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Mixtures : estimation and applications /

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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 compl...

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Bibliographic Details
Other Authors: Mengersen, Kerrie L., Robert, Christian P., 1961-, Titterington, D. M.
Format: eBook
Language:English
Published: Hoboken, N.J. : Wiley, 2011.
Subjects:
Mixture distributions (Probability theory)
Electronic books.
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245 0 0 |a Mixtures :  |b estimation and applications /  |c edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington. 
260 |a Hoboken, N.J. :  |b Wiley,  |c 2011. 
300 |a 1 online resource (xviii, 311 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references and index. 
505 0 0 |g Machine generated contents note:  |g 1.  |t The EM algorithm, variational approximations and expectation propagation for mixtures /  |r D. Michael Titterington --  |g 1.1.  |t Preamble --  |g 1.2.  |t The EM algorithm --  |g 1.2.1.  |t Introduction to the algorithm --  |g 1.2.2.  |t The E-step and the M-step for the mixing weights --  |g 1.2.3.  |t The M-step for mixtures of univariate Gaussian distributions --  |g 1.2.4.  |t M-step for mixtures of regular exponential family distributions formulated in terms of the natural parameters --  |g 1.2.5.  |t Application to other mixtures --  |g 1.2.6.  |t EM as a double expectation --  |g 1.3.  |t Variational approximations --  |g 1.3.1.  |t Preamble --  |g 1.3.2.  |t Introduction to variational approximations --  |g 1.3.3.  |t Application of variational Bayes to mixture problems --  |g 1.3.4.  |t Application to other mixture problems --  |g 1.3.5.  |t Recursive variational approximations --  |g 1.3.6.  |t Asymptotic results --  |g 1.4.  |t Expectation-propagation --  |g 1.4.1.  |t Introduction --  |g 1.4.2.  |t Overview of the recursive approach to be adopted. 
505 0 0 |g 1.4.3.  |t Finite Gaussian mixtures with an unknown mean parameter --  |g 1.4.4.  |t Mixture of two known distributions --  |g 1.4.5.  |t Discussion --  |t Acknowledgements --  |t References --  |g 2.  |t Online expectation maximisation /  |r Olivier Cappe --  |g 2.1.  |t Introduction --  |g 2.2.  |t Model and assumptions --  |g 2.3.  |t The EM algorithm and the limiting EM recursion --  |g 2.3.1.  |t The batch EM algorithm --  |g 2.3.2.  |t The limiting EM recursion --  |g 2.3.3.  |t Limitations of batch EM for long data records --  |g 2.4.  |t Online expectation maximisation --  |g 2.4.1.  |t The algorithm --  |g 2.4.2.  |t Convergence properties --  |g 2.4.3.  |t Application to finite mixtures --  |g 2.4.4.  |t Use for batch maximum-likelihood estimation --  |g 2.5.  |t Discussion --  |t References --  |g 3.  |t The limiting distribution of the EM test of the order of a finite mixture /  |r Pengfei Li --  |g 3.1.  |t Introduction --  |g 3.2.  |t The method and theory of the EM test --  |g 3.2.1.  |t The definition of the EM test statistic --  |g 3.2.2.  |t The limiting distribution of the EM test statistic --  |g 3.3.  |t Proofs. 
505 0 0 |g 3.4.  |t Discussion --  |t References --  |g 4.  |t Comparing Wald and likelihood regions applied to locally identifiable mixture models /  |r Bruce G. Lindsay --  |g 4.1.  |t Introduction --  |g 4.2.  |t Background on likelihood confidence regions --  |g 4.2.1.  |t Likelihood regions --  |g 4.2.2.  |t Profile likelihood regions --  |g 4.2.3.  |t Alternative methods --  |g 4.3.  |t Background on simulation and visualisation of the likelihood regions --  |g 4.3.1.  |t Modal simulation method --  |g 4.3.2.  |t Illustrative example --  |g 4.4.  |t Comparison between the likelihood regions and the Wald regions --  |g 4.4.1.  |t Volume/volume error of the confidence regions --  |g 4.4.2.  |t Differences in univariate intervals via worst case analysis --  |g 4.4.3.  |t Illustrative example (revisited) --  |g 4.5.  |t Application to a finite mixture model --  |g 4.5.1.  |t Nonidentifiabilities and likelihood regions for the mixture parameters --  |g 4.5.2.  |t Mixture likelihood region simulation and visualisation --  |g 4.5.3.  |t Adequacy of using the Wald confidence region. 
505 0 0 |g 4.6.  |t Data analysis --  |g 4.7.  |t Discussion --  |t References --  |g 5.  |t Mixture of experts modelling with social science applications /  |r Thomas Brendan Murphy --  |g 5.1.  |t Introduction --  |g 5.2.  |t Motivating examples --  |g 5.2.1.  |t Voting blocs --  |g 5.2.2.  |t Social and organisational structure --  |g 5.3.  |t Mixture models --  |g 5.4.  |t Mixture of experts models --  |g 5.5.  |t A mixture of experts model for ranked preference data --  |g 5.5.1.  |t Examining the clustering structure --  |g 5.6.  |t A mixture of experts latent position cluster model --  |g 5.7.  |t Discussion --  |t Acknowledgements --  |t References --  |g 6.  |t Modelling conditional densities using finite smooth mixtures /  |r Robert Kohn --  |g 6.1.  |t Introduction --  |g 6.2.  |t The model and prior --  |g 6.2.1.  |t Smooth mixtures --  |g 6.2.2.  |t The component models --  |g 6.2.3.  |t The prior --  |g 6.3.  |t Inference methodology --  |g 6.3.1.  |t The general MCMC scheme --  |g 6.3.2.  |t Updating & beta; and I using variable-dimension finite-step Newton proposals --  |g 6.3.3.  |t Model comparison --  |g 6.4.  |t Applications --  |g 6.4.1.  |t A small simulation study. 
505 0 0 |g 6.4.2.  |t LIDAR data --  |g 6.4.3.  |t Electricity expenditure data --  |g 6.5.  |t Conclusions --  |t Acknowledgements --  |t Appendix: Implementation details for the gamma and log-normal models --  |t References --  |g 7.  |t Nonparametric mixed membership modelling using the IBP compound Dirichlet process /  |r David M. Blei --  |g 7.1.  |t Introduction --  |g 7.2.  |t Mixed membership models --  |g 7.2.1.  |t Latent Dirichlet allocation --  |g 7.2.2.  |t Nonparametric mixed membership models --  |g 7.3.  |t Motivation --  |g 7.4.  |t Decorrelating prevalence and proportion --  |g 7.4.1.  |t Indian buffet process --  |g 7.4.2.  |t The IBP compound Dirichlet process --  |g 7.4.3.  |t An application of the ICD: focused topic models --  |g 7.4.4.  |t Inference --  |g 7.5.  |t Related models --  |g 7.6.  |t Empirical studies --  |g 7.7.  |t Discussion --  |t References --  |g 8.  |t Discovering nonbinary hierarchical structures with Bayesian rose trees /  |r Katherine A. Heller --  |g 8.1.  |t Introduction --  |g 8.2.  |t Prior work --  |g 8.3.  |t Rose trees, partitions and mixtures --  |g 8.4.  |t Avoiding needless cascades --  |g 8.4.1.  |t Cluster models. 
505 0 0 |g 8.5.  |t Greedy construction of Bayesian rose tree mixtures --  |g 8.5.1.  |t Prediction --  |g 8.5.2.  |t Hyperparameter optimisation --  |g 8.6.  |t Bayesian hierarchical clustering, Dirichlet process models and product partition models --  |g 8.6.1.  |t Mixture models and product partition models --  |g 8.6.2.  |t PCluster and Bayesian hierarchical clustering --  |g 8.7.  |t Results --  |g 8.7.1.  |t Optimality of tree structure --  |g 8.7.2.  |t Hierarchy likelihoods --  |g 8.7.3.  |t Partially observed data --  |g 8.7.4.  |t Psychological hierarchies --  |g 8.7.5.  |t Hierarchies of Gaussian process experts --  |g 8.8.  |t Discussion --  |t References --  |g 9.  |t Mixtures of factor analysers for the analysis of high-dimensional data /  |r Suren I. Rathnayake --  |g 9.1.  |t Introduction --  |g 9.2.  |t Single-factor analysis model --  |g 9.3.  |t Mixtures of factor analysers --  |g 9.4.  |t Mixtures of common factor analysers (MCFA) --  |g 9.5.  |t Some related approaches --  |g 9.6.  |t Fitting of factor-analytic models --  |g 9.7.  |t Choice of the number of factors q --  |g 9.8.  |t Example --  |g 9.9.  |t Low-dimensional plots via MCFA approach. 
505 0 0 |g 9.10.  |t Multivariate t-factor analysers --  |g 9.11.  |t Discussion --  |t Appendix --  |t References --  |g 10.  |t Dealing with label switching under model uncertainty /  |r Sylvia Fruhwirth-Schnatter --  |g 10.1.  |t Introduction --  |g 10.2.  |t Labelling through clustering in the point-process representation --  |g 10.2.1.  |t The point-process representation of a finite mixture model --  |g 10.2.2.  |t Identification through clustering in the point-process representation --  |g 10.3.  |t Identifying mixtures when the number of components is unknown --  |g 10.3.1.  |t The role of Dirichlet priors in overfitting mixtures --  |g 10.3.2.  |t The meaning of K for overfitting mixtures --  |g 10.3.3.  |t The point-process representation of overfitting mixtures --  |g 10.3.4.  |t Examples --  |g 10.4.  |t Overfitting heterogeneity of component-specific parameters --  |g 10.4.1.  |t Overfitting heterogeneity --  |g 10.4.2.  |t Using shrinkage priors on the component-specific location parameters --  |g 10.5.  |t Concluding remarks --  |t References --  |g 11.  |t Exact Bayesian analysis of mixtures /  |r Kerrie L. Mengersen. 
505 0 0 |g 11.1.  |t Introduction --  |g 11.2.  |t Formal derivation of the posterior distribution --  |g 11.2.1.  |t Locally conjugate priors --  |g 11.2.2.  |t True posterior distributions --  |g 11.2.3.  |t Poisson mixture --  |g 11.2.4.  |t Multinomial mixtures --  |g 11.2.5.  |t Normal mixtures --  |t References --  |g 12.  |t Manifold MCMC for mixtures /  |r Mark Girolami --  |g 12.1.  |t Introduction --  |g 12.2.  |t Markov chain Monte Carlo Methods --  |g 12.2.1.  |t Metropolis-Hastings --  |g 12.2.2.  |t Gibbs sampling --  |g 12.2.3.  |t Manifold Metropolis adjusted Langevin algorithm --  |g 12.2.4.  |t Manifold Hamiltonian Monte Carlo --  |g 12.3.  |t Finite Gaussian mixture models --  |g 12.3.1.  |t Gibbs sampler for mixtures of univariate Gaussians --  |g 12.3.2.  |t Manifold MCMC for mixtures of univariate Gaussians --  |g 12.3.3.  |t Metric tensor --  |g 12.3.4.  |t An illustrative example --  |g 12.4.  |t Experiments --  |g 12.5.  |t Discussion --  |t Acknowledgements --  |t Appendix --  |t References --  |g 13.  |t How many components in a finite mixture? /  |r Murray Aitkin --  |g 13.1.  |t Introduction --  |g 13.2.  |t The galaxy data --  |g 13.3.  |t The normal mixture model. 
505 0 0 |g 13.4.  |t Bayesian analyses --  |g 13.4.1.  |t Escobar and West --  |g 13.4.2.  |t Phillips and Smith --  |g 13.4.3.  |t Roeder and Wasserman --  |g 13.4.4.  |t Richardson and Green --  |g 13.4.5.  |t Stephens --  |g 13.5.  |t Posterior distributions for K (for flat prior) --  |g 13.6.  |t Conclusions from the Bayesian analyses --  |g 13.7.  |t Posterior distributions of the model deviances --  |g 13.8.  |t Asymptotic distributions --  |g 13.9.  |t Posterior deviances for the galaxy data --  |g 13.10.  |t Conclusions --  |t References --  |g 14.  |t Bayesian mixture models: a blood-free dissection of a sheep /  |r Graham E. Gardner --  |g 14.1.  |t Introduction --  |g 14.2.  |t Mixture models --  |g 14.2.1.  |t Hierarchical normal mixture --  |g 14.3.  |t Altering dimensions of the mixture model --  |g 14.4.  |t Bayesian mixture model incorporating spatial information --  |g 14.4.1.  |t Results --  |g 14.5.  |t Volume calculation --  |g 14.6.  |t Discussion --  |t References. 
588 0 |a Print version record. 
520 |a 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. 
650 0 |a Mixture distributions (Probability theory) 
655 0 |a Electronic books. 
700 1 |a Mengersen, Kerrie L.  |1 https://id.oclc.org/worldcat/entity/E39PBJwhFc93VthFcty9KYdvpP 
700 1 |a Robert, Christian P.,  |d 1961-  |1 https://id.oclc.org/worldcat/entity/E39PBJvxtCGQCFTQpWgvtWJ7HC 
700 1 |a Titterington, D. M.  |1 https://id.oclc.org/worldcat/entity/E39PCjBcrcRpGjpjpkkcR6X7jK 
758 |i has work:  |a Mixtures (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGP84cPpbmfwjmYjg9RYRq  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |t Mixtures.  |d Hoboken, N.J. : Wiley, 2011  |z 9781119993896  |w (DLC) 2010053469 
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