Finite Mixture and Markov Switching ModelsThe 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 modelling. 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. |
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Page viii
... filtering and the application of (switching) state space models in hydrology in 1984 and the wonderful hours we spent discussing our ideas en- couraged me to follow a scientific career. Sylvia Kaufmann drew my attention to Markov ...
... filtering and the application of (switching) state space models in hydrology in 1984 and the wonderful hours we spent discussing our ideas en- couraged me to follow a scientific career. Sylvia Kaufmann drew my attention to Markov ...
Page xvi
... Filtering for Special Cases . 323 11.2.4 Smoothing the States .. 324 11.2.5 Filtering and Smoothing for More General Models . . . . . 326 11.3 Parameter Estimation for Known States ... 327 11.3.1 The Complete - Data Likelihood Function ...
... Filtering for Special Cases . 323 11.2.4 Smoothing the States .. 324 11.2.5 Filtering and Smoothing for More General Models . . . . . 326 11.3 Parameter Estimation for Known States ... 327 11.3.1 The Complete - Data Likelihood Function ...
Page xviii
... Filtering for Switching Linear Gaussian State Space Models . . . 401 13.3.1 The Filtering Problem . 402 13.3.2 Bayesian Inference for a General Linear Regression Model ..... 402 13.3.3 Filtering for the Linear Gaussian State Space Model ...
... Filtering for Switching Linear Gaussian State Space Models . . . 401 13.3.1 The Filtering Problem . 402 13.3.2 Bayesian Inference for a General Linear Regression Model ..... 402 13.3.3 Filtering for the Linear Gaussian State Space Model ...
Page 188
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Page 238
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Contents
| 1 | |
| 5 | |
| 12 | |
| 25 | |
Practical Bayesian Inference for a Finite Mixture Model | 57 |
Finite Mixtures of Regression Models 241 | 99 |
Finite Mixture Models with Normal Components | 169 |
Data Analysis Based on Finite Mixtures | 203 |
Finite Mixture Models with Nonnormal Components | 277 |
Finite Markov Mixture Modeling 301 | 300 |
Statistical Inference for Markov Switching Models | 319 |
Switching State Space Models | 389 |
A Appendix | 431 |
References | 441 |
Index | 481 |
in Bayesian Analysis | 238 |
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Common terms and phrases
Algorithm allocations applied assumed asymptotic autocorrelation Bayes Bayes factor Bayesian estimation Bayesian inference bridge sampling Celeux Chib choosing classification clustering component parameters Computational conditional conjugate prior constraint covariance data augmentation defined discussed in Subsection EM algorithm finite mixture distribution finite mixture models Frühwirth-Schnatter Gibbs sampling heterogeneity hidden Markov chain identifiability importance density improper prior Kmax label switching likelihood function likelihood p(y marginal likelihood marginal posterior Markov chain Markov mixture Markov switching models MCMC draws Metropolis-Hastings algorithm mixture density mixture likelihood function mixture of Poisson mixtures of normals ML estimator multivariate mixtures normal distributions normal mixture number of components observations obtained outliers overfitting p(y MK parameter estimation permutation Poisson distributions posterior distribution posterior probability Pr(S Pr(St prior distribution Raftery regression models sampler simulation space models Statistical Synthetic Data Set tion univariate mixtures unknown variance weight distribution whereas