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Bayesian Model Discrimination And Bayes Factors For Normal Linear State Space Models
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Book Synopsis State Space and Unobserved Component Models by : James Durbin
Download or read book State Space and Unobserved Component Models written by James Durbin and published by Cambridge University Press. This book was released on 2004-06-10 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of developments in the theory and application of state space modeling, first published in 2004.
Book Synopsis Bayesian Signal Processing by : James V. Candy
Download or read book Bayesian Signal Processing written by James V. Candy and published by John Wiley & Sons. This book was released on 2016-07-12 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the Bayesian approach to statistical signal processing for a variety of useful model sets This book aims to give readers a unified Bayesian treatment starting from the basics (Baye’s rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on “Sequential Bayesian Detection,” a new section on “Ensemble Kalman Filters” as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to “fill-in-the gaps” of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical “sanity testing” lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theory metrics and their application to PF designs is fully developed and applied. These expansions of the book have been updated to provide a more cohesive discussion of Bayesian processing with examples and applications enabling the comprehension of alternative approaches to solving estimation/detection problems. The second edition of Bayesian Signal Processing features: “Classical” Kalman filtering for linear, linearized, and nonlinear systems; “modern” unscented and ensemble Kalman filters: and the “next-generation” Bayesian particle filters Sequential Bayesian detection techniques incorporating model-based schemes for a variety of real-world problems Practical Bayesian processor designs including comprehensive methods of performance analysis ranging from simple sanity testing and ensemble techniques to sophisticated information metrics New case studies on adaptive particle filtering and sequential Bayesian detection are covered detailing more Bayesian approaches to applied problem solving MATLAB® notes at the end of each chapter help readers solve complex problems using readily available software commands and point out other software packages available Problem sets included to test readers’ knowledge and help them put their new skills into practice Bayesian Signal Processing, Second Edition is written for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.
Book Synopsis Kendall's Advanced Theory of Statistic 2B by : Anthony O'Hagan
Download or read book Kendall's Advanced Theory of Statistic 2B written by Anthony O'Hagan and published by John Wiley & Sons. This book was released on 2010-03-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kendall's Advanced Theory of Statistics and Kendall's Library of Statistics The development of modern statistical theory in the past fifty years is reflected in the history of the late Sir Maurice Kenfall's volumes The Advanced Theory of Statistics. The Advanced Theory began life as a two-volume work, and since its first appearance in 1943, has been an indispensable source for the core theory of classical statistics. With Bayesian Inference, the same high standard has been applied to this important and exciting new body of theory.
Book Synopsis Handbook of Mixture Analysis by : Sylvia Fruhwirth-Schnatter
Download or read book Handbook of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and published by CRC Press. This book was released on 2019-01-04 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Informative Hypotheses by : Herbert Hoijtink
Download or read book Informative Hypotheses written by Herbert Hoijtink and published by CRC Press. This book was released on 2011-10-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: When scientists formulate their theories, expectations, and hypotheses, they often use statements like: ``I expect mean A to be bigger than means B and C"; ``I expect that the relation between Y and both X1 and X2 is positive"; and ``I expect the relation between Y and X1 to be stronger than the relation between Y and X2". Stated otherwise, they formulate their expectations in terms of inequality constraints among the parameters in which they are interested, that is, they formulate Informative Hypotheses. There is currently a sound theoretical foundation for the evaluation of informative hypotheses using Bayes factors, p-values and the generalized order restricted information criterion. Furthermore, software that is often free is available to enable researchers to evaluate the informative hypotheses using their own data. The road is open to challenge the dominance of the null hypothesis for contemporary research in behavioral, social, and other sciences.
Book Synopsis Handbook of Mixture Analysis by : Sylvia Fruhwirth-Schnatter
Download or read book Handbook of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and published by CRC Press. This book was released on 2019-01-04 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Statistical Rethinking by : Richard McElreath
Download or read book Statistical Rethinking written by Richard McElreath and published by CRC Press. This book was released on 2018-01-03 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :
Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1999 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Book Synopsis Accelerating Monte Carlo methods for Bayesian inference in dynamical models by : Johan Dahlin
Download or read book Accelerating Monte Carlo methods for Bayesian inference in dynamical models written by Johan Dahlin and published by Linköping University Electronic Press. This book was released on 2016-03-22 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target. Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal. Borde Riksbanken höja eller sänka reporäntan vid sitt nästa möte för att nå inflationsmålet? Vilka gener är förknippade med en viss sjukdom? Hur kan Netflix och Spotify veta vilka filmer och vilken musik som jag vill lyssna på härnäst? Dessa tre problem är exempel på frågor där statistiska modeller kan vara användbara för att ge hjälp och underlag för beslut. Statistiska modeller kombinerar teoretisk kunskap om exempelvis det svenska ekonomiska systemet med historisk data för att ge prognoser av framtida skeenden. Dessa prognoser kan sedan användas för att utvärdera exempelvis vad som skulle hända med inflationen i Sverige om arbetslösheten sjunker eller hur värdet på mitt pensionssparande förändras när Stockholmsbörsen rasar. Tillämpningar som dessa och många andra gör statistiska modeller viktiga för många delar av samhället. Ett sätt att ta fram statistiska modeller bygger på att kontinuerligt uppdatera en modell allteftersom mer information samlas in. Detta angreppssätt kallas för Bayesiansk statistik och är särskilt användbart när man sedan tidigare har bra insikter i modellen eller tillgång till endast lite historisk data för att bygga modellen. En nackdel med Bayesiansk statistik är att de beräkningar som krävs för att uppdatera modellen med den nya informationen ofta är mycket komplicerade. I sådana situationer kan man istället simulera utfallet från miljontals varianter av modellen och sedan jämföra dessa mot de historiska observationerna som finns till hands. Man kan sedan medelvärdesbilda över de varianter som gav bäst resultat för att på så sätt ta fram en slutlig modell. Det kan därför ibland ta dagar eller veckor för att ta fram en modell. Problemet blir särskilt stort när man använder mer avancerade modeller som skulle kunna ge bättre prognoser men som tar för lång tid för att bygga. I denna avhandling använder vi ett antal olika strategier för att underlätta eller förbättra dessa simuleringar. Vi föreslår exempelvis att ta hänsyn till fler insikter om systemet och därmed minska antalet varianter av modellen som behöver undersökas. Vi kan således redan utesluta vissa modeller eftersom vi har en bra uppfattning om ungefär hur en bra modell ska se ut. Vi kan också förändra simuleringen så att den enklare rör sig mellan olika typer av modeller. På detta sätt utforskas rymden av alla möjliga modeller på ett mer effektivt sätt. Vi föreslår ett antal olika kombinationer och förändringar av befintliga metoder för att snabba upp anpassningen av modellen till observationerna. Vi visar att beräkningstiden i vissa fall kan minska ifrån några dagar till någon timme. Förhoppningsvis kommer detta i framtiden leda till att man i praktiken kan använda mer avancerade modeller som i sin tur resulterar i bättre prognoser och beslut.
Book Synopsis Bayesian Essentials with R by : Jean-Michel Marin
Download or read book Bayesian Essentials with R written by Jean-Michel Marin and published by Springer Science & Business Media. This book was released on 2013-10-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels. It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics.
Author :Sylvia Frühwirth-Schnatter Publisher :Springer Science & Business Media ISBN 13 :0387357688 Total Pages :506 pages Book Rating :4.3/5 (873 download)
Book Synopsis Finite Mixture and Markov Switching Models by : Sylvia Frühwirth-Schnatter
Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bayesian Modeling Using WinBUGS by : Ioannis Ntzoufras
Download or read book Bayesian Modeling Using WinBUGS written by Ioannis Ntzoufras and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all data sets and code are available on the book's related Web site. Requiring only a working knowledge of probability theory and statistics, Bayesian Modeling Using WinBUGS serves as an excellent book for courses on Bayesian statistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of statistics, actuarial science, medicine, and the social sciences who use WinBUGS in their everyday work.
Book Synopsis Graphical Models in Applied Multivariate Statistics by : Joe Whittaker
Download or read book Graphical Models in Applied Multivariate Statistics written by Joe Whittaker and published by Wiley. This book was released on 2009-03-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. Graphical models--a subset of log-linear models--reveal the interrelationships between multiple variables and features of the underlying conditional independence. This introduction to the use of graphical models in the description and modeling of multivariate systems covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition. Many numerical examples and exercises with solutions are included. This book is aimed at students who require a course on applied multivariate statistics unified by the concept of conditional independence and researchers concerned with applying graphical modelling techniques.
Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Oxford Handbook of Computational and Mathematical Psychology by : Jerome R. Busemeyer
Download or read book The Oxford Handbook of Computational and Mathematical Psychology written by Jerome R. Busemeyer and published by . This book was released on 2015 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.
Book Synopsis Bayesian Core: A Practical Approach to Computational Bayesian Statistics by : Jean-Michel Marin
Download or read book Bayesian Core: A Practical Approach to Computational Bayesian Statistics written by Jean-Michel Marin and published by Springer Science & Business Media. This book was released on 2007-02-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Bayesian modeling book provides the perfect entry for gaining a practical understanding of Bayesian methodology. It focuses on standard statistical models and is backed up by discussed real datasets available from the book website.
Book Synopsis Bayesian Inference of State Space Models by : Kostas Triantafyllopoulos
Download or read book Bayesian Inference of State Space Models written by Kostas Triantafyllopoulos and published by Springer Nature. This book was released on 2021-11-12 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
