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Coherence and consonance are the two important concepts to ensure consistent conclusions drawn from multiple tests. Unlike coherence, consonance of a multiple testing procedure (MTP) has not yet received much attention. Although most of the MTPs used in practice are consonant, cases still exist that dissonant tests have to be used due to their unique advantages, for example, the likelihood ratio tests...
Around 1970, the author proposed a general theoretical approach to multiple decision problems (MDPs) of which multiple comparison problems (MCPs) are special cases. Suppose that a sample space is given together with a set of probability distributions defined over ${\cal X}$. Let a finite partition of the parameter space ...
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