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 xvii
... Conditional Heteroscedasticity .375 12.5.1 Motivating Example .375 12.5.2 Capturing Features of Financial Time Series Through Markov Switching Models .377 12.5.3 Switching ARCH Models 378 12.5.4 Statistical Inference for Switching ARCH ...
... Conditional Heteroscedasticity .375 12.5.1 Motivating Example .375 12.5.2 Capturing Features of Financial Time Series Through Markov Switching Models .377 12.5.3 Switching ARCH Models 378 12.5.4 Statistical Inference for Switching ARCH ...
Page 12
... conditional on the whole sequence of indicators S = ( S1 , ... , SN ) : = N N p ( y | S , v ) = [ [ p ( yi | Si , v ) = [ [ p ( yi | 0s ; ) . i = 1 i = 1 ( 1.23 ) A second layer of the model specifies the joint distribution p ( S ) of ...
... conditional on the whole sequence of indicators S = ( S1 , ... , SN ) : = N N p ( y | S , v ) = [ [ p ( yi | Si , v ) = [ [ p ( yi | 0s ; ) . i = 1 i = 1 ( 1.23 ) A second layer of the model specifies the joint distribution p ( S ) of ...
Page 26
... conditional probability Pr ( S ; = k | yi , v ) of the event { S1 = k } , having observed the event { Y = y ; } . Bayes ' rule shows how to compute this probability for each k = 1 , ... , K for observations from a discrete mixture ...
... conditional probability Pr ( S ; = k | yi , v ) of the event { S1 = k } , having observed the event { Y = y ; } . Bayes ' rule shows how to compute this probability for each k = 1 , ... , K for observations from a discrete mixture ...
Page 51
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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