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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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111103s2011 njua ob 001 0 eng d |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119995678 |
| Qualifying information |
(electronic bk.) |
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1119995671 |
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(electronic bk.) |
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| International Standard Book Number |
9781119995685 |
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(electronic bk.) |
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111999568X |
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(electronic bk.) |
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9781119993896 |
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(cloth) |
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111999389X |
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(cloth) |
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(OCoLC)742798716 |
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(OCoLC)794326191 |
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(OCoLC)808669906 |
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(OCoLC)816882892 |
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(OCoLC)880752033 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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QA273.6 |
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.M59 2011 |
| 072 #7 - |
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MAT |
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029000 |
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bisacsh |
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519.2/4 |
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22 |
| 049 ## - |
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MAIN |
| 245 00 - TITLE STATEMENT |
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| Title |
Mixtures : |
| Remainder of title |
estimation and applications / |
| Statement of responsibility, etc |
edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 online resource (xviii, 311 pages) : |
| Other physical details |
illustrations. |
| 650 #0 - |
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| Topical term or geographic name as entry element |
Mixture distributions (Probability theory) |
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| Topical term or geographic name as entry element |
Mixture distributions (Probability theory) |
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| Topical term or geographic name as entry element |
MATHEMATICS |
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| Topical term or geographic name as entry element |
Mixture distributions (Probability theory) |
| 700 1# - |
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| Personal name |
Mengersen, Kerrie L. |
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| Personal name |
Robert, Christian P., |
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| Personal name |
Titterington, D. M. |
| 856 40 - |
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| Uniform Resource Identifier |
https://doi.org/10.1002/9781119995678 |
| 264 #1 - |
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Hoboken, N.J. : |
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Wiley, |
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2011. |
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text |
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txt |
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rdacontent |
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computer |
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online resource |
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Wiley series in probability and statistics |
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Includes bibliographical references and index. |
| 505 00 - |
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Machine generated contents note: |
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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. |
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| -- |
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. |
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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. |
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| -- |
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. |
|
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| -- |
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. |
| 588 0# - |
|---|
| -- |
Print version record. |
| 520 ## - |
|---|
| -- |
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. |
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Probability & Statistics |
| -- |
General. |
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bisacsh |
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fast |
| -- |
(OCoLC)fst01024154 |
| 655 #4 - |
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| -- |
Electronic books. |
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| -- |
1961- |
| 776 08 - |
|---|
| -- |
Print version: |
| -- |
Mixtures. |
| -- |
Hoboken, N.J. : Wiley, 2011 |
| -- |
9781119993896 |
| -- |
(DLC) 2010053469 |
| -- |
(OCoLC)698450396 |
| 830 #0 - |
|---|
| -- |
Wiley series in probability and statistics. |
| 856 40 - |
|---|
| -- |
Wiley Online Library |
| 994 ## - |
|---|
| -- |
92 |
| -- |
DG1 |
