Evidence, information, and surprise

A numerical measure for “evidence” is defined in a probabilistic framework. The established mathematical concept of information or entropy (as defined in ergodic theory) can be obtained from this definition in a special case, although in general information is greater than evidence. In another, somewhat complementary, special case a numerical measure for “surprise” is derived from the definition of evidence. Some applications of the new concept of evidence are discussed, concerning statistics in general and the special kind of statistics performed by neurophysiologists, when they analyze the “response” of neurons, and perhaps by the neurons themselves.

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