Screen LibraryMixtures 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...
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| Group Author: | ; ; |
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| Published: |
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| Literature type: | Electronic eBook |
| Language: | English |
| Series: |
Wiley series in probability and statistics
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| Subjects: | |
| Online Access: |
http://onlinelibrary.wiley.com/book/10.1002/9781119995678 |
| Summary: |
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. |
| Carrier Form: | 1 online resource (xviii, 311 p.) : ill. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: |
9781119995678 (electronic bk.) 1119995671 (electronic bk.) 9781119995685 (electronic bk.) 111999568X (electronic bk.) |
| Access: | Due to publisher license, access is restricted to authorised GRAIL clients only. Please contact GRAIL staff. |
| Index Number: | QA273 |
| CLC: | O211.3 |
| Contents: |
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 -- 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 / 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 -- The limiting distribution of the EM test of the order of a finite mixture / The method and theory of the EM test -- The definition of the EM test statistic -- The limiting distribution of the EM test statistic -- Proofs Comparing Wald and likelihood regions applied to locally identifiable mixture models / 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 -- Mixture of experts modelling with social science applications / 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 -- Modelling conditional densities using finite smooth mixtures / The model and prior -- Smooth mixtures -- The component models -- The prior -- Inference methodology -- The general MCMC scheme -- Updating β and I using variable-dimension finite-step Newton proposals -- Model comparison -- Applications -- A small simulation study LIDAR data -- Electricity expenditure data -- Conclusions -- Appendix: Implementation details for the gamma and log-normal models -- Nonparametric mixed membership modelling using the IBP compound Dirichlet process / 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 -- Discovering nonbinary hierarchical structures with Bayesian rose trees / 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 -- Mixtures of factor analysers for the analysis of high-dimensional data / 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 -- Appendix -- Dealing with label switching under model uncertainty / 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 -- Exact Bayesian analysis of mixtures / Formal derivation of the posterior distribution -- Locally conjugate priors -- True posterior distributions -- Poisson mixture -- Multinomial mixtures -- Normal mixtures -- Manifold MCMC for mixtures / 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 -- How many components in a finite mixture? / 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 -- Bayesian mixture models: a blood-free dissection of a sheep / Hierarchical normal mixture -- Altering dimensions of the mixture model -- Bayesian mixture model incorporating spatial information -- Volume calculation -- References. |