Optimal Statistical Decisions
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RANDOM VARIABLES RANDOM VECTORS
SOME SPECIAL UNIVARIATE DISTRIBUTIONS
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assumed Assumption Bayes decision bounded called choose chosen computed consider continue cost decision problem defined definition degrees of freedom denote depends described discussion distribution with mean distribution with parameters equation estimate example Exercise exists expected expected gain experiment final finite fixed following relation function further Furthermore given Hence independent inequality integral interval least Lemma loss function mean multivariate normal distribution object observations observed values obtained optimal procedure parameter positive possible posterior distribution precision matrix preferences presented prior distribution probability probability distribution Proof properties Prove random sample random variable random vector result reward satisfied seen selected sequence Show simple space specified stage statistical statistician stopping rule subset sufficient Suppose taken terminated Theorem tion units unknown variance vector