

Affiliated Institutions

Stanford University US

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Publication Info

Year: 1974
Type: article
Volume: SMC-4
Issue: 1
Pages: 116-117
Citations: 250
Access: Closed

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APA Style

                            
                                    Thomas M. Cover
                                
                            (1974). 
                            The Best Two Independent Measurements Are Not the Two Best. 
                            IEEE Transactions on Systems Man and Cybernetics
                            , SMC-4
                            (1)
                            , 116-117.
                            https://doi.org/10.1109/tsmc.1974.5408535

Identifiers

DOI: 10.1109/tsmc.1974.5408535