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Variance Estimation For Bayesian Dynamic Linear Models
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Book Synopsis Variance Estimation for Bayesian Dynamic Linear Models by : Kostas Triantafyllopoulos
Download or read book Variance Estimation for Bayesian Dynamic Linear Models written by Kostas Triantafyllopoulos and published by LAP Lambert Academic Publishing. This book was released on 2010-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time series modelling and in particular multivariate time series have received considerable attention in the literature over the past 20 years. Time series data are met in almost all subject areas, such as in economics, engineering, medicine and genetics, to name but a few. One of the key problems of multivariate time series analysis is the estimation of the covariance matrix of the data, as this holds important information of the co-evolution and correlation of the component time series data of interest. The aim of this book is to provide an account of the recent developments on this subject area and subsequently to develop methodology for tackling the problem of variance estimation in time series. The book introduces the basic modelling framework for state space time series models and then it provides estimation algorithms, within the Bayesian paradigm, for several classes of models. The book is aimed at both masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers interested in time series methods.
Book Synopsis Bayesian Forecasting and Dynamic Models by : Mike West
Download or read book Bayesian Forecasting and Dynamic Models written by Mike West and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.
Book Synopsis Dynamic Linear Models with R by : Giovanni Petris
Download or read book Dynamic Linear Models with R written by Giovanni Petris and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used. A final chapter covers modern sequential Monte Carlo algorithms. The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.
Book Synopsis Linear Models by : Brenton R. Clarke
Download or read book Linear Models written by Brenton R. Clarke and published by John Wiley & Sons. This book was released on 2008-09-19 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful approach to the analysis of variance in the study of linear models Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. The author begins with a presentation of the classic fixed-effects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of least-squares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical two-way and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include: Vector space theory The theory of least squares estimation Gauss-Markov theorem Kronecker products Diagnostic and robust methods for linear models Likelihood approaches to estimation A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.
Book Synopsis Bayesian Analysis of Linear Models by : Broemeling
Download or read book Bayesian Analysis of Linear Models written by Broemeling and published by CRC Press. This book was released on 2017-11-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Bayesian statistics rapidly becoming accepted as a way to solve applied statisticalproblems, the need for a comprehensive, up-to-date source on the latest advances in thisfield has arisen.Presenting the basic theory of a large variety of linear models from a Bayesian viewpoint,Bayesian Analysis of Linear Models fills this need. Plus, this definitive volume containssomething traditional-a review of Bayesian techniques and methods of estimation, hypothesis,testing, and forecasting as applied to the standard populations ... somethinginnovative-a new approach to mixed models and models not generally studied by statisticianssuch as linear dynamic systems and changing parameter models ... and somethingpractical-clear graphs, eary-to-understand examples, end-of-chapter problems, numerousreferences, and a distribution appendix.Comprehensible, unique, and in-depth, Bayesian Analysis of Linear Models is the definitivemonograph for statisticians, econometricians, and engineers. In addition, this text isideal for students in graduate-level courses such as linear models, econometrics, andBayesian inference.
Book Synopsis Bayesian Analysis of Linear Models by : Lyle D. Broemeling
Download or read book Bayesian Analysis of Linear Models written by Lyle D. Broemeling and published by . This book was released on 1985 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Linear Models by : Dipak K. Dey
Download or read book Generalized Linear Models written by Dipak K. Dey and published by CRC Press. This book was released on 2000-05-25 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers
Book Synopsis Analysis of Variance for Random Models by : Hardeo Sahai
Download or read book Analysis of Variance for Random Models written by Hardeo Sahai and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: ANOVA models involving random effects have found widespread application to experimental design in varied fields such as biology, econometrics, and engineering. Volume I of this two-part work is a comprehensive presentation of methods and techniques for point estimation, interval estimation, and hypotheses tests for linear models involving random effects. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (non-orthogonal models). Accessible to readers with a modest mathematical and statistical background, the work will appeal to a broad audience of graduate students, researchers, and practitioners. It can be used as a graduate text or as a self-study reference.
Book Synopsis Bayesian Estimation and Experimental Design in Linear Regression Models by : Jürgen Pilz
Download or read book Bayesian Estimation and Experimental Design in Linear Regression Models written by Jürgen Pilz and published by . This book was released on 1991-07-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.
Book Synopsis Analysis of Variance for Random Models, Volume 2: Unbalanced Data by : Hardeo Sahai
Download or read book Analysis of Variance for Random Models, Volume 2: Unbalanced Data written by Hardeo Sahai and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs with a detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level. It also includes numerical examples to analyze data from a wide variety of disciplines as well as any worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example.
Book Synopsis Scalable Bayesian Inference for Generalized Multivariate Dynamic Linear Models by : Manan Saxena
Download or read book Scalable Bayesian Inference for Generalized Multivariate Dynamic Linear Models written by Manan Saxena and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Multivariate Dynamic Linear Models (GMDLMs) are a flexible class of multivariate time series models well-suited for non-Gaussian observations. They represent a special case within the more widely recognized multinomial logistic-normal (MLN) models. They are effective for analyzing sequence count data due to their ability to handle complex covariance structures and provide interpretability/control over the structure of the model. However, their current implementations are limited to small datasets, primarily because of computational inefficiency and increased variance in parameter estimates. Our work addresses the need for scalable Bayesian inference methods for these models. We develop an efficient method for obtaining a point estimate of our parameter by using the Kalman Filter and calculating closed-form gradients for our optimizer. Additionally, we provide uncertainty quantification of our parameter using Multinomial Dirichlet Bootstrap and refine these estimates further with Particle Refinement. We demonstrate that our inference scheme is considerably faster than STAN and provides a reliable approximation comparable to results obtained from MCMC.
Book Synopsis Cointegration and Long-Horizon Forecasting by : Mr.Peter F. Christoffersen
Download or read book Cointegration and Long-Horizon Forecasting written by Mr.Peter F. Christoffersen and published by International Monetary Fund. This book was released on 1997-05-01 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imposing cointegration on a forecasting system, if cointegration is present, is believed to improve long-horizon forecasts. Contrary to this belief, at long horizons nothing is lost by ignoring cointegration when the forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box-Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures—they fail to value the maintenance of cointegrating relationships among variables—and we suggest alternatives that explicitly do so.
Book Synopsis Dynamic Bayesian Models for Vector Time Series Analysis & Forecasting by :
Download or read book Dynamic Bayesian Models for Vector Time Series Analysis & Forecasting written by and published by . This book was released on 1989 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Bayesian Forecasting and Time Series Analysis by : Andy Pole
Download or read book Applied Bayesian Forecasting and Time Series Analysis written by Andy Pole and published by CRC Press. This book was released on 2018-10-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.
Book Synopsis The Variational Form of Bayes Estimators of Normal Variance in the Linear Models Case by : Alfredo J. Julian
Download or read book The Variational Form of Bayes Estimators of Normal Variance in the Linear Models Case written by Alfredo J. Julian and published by . This book was released on 1992 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä
Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Book Synopsis Recursive Estimation of Dynamic Linear Models by : R. D. Snyder
Download or read book Recursive Estimation of Dynamic Linear Models written by R. D. Snyder and published by . This book was released on 1984 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
