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Umfang: 1 online resource (xviii, 311 pages) : , illustrations

ISBN: 9781119995678 , 1119995671 , 9781119995685 , 111999568X

Inhalt: 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.

Anmerkung: The EM algorithm, variational approximations and expectation propagation for mixtures / , Preamble -- , The EM algorithm -- , Introduction to the algorithm -- , The E-step and the M-step for the mixing weights -- , The M-step for mixtures of univariate Gaussian distributions -- , M-step for mixtures of regular exponential family distributions formulated in terms of the natural parameters -- , Application to other mixtures -- , EM as a double expectation -- , Variational approximations -- , Preamble -- , Introduction to variational approximations -- , Application of variational Bayes to mixture problems -- , Application to other mixture problems -- , Recursive variational approximations -- , Asymptotic results -- , Expectation-propagation -- , Introduction -- , Overview of the recursive approach to be adopted. , Finite Gaussian mixtures with an unknown mean parameter -- , Mixture of two known distributions -- , Discussion -- , Acknowledgements -- , References -- , Online expectation maximisation / , Introduction -- , Model and assumptions -- , The EM algorithm and the limiting EM recursion -- , The batch EM algorithm -- , The limiting EM recursion -- , Limitations of batch EM for long data records -- , Online expectation maximisation -- , The algorithm -- , Convergence properties -- , Application to finite mixtures -- , Use for batch maximum-likelihood estimation -- , Discussion -- , References -- , The limiting distribution of the EM test of the order of a finite mixture / , Introduction -- , The method and theory of the EM test -- , The definition of the EM test statistic -- , The limiting distribution of the EM test statistic -- , Proofs. , Discussion -- , References -- , Comparing Wald and likelihood regions applied to locally identifiable mixture models / , Introduction -- , Background on likelihood confidence regions -- , Likelihood regions -- , Profile likelihood regions -- , Alternative methods -- , Background on simulation and visualisation of the likelihood regions -- , Modal simulation method -- , Illustrative example -- , Comparison between the likelihood regions and the Wald regions -- , Volume/volume error of the confidence regions -- , Differences in univariate intervals via worst case analysis -- , Illustrative example (revisited) -- , Application to a finite mixture model -- , Nonidentifiabilities and likelihood regions for the mixture parameters -- , Mixture likelihood region simulation and visualisation -- , Adequacy of using the Wald confidence region. , Data analysis -- , Discussion -- , References -- , Mixture of experts modelling with social science applications / , Introduction -- , Motivating examples -- , Voting blocs -- , Social and organisational structure -- , Mixture models -- , Mixture of experts models -- , A mixture of experts model for ranked preference data -- , Examining the clustering structure -- , A mixture of experts latent position cluster model -- , Discussion -- , Acknowledgements -- , References -- , Modelling conditional densities using finite smooth mixtures / , Introduction -- , The model and prior -- , Smooth mixtures -- , The component models -- , The prior -- , Inference methodology -- , The general MCMC scheme -- , Updating & beta; and I using variable-dimension finite-step Newton proposals -- , Model comparison -- , Applications -- , A small simulation study. , LIDAR data -- , Electricity expenditure data -- , Conclusions -- , Acknowledgements -- , Appendix: Implementation details for the gamma and log-normal models -- , References -- , Nonparametric mixed membership modelling using the IBP compound Dirichlet process / , Introduction -- , Mixed membership models -- , Latent Dirichlet allocation -- , Nonparametric mixed membership models -- , Motivation -- , Decorrelating prevalence and proportion -- , Indian buffet process -- , The IBP compound Dirichlet process -- , An application of the ICD: focused topic models -- , Inference -- , Related models -- , Empirical studies -- , Discussion -- , References -- , Discovering nonbinary hierarchical structures with Bayesian rose trees / , Introduction -- , Prior work -- , Rose trees, partitions and mixtures -- , Avoiding needless cascades -- , Cluster models. , Greedy construction of Bayesian rose tree mixtures -- , Prediction -- , Hyperparameter optimisation -- , Bayesian hierarchical clustering, Dirichlet process models and product partition models -- , Mixture models and product partition models -- , PCluster and Bayesian hierarchical clustering -- , Results -- , Optimality of tree structure -- , Hierarchy likelihoods -- , Partially observed data -- , Psychological hierarchies -- , Hierarchies of Gaussian process experts -- , Discussion -- , References -- , Mixtures of factor analysers for the analysis of high-dimensional data / , Introduction -- , Single-factor analysis model -- , Mixtures of factor analysers -- , Mixtures of common factor analysers (MCFA) -- , Some related approaches -- , Fitting of factor-analytic models -- , Choice of the number of factors q -- , Example -- , Low-dimensional plots via MCFA approach. , Multivariate t-factor analysers -- , Discussion -- , Appendix -- , References -- , Dealing with label switching under model uncertainty / , Introduction -- , Labelling through clustering in the point-process representation -- , The point-process representation of a finite mixture model -- , Identification through clustering in the point-process representation -- , Identifying mixtures when the number of components is unknown -- , The role of Dirichlet priors in overfitting mixtures -- , The meaning of K for overfitting mixtures -- , The point-process representation of overfitting mixtures -- , Examples -- , Overfitting heterogeneity of component-specific parameters -- , Overfitting heterogeneity -- , Using shrinkage priors on the component-specific location parameters -- , Concluding remarks -- , References -- , Exact Bayesian analysis of mixtures / , Introduction -- , Formal derivation of the posterior distribution -- , Locally conjugate priors -- , True posterior distributions -- , Poisson mixture -- , Multinomial mixtures -- , Normal mixtures -- , References -- , Manifold MCMC for mixtures / , Introduction -- , Markov chain Monte Carlo Methods -- , Metropolis-Hastings -- , Gibbs sampling -- , Manifold Metropolis adjusted Langevin algorithm -- , Manifold Hamiltonian Monte Carlo -- , Finite Gaussian mixture models -- , Gibbs sampler for mixtures of univariate Gaussians -- , Manifold MCMC for mixtures of univariate Gaussians -- , Metric tensor -- , An illustrative example -- , Experiments -- , Discussion -- , Acknowledgements -- , Appendix -- , References -- , How many components in a finite mixture? / , Introduction -- , The galaxy data -- , The normal mixture model. , Bayesian analyses -- , Escobar and West -- , Phillips and Smith -- , Roeder and Wasserman -- , Richardson and Green -- , Stephens -- , Posterior distributions for K (for flat prior) -- , Conclusions from the Bayesian analyses -- , Posterior distributions of the model deviances -- , Asymptotic distributions -- , Posterior deviances for the galaxy data -- , Conclusions -- , References -- , Bayesian mixture models: a blood-free dissection of a sheep / , Introduction -- , Mixture models -- , Hierarchical normal mixture -- , Altering dimensions of the mixture model -- , Bayesian mixture model incorporating spatial information -- , Results -- , Volume calculation -- , Discussion -- , References.

Weitere Ausg.: Print version: Mixtures. Hoboken, N.J. : Wiley, 2011 ISBN 9781119993896

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Electronic books. ; Electronic books. ; Electronic books.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119995678

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119995678

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119995678