Finite Mixture and Markov Switching Models

Author: Sylvia Frühwirth-Schnatter

Publisher: Springer Science & Business Media

ISBN: 0387357688

Category: Mathematics

Page: 494

View: 7098

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 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.

Handbook of Mixture Analysis

Author: Sylvia Fruhwirth-Schnatter,Christian P. Robert,Gilles Celeux

Publisher: Chapman & Hall/CRC

ISBN: 9781498763813


Page: 624

View: 5201

Mixture analysis is very active research topic in statistics and machine learning. It is a good timing for a Handbook to present a broad overview of the methods and applications, suitable for graduate students and young researchers new to the field. This Handbook is divided into two main parts; the first part covers all the methods, with illustrative examples and guidance on computing where appropriate; and the second part includes some more advanced methodological topics, and a series of case studies presenting applications of mixture analysis in a number of fields, including genomics, medicine, economics, finance and more.


Estimation and Applications

Author: Kerrie L. Mengersen,Christian Robert,Mike Titterington

Publisher: John Wiley & Sons

ISBN: 1119998441

Category: Mathematics

Page: 330

View: 6128

This book uses the EM (expectation maximization) algorithm tosimultaneously estimate the missing data and unknown parameter(s)associated with a data set. The parameters describe the componentdistributions of the mixture; the distributions may be continuousor discrete. The editors provide a complete account of the applications,mathematical structure and statistical analysis of finite mixturedistributions along with MCMC computational methods, together witha range of detailed discussions covering the applications of themethods and features chapters from the leading experts on thesubject. The applications are drawn from scientific discipline,including biostatistics, computer science, ecology and finance.This area of statistics is important to a range of disciplines, andits methodology attracts interest from researchers in the fields inwhich it can be applied.

Finite Mixture Models

Author: Geoffrey McLachlan,David Peel

Publisher: John Wiley & Sons

ISBN: 047165406X

Category: Mathematics

Page: 419

View: 5263

An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts. Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and pattern recognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

Medical Applications of Finite Mixture Models

Author: Peter Schlattmann

Publisher: Springer Science & Business Media

ISBN: 3540686517

Category: Medical

Page: 246

View: 556

Patients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the “average” patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author’s point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods.

Time Series

Modeling, Computation, and Inference

Author: Raquel Prado,Mike West

Publisher: CRC Press

ISBN: 1439882754

Category: Mathematics

Page: 368

View: 7290

Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers. The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB® code, and other material are available on the authors’ websites. Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.

Handbook of Research Methods and Applications in Empirical Finance

Author: Adrian R. Bell,Chris Brooks,Marcel Prokopczuk

Publisher: Edward Elgar Publishing

ISBN: 0857936093

Category: Business & Economics

Page: 504

View: 9633

This impressive Handbook presents the quantitative techniques that are commonly employed in empirical finance research together with real-world, state-of-the-art research examples. Written by international experts in their field, the unique approach describes a question or issue in finance and then demonstrates the methodologies that may be used to solve it. All of the techniques described are used to address real problems rather than being presented for their own sake, and the areas of application have been carefully selected so that a broad range of methodological approaches can be covered. The Handbook is aimed primarily at doctoral researchers and academics who are engaged in conducting original empirical research in finance. In addition, the book will be useful to researchers in the financial markets and also advanced Masters-level students who are writing dissertations.

Inference in Hidden Markov Models

Author: Olivier Cappé,Eric Moulines,Tobias Ryden

Publisher: Springer Science & Business Media

ISBN: 0387289828

Category: Mathematics

Page: 653

View: 6050

This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.

Advances in Data Analysis, Data Handling and Business Intelligence

Proceedings of the 32nd Annual Conference of the Gesellschaft für Klassifikation e.V., Joint Conference with the British Classification Society (BCS) and the Dutch/Flemish Classification Society (VOC), Helmut-Schmidt-University, Hamburg, July 16-18, 2008

Author: Andreas Fink,Berthold Lausen,Wilfried Seidel,Alfred Ultsch

Publisher: Springer Science & Business Media

ISBN: 9783642010446

Category: Computers

Page: 695

View: 7329

Data Analysis, Data Handling and Business Intelligence are research areas at the intersection of computer science, artificial intelligence, mathematics, and statistics. They cover general methods and techniques that can be applied to a vast set of applications such as in marketing, finance, economics, engineering, linguistics, archaeology, musicology, medical science, and biology. This volume contains the revised versions of selected papers presented during the 32nd Annual Conference of the German Classification Society (Gesellschaft für Klassifikation, GfKl). The conference, which was organized in cooperation with the British Classification Society (BCS) and the Dutch/Flemish Classification Society (VOC), was hosted by Helmut-Schmidt-University, Hamburg, Germany, in July 2008.

Recent Advances in Linear Models and Related Areas

Essays in Honour of Helge Toutenburg

Author: Shalabh,Christian Heumann

Publisher: Springer Science & Business Media

ISBN: 3790820644

Category: Mathematics

Page: 445

View: 5783

This collection contains invited papers by distinguished statisticians to honour and acknowledge the contributions of Professor Dr. Dr. Helge Toutenburg to Statistics on the occasion of his sixty-?fth birthday. These papers present the most recent developments in the area of the linear model and its related topics. Helge Toutenburg is an established statistician and currently a Professor in the Department of Statistics at the University of Munich (Germany) and Guest Professor at the University of Basel (Switzerland). He studied Mathematics in his early years at Berlin and specialized in Statistics. Later he completed his dissertation (Dr. rer. nat. ) in 1969 on optimal prediction procedures at the University of Berlin and completed the post-doctoral thesis in 1989 at the University of Dortmund on the topic of mean squared error superiority. He taught at the Universities of Berlin, Dortmund and Regensburg before joining the University of Munich in 1991. He has various areas of interest in which he has authored and co-authored over 130 research articles and 17 books. He has made pioneering contributions in several areas of statistics, including linear inference, linear models, regression analysis, quality engineering, Taguchi methods, analysis of variance, design of experiments, and statistics in medicine and dentistry.

Nonlinear Mixture Models

A Bayesian Approach

Author: Tatiana Tatarinova,Alan Schumitzky

Publisher: World Scientific

ISBN: 1783266279

Category: Mathematics

Page: 296

View: 1297

This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature. In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field. Contents:IntroductionMathematical Description of Nonlinear Mixture ModelsLabel Switching and TrappingTreatment of Mixture Models with an Unknown Number of ComponentsApplications of BDMCMC, KLMCMC, and RPSNonparametric MethodsBayesian Clustering Methods Readership: Graduate students and researchers in bioinformatics, mathematical biology, probability and statistics, mathematical modeling, and pharmacokinetics. Keywords:Nonlinear Mixture Models;Bayesian Analysis;Monte Carlo Markov Chain

The Methods of Distances in the Theory of Probability and Statistics

Author: Svetlozar T. Rachev,Lev Klebanov,Stoyan V. Stoyanov,Frank Fabozzi

Publisher: Springer Science & Business Media

ISBN: 1461448697

Category: Mathematics

Page: 619

View: 9888

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)

Amstat News

Author: N.A

Publisher: N.A


Category: Statistics

Page: N.A

View: 3352

Missing Data Methods

Time-Series Methods and Applications

Author: David M. Drukker

Publisher: Emerald Group Publishing

ISBN: 1780525273

Category: Business & Economics

Page: 290

View: 2809

Part of the "Advances in Econometrics" series, this title contains chapters covering topics such as: Missing-Data Imputation in Nonstationary Panel Data Models; Markov Switching Models in Empirical Finance; Bayesian Analysis of Multivariate Sample Selection Models Using Gaussian Copulas; and, Consistent Estimation and Orthogonality.

Bayesian Nonparametrics

Author: J.K. Ghosh,R.V. Ramamoorthi

Publisher: Springer Science & Business Media

ISBN: 0387226540

Category: Mathematics

Page: 308

View: 3123

This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Image Segmentation and Compression Using Hidden Markov Models

Author: Jia Li,Robert M. Gray

Publisher: Springer Science & Business Media

ISBN: 9780792378990

Category: Computers

Page: 141

View: 2507

In the current age of information technology, the issues of distributing and utilizing images efficiently and effectively are of substantial concern. Solutions to many of the problems arising from these issues are provided by techniques of image processing, among which segmentation and compression are topics of this book. Image segmentation is a process for dividing an image into its constituent parts. For block-based segmentation using statistical classification, an image is divided into blocks and a feature vector is formed for each block by grouping statistics of its pixel intensities. Conventional block-based segmentation algorithms classify each block separately, assuming independence of feature vectors. Image Segmentation and Compression Using Hidden Markov Models presents a new algorithm that models the statistical dependence among image blocks by two dimensional hidden Markov models (HMMs). Formulas for estimating the model according to the maximum likelihood criterion are derived from the EM algorithm. To segment an image, optimal classes are searched jointly for all the blocks by the maximum a posteriori (MAP) rule. The 2-D HMM is extended to multiresolution so that more context information is exploited in classification and fast progressive segmentation schemes can be formed naturally. The second issue addressed in the book is the design of joint compression and classification systems using the 2-D HMM and vector quantization. A classifier designed with the side goal of good compression often outperforms one aimed solely at classification because overfitting to training data is suppressed by vector quantization. Image Segmentation and Compression Using Hidden Markov Models is an essential reference source for researchers and engineers working in statistical signal processing or image processing, especially those who are interested in hidden Markov models. It is also of value to those working on statistical modeling.

Integrated Uncertainty in Knowledge Modelling and Decision Making

6th International Symposium, IUKM 2018, Hanoi, Vietnam, March 15-17, 2018, Proceedings

Author: Van-Nam Huynh,Masahiro Inuiguchi,Dang Hung Tran,Thierry Denoeux

Publisher: Springer

ISBN: 3319754297

Category: Computers

Page: 478

View: 8810

This book constitutes the refereed proceedings of the 6th International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, IUKM 2018, held in Hanoi, Vietnam, in March 2018.The 39 revised full papers presented in this book were carefully reviewed and selected from 76 initial submissions. The papers are organized in topical sections on uncertainty management and decision support; clustering and classification; machine learning applications; statistical methods; and econometric applications.