Celeux G., Frühwirth-Schnatter S., Robert C.P. (eds.) Handbook of Mixture Analysis

Milton: hapman and Hall/CRC, 2018. — 522 p.Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.Half Title
Title Page
Copyright PageEditorsList of Symbols
Foundations and Methods
Introduction to Finite Mixtures
Introduction and Motivation
Basic formulation
Likelihood
Latent allocation variables
A little history
Generalizations
Infinite mixtures
Continuous mixtures
Finite mixtures with nonparametric components
Covariates and mixtures of experts
Hidden Markov models
Spatial mixtures
Some Technical Concerns
Identifiability Label switching Inference
Frequentist inference, and the role of EM
Bayesian inference, and the role of MCMC
Variable number of components
Modes versus components
Clustering and classification
Concluding RemarksEM Methods for Finite MixturesThe EM Algorithm
Description of EM for finite mixtures
EM as an alternating-maximization algorithm
Convergence and Behavior of EM
Cousin Algorithms of EM
Stochastic versions of the EM algorithm
The Classification EM algorithm Accelerating the EM Algorithm Initializing the EM Algorithm
Random initialization
Hierarchical initialization
Recursive initialization
Avoiding Spurious Local Maximizers
Concluding RemarksAn Expansive View of EM AlgorithmsThe Product-of-Sums Formulation
Iterative algorithms and the ascent property
Creating a minorizing surrogate function
Likelihood as a Product of Sums
Non-standard Examples of EM Algorithms
Modes of a density
Gradient MAXIMA
Two-step EM Stopping Rules for EM Algorithms Concluding RemarksBayesian Mixture Models: Theory and MethodsBayesian Mixtures: From Priors to Posteriors
Models and representations
Impact of the prior distribution
Conjugate priors
Improper and non-informative priors
Data-dependent priors
Priors for overfitted mixtures
Asymptotic Properties of the Posterior Distribution in the Finite Case
Posterior concentration around the marginal density
Recovering the parameters in the well-behaved case Boundary parameters: overfitted mixtures Asymptotic behaviour of posterior estimates of the number of components
Concluding RemarksComputational Solutions for Bayesian Inference in Mixture ModelsAlgorithms for Posterior Sampling
A computational problem? Which computational problem?
Gibbs sampling
Metropolis-Hastings schemes
Reversible jump MCMC
Sequential Monte Carlo
Nested sampling
Bayesian Inference in the Model-Based Clustering Context
Simulation Studies