## Information theory and decision making |

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### Contents

Introduction | 1 |

KullbackLeibler information and testing | 36 |

Statistical experiments and information | 59 |

5 other sections not shown

### Common terms and phrases

A(uvy accepts HQ amount of information assume asymptotically Bayes decision Bayes r.t. Bayes risk Bayes test binomial densities binomial experiment channel Chernoff information number common input space composite hypotheses concave function concave uncertainty function condition conditional entropy consider convex convex functions corollary to theorem decision problem denote densities f density function dichotomous experiments equality equation equivalent Example exists exponential family Figure finite experiments Fisher information fixed fl(x fQ(x Hence hypothesis H independent inequality Lebesgue measure Lemma likelihood matrix maximized measurable space measure minimax non-negative observations obtain optimal design output space parameters posterior probabilities prior distribution prior knowledge priori probability probability distribution probability spaces prove random variables respectively risk function RX(C Sakaguchi sampling as long sampling rule satisfies sequential design stoch stochastic stochastic matrix strategy sufficient statistic Suppose T(xjy theorem 2.1 vector Wald sequential weighted average yield