Mcmc Estimation Of Classical And Dynamic Switching And Mixture Models
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MCMC Estimation of Classical and Dynamic Switching and Mixture Models
In the present paper we discuss Bayesian estimation of a very general model class where the distribution of the observations is assumed to depend on a latent mixture or switching variable taking values in a discrete state space. This model class covers e.g. finite mixture modelling, Markov switching autoregressive modelling and dynamic linear models with switching. Joint Bayesian estimation of all latent variables, model parameters and parameters determining the probability law of the switching variable is carried out by a new Markov Chain Monte Carlo method called permutation sampling. Estimation of switching and mixture models is known to be faced with identifiability problems as switching and mixture are identifiable only up to permutations of the indices of the states. For a Bayesian analysis the posterior has to be constrained in such a way that identifiablity constraints are fulfilled. The permutation sampler is designed to sample efficiently from the constrained posterior, by first sampling from the unconstrained posterior - which often can be done in a convenient multimove manner - and then by applying a suitable permutation, if the identifiability constraint is violated. We present simple conditions on the prior which ensure that this method is a valid Markov Chain Monte Carlo method (that is invariance, irreducibility and aperiodicity hold). Three case studies are presented, including finite mixture modelling of fetal lamb data, Markov switching Autoregressive modelling of the U.S. quarterly real GDP data, and modelling the U .S./U.K. real exchange rate by a dynamic linear model with Markov switching heteroscedasticity. (author's abstract).
Handbook of Mixture Analysis
Author: Sylvia Fruhwirth-Schnatter
language: en
Publisher: CRC Press
Release Date: 2019-01-04
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.
Advances in Markov-Switching Models
Author: James D. Hamilton
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
This book is a collection of state-of-the-art papers on the properties of business cycles and financial analysis. The individual contributions cover new advances in Markov-switching models with applications to business cycle research and finance. The introduction surveys the existing methods and new results of the last decade. Individual chapters study features of the U. S. and European business cycles with particular focus on the role of monetary policy, oil shocks and co movements among key variables. The short-run versus long-run consequences of an economic recession are also discussed. Another area that is featured is an extensive analysis of currency crises and the possibility of bubbles or fads in stock prices. A concluding chapter offers useful new results on testing for this kind of regime-switching behaviour. Overall, the book provides a state-of-the-art over view of new directions in methods and results for estimation and inference based on the use of Markov-switching time-series analysis. A special feature of the book is that it includes an illustration of a wide range of applications based on a common methodology. It is expected that the theme of the book will be of particular interest to the macroeconomics readers as well as econometrics professionals, scholars and graduate students. We wish to express our gratitude to the authors for their strong contributions and the reviewers for their assistance and careful attention to detail in their reports.