LEADER 05463nam 2200697Ia 450 001 9910462657803321 005 20200520144314.0 010 $a1-280-77576-9 010 $a9786613686152 010 $a1-118-35975-5 035 $a(CKB)2670000000206484 035 $a(EBL)945113 035 $a(OCoLC)796383239 035 $a(SSID)ssj0000676781 035 $a(PQKBManifestationID)11415815 035 $a(PQKBTitleCode)TC0000676781 035 $a(PQKBWorkID)10683718 035 $a(PQKB)11778240 035 $a(MiAaPQ)EBC945113 035 $a(JP-MeL)3000065417 035 $a(CaSebORM)9781118359778 035 $a(PPN)164315020 035 $a(Au-PeEL)EBL945113 035 $a(CaPaEBR)ebr10570748 035 $a(CaONFJC)MIL368615 035 $a(EXLCZ)992670000000206484 100 $a20120228d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBayesian statistics$b[electronic resource] $ean introduction /$fPeter M. Lee 205 $a4th ed. 210 $aChichester, West Sussex ;$aHoboken, N.J. $d2012 215 $a1 online resource (488 p.) 300 $aDescription based upon print version of record. 311 $a1-118-35977-1 311 $a1-118-33257-1 320 $aIncludes bibliographical references and index. 327 $aBayesian Statistics; Contents; Preface; Preface to the First Edition; 1 Preliminaries; 1.1 Probability and Bayes' Theorem; 1.1.1 Notation; 1.1.2 Axioms for probability; 1.1.3 'Unconditional' probability; 1.1.4 Odds; 1.1.5 Independence; 1.1.6 Some simple consequences of the axioms; Bayes' Theorem; 1.2 Examples on Bayes' Theorem; 1.2.1 The Biology of Twins; 1.2.2 A political example; 1.2.3 A warning; 1.3 Random variables; 1.3.1 Discrete random variables; 1.3.2 The binomial distribution; 1.3.3 Continuous random variables; 1.3.4 The normal distribution; 1.3.5 Mixed random variables 327 $a1.4 Several random variables1.4.1 Two discrete random variables; 1.4.2 Two continuous random variables; 1.4.3 Bayes' Theorem for random variables; 1.4.4 Example; 1.4.5 One discrete variable and one continuous variable; 1.4.6 Independent random variables; 1.5 Means and variances; 1.5.1 Expectations; 1.5.2 The expectation of a sum and of a product; 1.5.3 Variance, precision and standard deviation; 1.5.4 Examples; 1.5.5 Variance of a sum; covariance and correlation; 1.5.6 Approximations to the mean and variance of a function of a random variable; 1.5.7 Conditional expectations and variances 327 $a1.5.8 Medians and modes1.6 Exercises on Chapter 1; 2 Bayesian inference for the normal distribution; 2.1 Nature of Bayesian inference; 2.1.1 Preliminary remarks; 2.1.2 Post is prior times likelihood; 2.1.3 Likelihood can be multiplied by any constant; 2.1.4 Sequential use of Bayes' Theorem; 2.1.5 The predictive distribution; 2.1.6 A warning; 2.2 Normal prior and likelihood; 2.2.1 Posterior from a normal prior and likelihood; 2.2.2 Example; 2.2.3 Predictive distribution; 2.2.4 The nature of the assumptions made; 2.3 Several normal observations with a normal prior; 2.3.1 Posterior distribution 327 $a2.3.2 Example2.3.3 Predictive distribution; 2.3.4 Robustness; 2.4 Dominant likelihoods; 2.4.1 Improper priors; 2.4.2 Approximation of proper priors by improper priors; 2.5 Locally uniform priors; 2.5.1 Bayes' postulate; 2.5.2 Data translated likelihoods; 2.5.3 Transformation of unknown parameters; 2.6 Highest density regions; 2.6.1 Need for summaries of posterior information; 2.6.2 Relation to classical statistics; 2.7 Normal variance; 2.7.1 A suitable prior for the normal variance; 2.7.2 Reference prior for the normal variance; 2.8 HDRs for the normal variance 327 $a2.8.1 What distribution should we be considering?2.8.2 Example; 2.9 The role of sufficiency; 2.9.1 Definition of sufficiency; 2.9.2 Neyman's factorization theorem; 2.9.3 Sufficiency principle; 2.9.4 Examples; 2.9.5 Order statistics and minimal sufficient statistics; 2.9.6 Examples on minimal sufficiency; 2.10 Conjugate prior distributions; 2.10.1 Definition and difficulties; 2.10.2 Examples; 2.10.3 Mixtures of conjugate densities; 2.10.4 Is your prior really conjugate?; 2.11 The exponential family; 2.11.1 Definition; 2.11.2 Examples; 2.11.3 Conjugate densities 327 $a2.11.4 Two-parameter exponential family 330 $aBayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develo 606 $aBayesian statistical decision theory 606 $aMathematical statistics 608 $aElectronic books. 615 0$aBayesian statistical decision theory. 615 0$aMathematical statistics. 676 $a519.5/42 700 $aLee$b Peter M$0102003 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462657803321 996 $aBayesian Statistics$9439908 997 $aUNINA