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Handbook of Mixture Analysis [[electronic resource] /] / edited by Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert
| Handbook of Mixture Analysis [[electronic resource] /] / edited by Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert |
| Pubbl/distr/stampa | Milton, : Chapman and Hall/CRC, 2018 |
| Descrizione fisica | 1 online resource (522 pages) |
| Disciplina | 519.24 |
| Altri autori (Persone) |
Frühwirth-SchnatterSylvia <1959->
CeleuxGilles RobertChristian P. <1961-> |
| Collana | Chapman & Hall/CRC handbooks of modern statistical methods |
| Soggetto topico |
Mixture distributions (Probability theory)
Distribution (Probability theory) |
| ISBN |
0-429-50886-7
0-429-50824-7 0-429-05591-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Editors; Contributors; List of Symbols; I: Foundations and Methods; 1: Introduction to Finite Mixtures; 1.1 Introduction and Motivation; 1.1.1 Basic formulation; 1.1.2 Likelihood; 1.1.3 Latent allocation variables; 1.1.4 A little history; 1.2 Generalizations; 1.2.1 Infinite mixtures; 1.2.2 Continuous mixtures; 1.2.3 Finite mixtures with nonparametric components; 1.2.4 Covariates and mixtures of experts; 1.2.5 Hidden Markov models; 1.2.6 Spatial mixtures; 1.3 Some Technical Concerns; 1.3.1 Identifiability
1.3.2 Label switching1.4 Inference; 1.4.1 Frequentist inference, and the role of EM; 1.4.2 Bayesian inference, and the role of MCMC; 1.4.3 Variable number of components; 1.4.4 Modes versus components; 1.4.5 Clustering and classification; 1.5 Concluding Remarks; Bibliography; 2: EM Methods for Finite Mixtures; 2.1 Introduction; 2.2 The EM Algorithm; 2.2.1 Description of EM for finite mixtures; 2.2.2 EM as an alternating-maximization algorithm; 2.3 Convergence and Behavior of EM; 2.4 Cousin Algorithms of EM; 2.4.1 Stochastic versions of the EM algorithm; 2.4.2 The Classification EM algorithm 2.5 Accelerating the EM Algorithm2.6 Initializing the EM Algorithm; 2.6.1 Random initialization; 2.6.2 Hierarchical initialization; 2.6.3 Recursive initialization; 2.7 Avoiding Spurious Local Maximizers; 2.8 Concluding Remarks; Bibliography; 3: An Expansive View of EM Algorithms; 3.1 Introduction; 3.2 The Product-of-Sums Formulation; 3.2.1 Iterative algorithms and the ascent property; 3.2.2 Creating a minorizing surrogate function; 3.3 Likelihood as a Product of Sums; 3.4 Non-standard Examples of EM Algorithms; 3.4.1 Modes of a density; 3.4.2 Gradient maxima; 3.4.3 Two-step EM 3.5 Stopping Rules for EM Algorithms3.6 Concluding Remarks; Bibliography; 4: Bayesian Mixture Models: Theory and Methods; 4.1 Introduction; 4.2 Bayesian Mixtures: From Priors to Posteriors; 4.2.1 Models and representations; 4.2.2 Impact of the prior distribution; 4.2.2.1 Conjugate priors; 4.2.2.2 Improper and non-informative priors; 4.2.2.3 Data-dependent priors; 4.2.2.4 Priors for overfitted mixtures; 4.3 Asymptotic Properties of the Posterior Distribution in the Finite Case; 4.3.1 Posterior concentration around the marginal density; 4.3.2 Recovering the parameters in the well-behaved case 4.3.3 Boundary parameters: overfitted mixtures4.3.4 Asymptotic behaviour of posterior estimates of the number of components; 4.4 Concluding Remarks; Bibliography; 5: Computational Solutions for Bayesian Inference in Mixture Models; 5.1 Introduction; 5.2 Algorithms for Posterior Sampling; 5.2.1 A computational problem? Which computational problem?; 5.2.2 Gibbs sampling; 5.2.3 Metropolis-Hastings schemes; 5.2.4 Reversible jump MCMC; 5.2.5 Sequential Monte Carlo; 5.2.6 Nested sampling; 5.3 Bayesian Inference in the Model-Based Clustering Context; 5.4 Simulation Studies |
| Record Nr. | UNINA-9910838292903321 |
| Milton, : Chapman and Hall/CRC, 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
| Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington |
| Pubbl/distr/stampa | Chichester, West Sussex, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina |
519.2/4
519.24 |
| Altri autori (Persone) |
MengersenKerrie L
RobertChristian P. <1961-> TitteringtonD. M |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Mixture distributions (Probability theory)
Distribution (Probability theory) |
| ISBN |
1-283-40559-8
9786613405593 1-119-99568-X 1-119-99567-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Mixtures: Estimation and Applications; Contents; Preface; Acknowledgements; List of contributors; 1 The EM algorithm, variational approximations and expectation propagation for mixtures; 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 approximations1.3.1 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; 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; 2.1 Introduction 2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion; 2.3.1 The batch EM algorithm; 2.3.2 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; 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 statistic3.3 Proofs; 3.4 Discussion; References; 4 Comparing Wald and likelihood regions applied to locally identifiable mixture models; 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 analysis4.4.3 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; 4.6 Data analysis; 4.7 Discussion; References; 5 Mixture of experts modelling with social science applications; 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 |
| Record Nr. | UNINA-9910130863803321 |
| Chichester, West Sussex, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
| Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington |
| Pubbl/distr/stampa | Chichester, West Sussex, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina |
519.2/4
519.24 |
| Altri autori (Persone) |
MengersenKerrie L
RobertChristian P. <1961-> TitteringtonD. M |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Mixture distributions (Probability theory)
Distribution (Probability theory) |
| ISBN |
1-283-40559-8
9786613405593 1-119-99568-X 1-119-99567-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Mixtures: Estimation and Applications; Contents; Preface; Acknowledgements; List of contributors; 1 The EM algorithm, variational approximations and expectation propagation for mixtures; 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 approximations1.3.1 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; 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; 2.1 Introduction 2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion; 2.3.1 The batch EM algorithm; 2.3.2 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; 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 statistic3.3 Proofs; 3.4 Discussion; References; 4 Comparing Wald and likelihood regions applied to locally identifiable mixture models; 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 analysis4.4.3 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; 4.6 Data analysis; 4.7 Discussion; References; 5 Mixture of experts modelling with social science applications; 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 |
| Record Nr. | UNINA-9910809170003321 |
| Chichester, West Sussex, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||