Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions
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Misclassifications, or noises, in the sampling stage of a Bayesian scheme can seriously affect the values of decision criteria such as the Bayes Risk and the Expected Value of Sample Information. This problem does not seem to be much addressed in the existing literature. In this article, using an approach based on hypergeometric functions and numerical computation, we study the effects of these noises under the two most important loss functions: the quadratic and the absolute value. A numerical example illustrates these effects in a representative case, using both loss functions, and provides additional insights into the general problem.
Keywords and PhrasesNoises Decision Beta distribution Square error loss Bayes risk Expected Value of Sample Information Hypergeometric functions Picard’s Theorem
AMS Classification62C10 62N10
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