05521nam 2200673Ia 450 991013086380332120170925032533.01-283-40559-897866134055931-119-99568-X1-119-99567-1(CKB)3460000000003368(EBL)693765(SSID)ssj0000477753(PQKBManifestationID)11913407(PQKBTitleCode)TC0000477753(PQKBWorkID)10512734(PQKB)11287034(MiAaPQ)EBC693765(OCoLC)729731034(PPN)197874525(EXLCZ)99346000000000336820110125d2011 uy 0engur|n|---|||||txtccrMixtures[electronic resource] estimation and applications /edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael TitteringtonChichester, West Sussex Wiley20111 online resource (331 p.)Wiley series in probability and statisticsDescription based upon print version of record.1-119-99389-X Includes bibliographical references and index.Mixtures: 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 expectation1.3 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 Introduction2.2 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 statistic3.2.2 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 regions4.4.2 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 models5.4 Mixture of experts modelsThis 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 subjeWiley series in probability and statistics.Mixture distributions (Probability theory)Distribution (Probability theory)Mixture distributions (Probability theory)Distribution (Probability theory)519.2/4519.24Mengersen Kerrie L878005Robert Christian P.1961-55943Titterington D. M451121MiAaPQMiAaPQMiAaPQBOOK9910130863803321Mixtures1960212UNINA