LEADER 05472nam 2200661Ia 450 001 9910809170003321 005 20200520144314.0 010 $a1-283-40559-8 010 $a9786613405593 010 $a1-119-99568-X 010 $a1-119-99567-1 035 $a(CKB)3460000000003368 035 $a(EBL)693765 035 $a(SSID)ssj0000477753 035 $a(PQKBManifestationID)11913407 035 $a(PQKBTitleCode)TC0000477753 035 $a(PQKBWorkID)10512734 035 $a(PQKB)11287034 035 $a(MiAaPQ)EBC693765 035 $a(OCoLC)729731034 035 $a(PPN)197874525 035 $a(EXLCZ)993460000000003368 100 $a20110125d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMixtures $eestimation and applications /$fedited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington 210 $aChichester, West Sussex $cWiley$d2011 215 $a1 online resource (331 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a1-119-99389-X 320 $aIncludes bibliographical references and index. 327 $aMixtures: Estimation and Applications; Contents; Preface; Acknowledgements; List of contributors; 1 The EM algorithm, variational approximations and expectation propagation for mixtures; 1.1 Preamble; 1.2 The EM algorithm; 1.2.1 Introduction to the algorithm; 1.2.2 The E-step and the M-step for the mixing weights; 1.2.3 The M-step for mixtures of univariate Gaussian distributions; 1.2.4 M-step for mixtures of regular exponential family distributions formulated in terms of the natural parameters; 1.2.5 Application to other mixtures; 1.2.6 EM as a double expectation 327 $a1.3 Variational approximations1.3.1 Preamble; 1.3.2 Introduction to variational approximations; 1.3.3 Application of variational Bayes to mixture problems; 1.3.4 Application to other mixture problems; 1.3.5 Recursive variational approximations; 1.3.6 Asymptotic results; 1.4 Expectation-propagation; 1.4.1 Introduction; 1.4.2 Overview of the recursive approach to be adopted; 1.4.3 Finite Gaussian mixtures with an unknown mean parameter; 1.4.4 Mixture of two known distributions; 1.4.5 Discussion; Acknowledgements; References; 2 Online expectation maximisation; 2.1 Introduction 327 $a2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion; 2.3.1 The batch EM algorithm; 2.3.2 The limiting EM recursion; 2.3.3 Limitations of batch EM for long data records; 2.4 Online expectation maximisation; 2.4.1 The algorithm; 2.4.2 Convergence properties; 2.4.3 Application to finite mixtures; 2.4.4 Use for batch maximum-likelihood estimation; 2.5 Discussion; References; 3 The limiting distribution of the EM test of the order of a finite mixture; 3.1 Introduction; 3.2 The method and theory of the EM test; 3.2.1 The definition of the EM test statistic 327 $a3.2.2 The limiting distribution of the EM test statistic3.3 Proofs; 3.4 Discussion; References; 4 Comparing Wald and likelihood regions applied to locally identifiable mixture models; 4.1 Introduction; 4.2 Background on likelihood confidence regions; 4.2.1 Likelihood regions; 4.2.2 Profile likelihood regions; 4.2.3 Alternative methods; 4.3 Background on simulation and visualisation of the likelihood regions; 4.3.1 Modal simulation method; 4.3.2 Illustrative example; 4.4 Comparison between the likelihood regions and the Wald regions; 4.4.1 Volume/volume error of the confidence regions 327 $a4.4.2 Differences in univariate intervals via worst case analysis4.4.3 Illustrative example (revisited); 4.5 Application to a finite mixture model; 4.5.1 Nonidentifiabilities and likelihood regions for the mixture parameters; 4.5.2 Mixture likelihood region simulation and visualisation; 4.5.3 Adequacy of using the Wald confidence region; 4.6 Data analysis; 4.7 Discussion; References; 5 Mixture of experts modelling with social science applications; 5.1 Introduction; 5.2 Motivating examples; 5.2.1 Voting blocs; 5.2.2 Social and organisational structure; 5.3 Mixture models 327 $a5.4 Mixture of experts models 330 $aThis book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete. The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subje 410 0$aWiley series in probability and statistics. 606 $aMixture distributions (Probability theory) 606 $aDistribution (Probability theory) 615 0$aMixture distributions (Probability theory) 615 0$aDistribution (Probability theory) 676 $a519.2/4 701 $aMengersen$b Kerrie L$01654858 701 $aRobert$b Christian P.$f1961-$055943 701 $aTitterington$b D. M$0451121 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910809170003321 996 $aMixtures$94006943 997 $aUNINA LEADER 02835nam 22005175 450 001 9910255031503321 005 20251107103438.0 010 $a9783319558073 010 $a3319558072 024 7 $a10.1007/978-3-319-55807-3 035 $a(PPN)287996247 035 $a(CKB)4220000000000214 035 $a(DE-He213)978-3-319-55807-3 035 $a(MiAaPQ)EBC4855822 035 $a(Perlego)3496594 035 $a(MiAaPQ)EBC6242041 035 $a(EXLCZ)994220000000000214 100 $a20170506d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHuman Agency and Behavioral Economics $eNudging Fast and Slow /$fby Cass R. Sunstein 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Palgrave Macmillan,$d2017. 215 $a1 online resource (VII, 116 pages) 225 1 $aPalgrave Advances in Behavioral Economics,$x2662-3854 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1. Introduction: Agency and Control -- 2. People Like Nudges (Mostly) -- 3. People Prefer Educative Nudges (Kind Of) -- 4. How to Choose -- 5. ?What Route Would You Like Me To Take?? Paternalists Who Force Choices. 330 $aThis Palgrave Pivot offers comprehensive evidence about what people actually think of "nudge" policies designed to steer decision makers' choices in positive directions. The data reveal that people in diverse nations generally favor nudges by strong majorities, with a preference for educative efforts - such as calorie labels - that equip individuals to make the best decisions for their own lives. On the other hand, there are significant arguments for noneducational nudges - such as automatic enrollment in savings plans - as they allow people to devote their scarce time and attention to their most pressing concerns.    The decision to use either educative or noneducative nudges raises fundamental questions about human freedom in both theory and practice. Sunstein's findings and analysis offer lessons for those involved in law and policy who are choosing which method to support as the most effective way to encourage lifestyle changes. 410 0$aPalgrave Advances in Behavioral Economics,$x2662-3854 606 $aExperimental economics 606 $aFinance, Public 606 $aExperimental Economics 606 $aPublic Economics 615 0$aExperimental economics. 615 0$aFinance, Public. 615 14$aExperimental Economics. 615 24$aPublic Economics. 676 $a330.019 700 $aSunstein$b Cass R$0145553 906 $aBOOK 912 $a9910255031503321 996 $aHuman agency and behavioral economics$92105732 997 $aUNINA