Markov Chain Monte Carlo

Stochastic Simulation for Bayesian Inference, Second Edition

Author: Dani Gamerman,Hedibert F. Lopes

Publisher: CRC Press

ISBN: 9781584885870

Category: Mathematics

Page: 344

View: 3101

While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.

Bayesian Models for Astrophysical Data

Using R, JAGS, Python, and Stan

Author: Joseph M. Hilbe,Rafael S. de Souza,Emille E. O. Ishida

Publisher: Cambridge University Press

ISBN: 1108210740

Category: Mathematics

Page: N.A

View: 2204

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Industrial Tomography

Systems and Applications

Author: Mi Wang

Publisher: Elsevier

ISBN: 1782421238

Category: Computers

Page: 772

View: 5063

Industrial Tomography: Systems and Applications thoroughly explores the important tomographic techniques of industrial tomography, also discussing image reconstruction, systems, and applications. The text presents complex processes, including the way three-dimensional imaging is used to create multiple cross-sections, and how computer software helps monitor flows, filtering, mixing, drying processes, and chemical reactions inside vessels and pipelines. Readers will find a comprehensive discussion on the ways tomography systems can be used to optimize the performance of a wide variety of industrial processes. Provides a comprehensive discussion on the different formats of tomography Includes an excellent overview of image reconstruction using a wide range of applications Presents a comprehensive discussion of tomography systems and their application in a wide variety of industrial processes

Stochastic Processes

An Introduction, Second Edition

Author: Peter Watts Jones,Peter Smith

Publisher: Chapman and Hall/CRC


Category: Mathematics

Page: 221

View: 9684

This text begins with a review of relevant fundamental probability. It then covers several basic gambling problems, random walks, and Markov chains. The authors go on to develop random processes continuous in time, including Poisson, birth and death processes, and general population models.

Bayesian Methods

A Social and Behavioral Sciences Approach, Second Edition

Author: Jeff Gill

Publisher: CRC Press

ISBN: 1584885629

Category: Mathematics

Page: 752

View: 8692

The first edition of Bayesian Methods: A Social and Behavioral Sciences Approach helped pave the way for Bayesian approaches to become more prominent in social science methodology. While the focus remains on practical modeling and basic theory as well as on intuitive explanations and derivations without skipping steps, this second edition incorporates the latest methodology and recent changes in software offerings. New to the Second Edition Two chapters on Markov chain Monte Carlo (MCMC) that cover ergodicity, convergence, mixing, simulated annealing, reversible jump MCMC, and coupling Expanded coverage of Bayesian linear and hierarchical models More technical and philosophical details on prior distributions A dedicated R package (BaM) with data and code for the examples as well as a set of functions for practical purposes such as calculating highest posterior density (HPD) intervals Requiring only a basic working knowledge of linear algebra and calculus, this text is one of the few to offer a graduate-level introduction to Bayesian statistics for social scientists. It first introduces Bayesian statistics and inference, before moving on to assess model quality and fit. Subsequent chapters examine hierarchical models within a Bayesian context and explore MCMC techniques and other numerical methods. Concentrating on practical computing issues, the author includes specific details for Bayesian model building and testing and uses the R and BUGS software for examples and exercises.

A Primer on Linear Models

Author: John F. Monahan

Publisher: Chapman and Hall/CRC

ISBN: 9781420062014

Category: Mathematics

Page: 304

View: 3557

A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

A Course in Categorical Data Analysis

Author: Thomas Leonard

Publisher: Chapman & Hall

ISBN: 9780849303234

Category: Medical

Page: 183

View: 4367

Developed from long experience in teaching categorical analysis to a multidisciplinary mix of undergraduate and graduate students, A Course in Categorical Data Analysis presents the easiest, most straightforward ways of extracting real-life conclusions from contingency tables. The author uses a Fisherian approach to categorical data analysis and incorporates numerous examples and real data sets. Although he offers S-PLUS routines through the Interest, readers do not need full knowledge of a statistical software package.

Introduction to Probability with R

Author: Kenneth Baclawski

Publisher: Chapman and Hall/CRC

ISBN: 9781420065213

Category: Mathematics

Page: 384

View: 3336

Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.

Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 9780203492284

Category: Mathematics

Page: 312

View: 1401

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those fo

Applied Stochastic Modelling, Second Edition

Author: Byron J.T. Morgan

Publisher: CRC Press

ISBN: 1420011650

Category: Mathematics

Page: 368

View: 3779

Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of interesting real-world applications. It also successfully revises standard probability and statistical theory. Along with an updated bibliography and improved figures, this edition offers numerous updates throughout. New to the Second Edition An extended discussion on Bayesian methods A large number of new exercises A new appendix on computational methods The book covers both contemporary and classical aspects of statistics, including survival analysis, Kernel density estimation, Markov chain Monte Carlo, hypothesis testing, regression, bootstrap, and generalised linear models. Although the book can be used without reference to computational programs, the author provides the option of using powerful computational tools for stochastic modelling. All of the data sets and MATLAB® and R programs found in the text as well as lecture slides and other ancillary material are available for download at Continuing in the bestselling tradition of its predecessor, this textbook remains an excellent resource for teaching students how to fit stochastic models to data.

Mathematische Statistik

Author: Claudia Czado,Thorsten Schmidt

Publisher: Springer-Verlag

ISBN: 364217261X

Category: Mathematics

Page: 280

View: 415

Das Buch liefert einen Überblick über die Theorie statistischer Schätz- und Testverfahren. Die Autoren bieten eine verständliche und praxisorientierte Schritt-für-Schritt Einführung in die mathematischen Methoden der Statistik. Um Lesern den Einstieg in die Materie zu erleichtern, präsentieren sie elementare Beweise ohne maßtheoretische Hilfsmittel und bieten viele ausgearbeitete Anwendungsbeispiele. Anhand einer umfangreichen Aufgabensammlung am Ende jedes Kapitels können Leser ihren Lernfortschritt überprüfen.

Handbook of Applied Hydrology, Second Edition

Author: Vijay P. Singh

Publisher: McGraw Hill Professional

ISBN: 0071835105

Category: Technology & Engineering

Page: 1808

View: 7478

Fully Updated Hydrology Principles, Methods, and Applications Thoroughly revised for the first time in 50 years, this industry-standard resource features chapter contributions from a “who’s who” of international hydrology experts. Compiled by a colleague of the late Dr. Chow, Chow’s Handbook of Applied Hydrology, Second Edition, covers scientific and engineering fundamentals and presents all-new methods, processes, and technologies. Complete details are provided for the full range of ecosystems and models. Advanced chapters look to the future of hydrology, including climate change impacts, extraterrestrial water, social hydrology, and water security. Chow’s Handbook of Applied Hydrology, Second Edition, covers: · The Fundamentals of Hydrology · Data Collection and Processing · Hydrology Methods · Hydrologic Processes and Modeling · Sediment and Pollutant Transport · Hydrometeorologic and Hydrologic Extremes · Systems Hydrology · Hydrology of Large River and Lake Basins · Applications and Design · The Future of Hydrology

Stochastic Modeling of Scientific Data

Author: Peter Guttorp,Vladimir N. Minin

Publisher: CRC Press

ISBN: 9780412992810

Category: Mathematics

Page: 384

View: 1928

Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Die Monte-Carlo-Methode

Beispiele unter Excel VBA

Author: Harald Nahrstedt

Publisher: Springer-Verlag

ISBN: 3658101490

Category: Mathematics

Page: 45

View: 4892

Harald Nahrstedt zeigt hier den pragmatisch technischen und weniger den wissenschaftlichen Ansatz, wie Excel mit seinen Programmiermöglichkeiten sich immer mehr zu einem universellen Arbeitsmittel entwickelt. So ist die Simulation mit Hilfe von Pseudozufallszahlen ein schneller und preiswerter Weg zu fachlichen Aussagen. Den Rahmen dieser Abhandlung bildet der geschichtliche Hintergrund.

Angststörungen bei Kindern und Jugendlichen

Author: Franz Borgwald

Publisher: GRIN Verlag

ISBN: 3640968980

Category: Psychology

Page: 15

View: 9721

Studienarbeit aus dem Jahr 2011 im Fachbereich Psychologie - Entwicklungspsychologie, Ernst-Moritz-Arndt-Universität Greifswald, Sprache: Deutsch, Abstract: „Angst ist ein Gefühlszustand, der gekennzeichnet ist durch negative Emotionen und körperliche Symptome von Anspannung. Der Begriff Angst leitet sich von dem lateinischen Wort „anxius“ ab und definiert einen Zustand von Erregung und Belastung.“ (ESSAU, Cecilia A., 2003) In der Wissenschaft wird die Angst in ihrer Ursache und Wirkung, sowohl gegenwärtig als auch zukunftsorientiert als eine komplexe Erfahrung verstanden. Sie äußert sich körperlich, kognitiv und im Verhalten. Angststörungen bei Kindern und Jugendlichen sind ernstzunehmende Störungen. Es gibt unterschiedliche Risikofaktoren auf der familiären Ebene, der kognitiven Ebene und im Bereich unterschiedlicher Lebensereignisse. Mit Lebensereignissen sind Augenblicke gemeint, in denen das Kind oder der Jugendliche eine extreme negative Erfahrung gemacht hat. Aufgrund dieser unterschiedlichsten Risikofaktoren gilt es als Lehrer, eine Sensibilität für Symptome möglicher Angstreaktionen zu entwickeln. Kinder werden ihre Gefühle je nach Alter direkt oder indirekt beschreiben können. In jedem Fall gilt es, Beobachtungen mit den Eltern bzw. anderen Lehrern abzugleichen und eventuell einen Therapeuten zur Behandlung aufzusuchen. Durch die Klassifikationsmöglichkeiten nach DSM-III und ICD-10 ist es heute möglich, nach einer genauen Diagnose und einer dazu passenden Behandlung weitere Folgen und eine Verfestigung der jeweiligen Angststörung zu verhindern.

Statistik I

Grundlagen der Wahrscheinlichkeitstheorie

Author: Roland Dillmann

Publisher: Springer-Verlag

ISBN: 3642958869

Category: Mathematics

Page: 270

View: 6107

Das vorliegende Lehrbuch ist der 1. Band einer 2-teiligen Einführung in die Statistik. Es wendet sich an Studienanfänger und soll die inhaltlichen Probleme, die hinter der statistischen Begriffsbildung stehen, vermitteln und das Verständnis der mathematischen Bezüge fördern. Band 1 beschäftigt sich mit den Grundlagen der Wahrscheinlichkeitstheorie. Die wichtigsten Begriffe und Konzepte werden dargestellt und mit zahlreichen Beispielen erläutert. Wahrscheinlichkeitsverteilungen, Verteilungs- und Dichtefunktionen, Stichproben und Kennzahlen für Stichproben und Zufallsvariablen sowie das Gesetz der großen Zahlen werden in verständlicher Weise dargelegt und die Bedeutung von Wahrscheinlichkeit und Wahrscheinlichkeitstheorie in der Ökonomie wird ebenfalls beachtet.


Author: N.A

Publisher: N.A


Category: American literature

Page: N.A

View: 2224