TY  - BOOK
AU  - Mengersen,Kerrie L.
AU  - Robert,Christian P.
AU  - Titterington,D.M.
TI  - Mixtures: estimation and applications 
T2  - Wiley series in probability and statistics
SN  - 9781119995678
AV  - QA273.6 .M59 2011
U1  - 519.2/4 22
PY  - 2011///
CY  - Hoboken, N.J.
PB  - Wiley
KW  - Mixture distributions (Probability theory)
KW  - MATHEMATICS
KW  - Probability & Statistics
KW  - General
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references and index; Machine generated contents note; 1; The EM algorithm, variational approximations and expectation propagation for mixtures; D. Michael Titterington --; 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 --; 1.3; Variational approximations --; 1.3.1; 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; Olivier Cappe --; 2.1; Introduction --; 2.2; Model and assumptions --; 2.3; 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; Pengfei Li --; 3.1; Introduction --; 3.2; The method and theory of the EM test --; 3.2.1; The definition of the EM test statistic --; 3.2.2; The limiting distribution of the EM test statistic --; 3.3; Proofs; 3.4; Discussion --; References --; 4; Comparing Wald and likelihood regions applied to locally identifiable mixture models; Bruce G. Lindsay --; 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 --; 4.4.2; Differences in univariate intervals via worst case analysis --; 4.4.3; 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; Thomas Brendan Murphy --; 5.1; Introduction --; 5.2; Motivating examples --; 5.2.1; Voting blocs --; 5.2.2; Social and organisational structure --; 5.3; Mixture models --; 5.4; Mixture of experts models --; 5.5; A mixture of experts model for ranked preference data --; 5.5.1; Examining the clustering structure --; 5.6; A mixture of experts latent position cluster model --; 5.7; Discussion --; Acknowledgements --; References --; 6; Modelling conditional densities using finite smooth mixtures; Robert Kohn --; 6.1; Introduction --; 6.2; The model and prior --; 6.2.1; Smooth mixtures --; 6.2.2; The component models --; 6.2.3; The prior --; 6.3; Inference methodology --; 6.3.1; The general MCMC scheme --; 6.3.2; Updating & beta; and I using variable-dimension finite-step Newton proposals --; 6.3.3; Model comparison --; 6.4; Applications --; 6.4.1; A small simulation study; 6.4.2; LIDAR data --; 6.4.3; Electricity expenditure data --; 6.5; Conclusions --; Acknowledgements --; Appendix: Implementation details for the gamma and log-normal models --; References --; 7; Nonparametric mixed membership modelling using the IBP compound Dirichlet process; David M. Blei --; 7.1; Introduction --; 7.2; Mixed membership models --; 7.2.1; Latent Dirichlet allocation --; 7.2.2; Nonparametric mixed membership models --; 7.3; Motivation --; 7.4; Decorrelating prevalence and proportion --; 7.4.1; Indian buffet process --; 7.4.2; The IBP compound Dirichlet process --; 7.4.3; An application of the ICD: focused topic models --; 7.4.4; Inference --; 7.5; Related models --; 7.6; Empirical studies --; 7.7; Discussion --; References --; 8; Discovering nonbinary hierarchical structures with Bayesian rose trees; Katherine A. Heller --; 8.1; Introduction --; 8.2; Prior work --; 8.3; Rose trees, partitions and mixtures --; 8.4; Avoiding needless cascades --; 8.4.1; Cluster models; 8.5; Greedy construction of Bayesian rose tree mixtures --; 8.5.1; Prediction --; 8.5.2; Hyperparameter optimisation --; 8.6; Bayesian hierarchical clustering, Dirichlet process models and product partition models --; 8.6.1; Mixture models and product partition models --; 8.6.2; PCluster and Bayesian hierarchical clustering --; 8.7; Results --; 8.7.1; Optimality of tree structure --; 8.7.2; Hierarchy likelihoods --; 8.7.3; Partially observed data --; 8.7.4; Psychological hierarchies --; 8.7.5; Hierarchies of Gaussian process experts --; 8.8; Discussion --; References --; 9; Mixtures of factor analysers for the analysis of high-dimensional data; Suren I. Rathnayake --; 9.1; Introduction --; 9.2; Single-factor analysis model --; 9.3; Mixtures of factor analysers --; 9.4; Mixtures of common factor analysers (MCFA) --; 9.5; Some related approaches --; 9.6; Fitting of factor-analytic models --; 9.7; Choice of the number of factors q --; 9.8; Example --; 9.9; Low-dimensional plots via MCFA approach; 9.10; Multivariate t-factor analysers --; 9.11; Discussion --; Appendix --; References --; 10; Dealing with label switching under model uncertainty; Sylvia Fruhwirth-Schnatter --; 10.1; Introduction --; 10.2; Labelling through clustering in the point-process representation --; 10.2.1; The point-process representation of a finite mixture model --; 10.2.2; Identification through clustering in the point-process representation --; 10.3; Identifying mixtures when the number of components is unknown --; 10.3.1; The role of Dirichlet priors in overfitting mixtures --; 10.3.2; The meaning of K for overfitting mixtures --; 10.3.3; The point-process representation of overfitting mixtures --; 10.3.4; Examples --; 10.4; Overfitting heterogeneity of component-specific parameters --; 10.4.1; Overfitting heterogeneity --; 10.4.2; Using shrinkage priors on the component-specific location parameters --; 10.5; Concluding remarks --; References --; 11; Exact Bayesian analysis of mixtures; Kerrie L. Mengersen; 11.1; Introduction --; 11.2; Formal derivation of the posterior distribution --; 11.2.1; Locally conjugate priors --; 11.2.2; True posterior distributions --; 11.2.3; Poisson mixture --; 11.2.4; Multinomial mixtures --; 11.2.5; Normal mixtures --; References --; 12; Manifold MCMC for mixtures; Mark Girolami --; 12.1; Introduction --; 12.2; Markov chain Monte Carlo Methods --; 12.2.1; Metropolis-Hastings --; 12.2.2; Gibbs sampling --; 12.2.3; Manifold Metropolis adjusted Langevin algorithm --; 12.2.4; Manifold Hamiltonian Monte Carlo --; 12.3; Finite Gaussian mixture models --; 12.3.1; Gibbs sampler for mixtures of univariate Gaussians --; 12.3.2; Manifold MCMC for mixtures of univariate Gaussians --; 12.3.3; Metric tensor --; 12.3.4; An illustrative example --; 12.4; Experiments --; 12.5; Discussion --; Acknowledgements --; Appendix --; References --; 13; How many components in a finite mixture?; Murray Aitkin --; 13.1; Introduction --; 13.2; The galaxy data --; 13.3; The normal mixture model; 13.4; Bayesian analyses --; 13.4.1; Escobar and West --; 13.4.2; Phillips and Smith --; 13.4.3; Roeder and Wasserman --; 13.4.4; Richardson and Green --; 13.4.5; Stephens --; 13.5; Posterior distributions for K (for flat prior) --; 13.6; Conclusions from the Bayesian analyses --; 13.7; Posterior distributions of the model deviances --; 13.8; Asymptotic distributions --; 13.9; Posterior deviances for the galaxy data --; 13.10; Conclusions --; References --; 14; Bayesian mixture models: a blood-free dissection of a sheep; Graham E. Gardner --; 14.1; Introduction --; 14.2; Mixture models --; 14.2.1; Hierarchical normal mixture --; 14.3; Altering dimensions of the mixture model --; 14.4; Bayesian mixture model incorporating spatial information --; 14.4.1; Results --; 14.5; Volume calculation --; 14.6; Discussion --; References
N2  - This 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
UR  - https://doi.org/10.1002/9781119995678
ER  -