Frühwirth-Schnatter S. Finite Mixture and Markov Switching Models

Springer, 2006. — 492 p. — (Springer Series in Statistics). — ISBN: 978-0387-32909-3.The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modeling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.Finite Mixture ModelingFinite Mixture Distributions
Identifiability of a Finite Mixture Distribution
Statistical Inference for a Finite Mixture Model with
Known Number of ComponentsClassification for Known Component Parameters
Parameter Estimation for Known Allocation
Parameter Estimation When the Allocations Are Unknown
Practical Bayesian Inference for a Finite Mixture Model with Known Number of ComponentsChoosing the Prior for the Parameters of a Mixture Model
Some Properties of the Mixture Posterior Density
Classification Without Parameter Estimation
Parameter Estimation Through Data Augmentation and MCMC
Other Monte Carlo Methods Useful for Mixture Models
Bayesian Inference for Finite Mixture Models Using Posterior Draws
Statistical Inference for Finite Mixture Models Under Model Specification UncertaintyParameter Estimation Under Model
Informal Methods for Identifying the Number of Components
Likelihood-Based Methods
Bayesian Inference Under Model Uncertainty
Computational Tools for Bayesian Inference for Finite Mixtures Models Under Model Specification UncertaintyTrans-Dimensional Markov Chain Monte Carlo Methods
Marginal Likelihoods for Finite Mixture Models
Simulation-Based Approximations of the Marginal Likelihood
Approximations to the Marginal Likelihood Based on Density Ratios
Reversible Jump MCMC Versus Marginal Likelihoods?
Finite Mixture Models with Normal Components
Finite Mixtures of Normal Distributions
Bayesian Estimation of Univariate Mixtures of Normals
Bayesian Estimation of Multivariate Mixtures of Normals
Further Issues
Data Analysis Based on Finite Mixtures
Model-Based Clustering
Outlier Modeling
Robust Finite Mixtures Based on the Student-t Distribution
Further Issues
Finite Mixtures of Regression ModelsFinite Mixture of Multiple Regression Models
Statistical Inference for Finite Mixtures of Multiple Regression Models
Mixed-Effects Finite Mixtures of Regression Models
Finite Mixture Models for Repeated Measurements
Further Issues
Finite Mixture Models with Nonnormal Components
Finite Mixtures of Exponential Distributions
Finite Mixtures of Poisson Distributions
Finite Mixture Models for Binary and Categorical Data
Finite Mixtures of Generalized Linear Models
Finite Mixture Models for Multivariate Binary and Categorical Data
Further Issues
Finite Markov Mixture ModelingFinite Markov Mixture Distributions
Statistical Modeling Based on Finite Markov Mixture Distributions
Statistical Inference for Markov Switching ModelsState Estimation for Known Parameters
Parameter Estimation for Known States
Parameter Estimation When the States are Unknown
Bayesian Parameter Estimation with Known Number of States
Statistical Inference Under Model Specification Uncertainty
Modeling Overdispersion and Autocorrelation in Time Series of Count Data
Nonlinear Time Series Analysis Based on Markov Switching ModelsThe Markov Switching Autoregressive Model
Markov Switching Dynamic Regression Models
Prediction of Time Series Based on Markov Switching Models
Markov Switching Conditional Heteroscedasticity
Some Extensions
Switching State Space Models
State Space Modeling
Nonlinear Time Series Analysis Based on Switching State Space Models
Filtering for Switching Linear Gaussian State Space Models
Parameter Estimation for Switching State Space Models
Practical Bayesian Estimation Using MCMC
Further Issues
Illustrative Application to Modeling Exchange Rate DataSummary of Probability Distributions
Software