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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Results 1-5 of 56
Page x
... Density 3.3.1 Invariance of the Posterior Distribution 3.3.2 Invariance of Seemingly Component- Specific Functionals ... Importance Sampling for the Allocations 84 3.7 Bayesian Inference for Finite Mixture Models Using Posterior Draws.
... Density 3.3.1 Invariance of the Posterior Distribution 3.3.2 Invariance of Seemingly Component- Specific Functionals ... Importance Sampling for the Allocations 84 3.7 Bayesian Inference for Finite Mixture Models Using Posterior Draws.
Page xii
... Importance Sampling ... 5.4.4 Reciprocal Importance Sampling 5.4.5 Harmonic Mean Estimator . 5.4.6 Bridge Sampling ... Density Ratios ... 146 147 . 148 150 154 . 159 159 5.5.1 The Posterior Density Ratio 5.5.2 159 6.1.2 Chib's Estimator ...
... Importance Sampling ... 5.4.4 Reciprocal Importance Sampling 5.4.5 Harmonic Mean Estimator . 5.4.6 Bridge Sampling ... Density Ratios ... 146 147 . 148 150 154 . 159 159 5.5.1 The Posterior Density Ratio 5.5.2 159 6.1.2 Chib's Estimator ...
Page 4
... density pk ( y ) is referred to as the component density . K is called the ... important example being finite mixtures of multivariate normal distributions ... densities with differ- ent means and different variances is the oldest known ...
... density pk ( y ) is referred to as the component density . K is called the ... important example being finite mixtures of multivariate normal distributions ... densities with differ- ent means and different variances is the oldest known ...
Page 6
... density . If hetero- geneity among the groups is large , the within - group ... important to understand how many modes exist in the mixture density . This ... densities have been derived recently in Ray and Lindsay ( 2005 ) , generalizing ...
... density . If hetero- geneity among the groups is large , the within - group ... important to understand how many modes exist in the mixture density . This ... densities have been derived recently in Ray and Lindsay ( 2005 ) , generalizing ...
Page 12
... important special case , discussed in much detail in Chap- ter 6 , is mixtures of normal distribution . Chapter 7 ... density estimation . Chapter 9 is devoted to a thorough discussion of finite mixture modeling of non - Gaussian data ...
... important special case , discussed in much detail in Chap- ter 6 , is mixtures of normal distribution . Chapter 7 ... density estimation . Chapter 9 is devoted to a thorough discussion of finite mixture modeling of non - Gaussian data ...
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