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Mixtures : estimation and applications /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mixture distributions (Probability theory) | |
| 650 | 6 | |a Distribution composée (Théorie des probabilités) | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Mixture distributions (Probability theory) |2 fast | |
| 700 | 1 | |a Mengersen, Kerrie L. | |
| 700 | 1 | |a Robert, Christian P., |d 1961- |1 https://id.oclc.org/worldcat/entity/E39PBJvxtCGQCFTQpWgvtWJ7HC | |
| 700 | 1 | |a Titterington, D. M. | |
| 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 |w (OCoLC)698450396 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=693765 |z Texto completo |
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