Abstract
The most commonly used expression in Statistics is information; yet, we have no agreement on the definition or usage of this concept. However, in the particular situation where the problem is to predict a future value of a random variable X with a known probability distribution p(.), we all seem to agree that the information on the yet unobserved future value of X may be characterized by the function p(.) itself. And if we have another variable Y such that the conditional distribution p(.|Y) of X, given Y, is also known then, having observed Y, we can claim that the information on X has shifted from p(.) to p(.| Y). [To avoid a multiplicity of notations, we do not distinguish between a random variable X, an observed value of X and a typical point in the sample space of X.] If p(.|Y) is the same for all values of Y, then X is stochastically independent of Y. In this case Y is said to have no information on X. And we know how to prove then that X has no information on Y.
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© 1988 Springer-Verlag New York Inc.
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Ghosh, J.K. (1988). Ancillary Statistics, Pivotal Quantities and Confidence Statements. In: Ghosh, J.K. (eds) Statistical Information and Likelihood. Lecture Notes in Statistics, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3894-2_9
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DOI: https://doi.org/10.1007/978-1-4612-3894-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96751-6
Online ISBN: 978-1-4612-3894-2
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