Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Author: Jean-Michel Marin,Christian Robert

Publisher: Springer Science & Business Media

ISBN: 0387389830

Category: Mathematics

Page: 258

View: 5776

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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. 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.

Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Author: Jean-Michel Marin,Christian Robert

Publisher: Springer Science & Business Media

ISBN: 0387389792

Category: Computers

Page: 255

View: 1618

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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications.

Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Author: Jean-Michel Marin,Christian Robert

Publisher: Springer

ISBN: 9781441922861

Category: Mathematics

Page: 258

View: 2246

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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. 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.

The Bayesian Choice

From Decision-Theoretic Foundations to Computational Implementation

Author: Christian Robert

Publisher: Springer Science & Business Media

ISBN: 0387715991

Category: Mathematics

Page: 606

View: 9360

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This is an introduction to Bayesian statistics and decision theory, including advanced topics such as Monte Carlo methods. This new edition contains several revised chapters and a new chapter on model choice.

Bayesian Essentials with R

Author: Jean-Michel Marin,Christian P. Robert

Publisher: Springer Science & Business Media

ISBN: 1461486874

Category: Computers

Page: 296

View: 8020

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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.

A First Course in Bayesian Statistical Methods

Author: Peter D. Hoff

Publisher: Springer Science & Business Media

ISBN: 9780387924076

Category: Mathematics

Page: 272

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A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

Bayesian and Frequentist Regression Methods

Author: Jon Wakefield

Publisher: Springer Science & Business Media

ISBN: 1441909257

Category: Mathematics

Page: 697

View: 3214

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Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

Introducing Monte Carlo Methods with R

Author: Christian Robert,George Casella

Publisher: Springer Science & Business Media

ISBN: 1441915753

Category: Computers

Page: 284

View: 3066

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This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.

Bayesian Networks and Decision Graphs

Author: Thomas Dyhre Nielsen,FINN VERNER JENSEN

Publisher: Springer Science & Business Media

ISBN: 9780387682815

Category: Science

Page: 448

View: 2022

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This is a brand new edition of an essential work on Bayesian networks and decision graphs. It is an introduction to probabilistic graphical models including Bayesian networks and influence diagrams. The reader is guided through the two types of frameworks with examples and exercises, which also give instruction on how to build these models. Structured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.

Statistical Models and Methods for Financial Markets

Author: Tze Leung Lai,Haipeng Xing

Publisher: Springer Science & Business Media

ISBN: 0387778276

Category: Business & Economics

Page: 356

View: 4955

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The idea of writing this bookarosein 2000when the ?rst author wasassigned to teach the required course STATS 240 (Statistical Methods in Finance) in the new M. S. program in ?nancial mathematics at Stanford, which is an interdisciplinary program that aims to provide a master’s-level education in applied mathematics, statistics, computing, ?nance, and economics. Students in the programhad di?erent backgroundsin statistics. Some had only taken a basic course in statistical inference, while others had taken a broad spectrum of M. S. - and Ph. D. -level statistics courses. On the other hand, all of them had already taken required core courses in investment theory and derivative pricing, and STATS 240 was supposed to link the theory and pricing formulas to real-world data and pricing or investment strategies. Besides students in theprogram,thecoursealso attractedmanystudentsfromother departments in the university, further increasing the heterogeneity of students, as many of them had a strong background in mathematical and statistical modeling from the mathematical, physical, and engineering sciences but no previous experience in ?nance. To address the diversity in background but common strong interest in the subject and in a potential career as a “quant” in the ?nancialindustry,thecoursematerialwascarefullychosennotonlytopresent basic statistical methods of importance to quantitative ?nance but also to summarize domain knowledge in ?nance and show how it can be combined with statistical modeling in ?nancial analysis and decision making. The course material evolved over the years, especially after the second author helped as the head TA during the years 2004 and 2005.

Monte Carlo Statistical Methods

Author: Christian Robert,George Casella

Publisher: Springer Science & Business Media

ISBN: 1475741456

Category: Mathematics

Page: 649

View: 4200

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We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

Bayesian Computation with R

Author: Jim Albert

Publisher: Springer Science & Business Media

ISBN: 0387922989

Category: Mathematics

Page: 300

View: 9174

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There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).

All of Statistics

A Concise Course in Statistical Inference

Author: Larry Wasserman

Publisher: Springer Science & Business Media

ISBN: 0387217363

Category: Mathematics

Page: 442

View: 2786

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Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

The Contribution of Young Researchers to Bayesian Statistics

Proceedings of BAYSM2013

Author: Ettore Lanzarone,Francesca Ieva

Publisher: Springer Science & Business Media

ISBN: 3319020846

Category: Mathematics

Page: 214

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The first Bayesian Young Statisticians Meeting, BAYSM 2013, has provided a unique opportunity for young researchers, M.S. students, Ph.D. students, and post-docs dealing with Bayesian statistics to connect with the Bayesian community at large, exchange ideas, and network with scholars working in their field. The Workshop, which took place June 5th and 6th 2013 at CNR-IMATI, Milan, has promoted further research in all the fields where Bayesian statistics may be employed under the guidance of renowned plenary lecturers and senior discussants. A selection of the contributions to the meeting and the summary of one of the plenary lectures compose this volume.

Statistical Rethinking

A Bayesian Course with Examples in R and Stan

Author: Richard McElreath

Publisher: CRC Press

ISBN: 1315362619

Category: Mathematics

Page: 487

View: 9350

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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.

Bayesian Ideas and Data Analysis

An Introduction for Scientists and Statisticians

Author: Ronald Christensen,Wesley Johnson,Adam Branscum,Timothy E Hanson

Publisher: CRC Press

ISBN: 1439803552

Category: Mathematics

Page: 516

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Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data. The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions. The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data. Data sets and codes are provided on a supplemental website.

Introductory Statistics with R

Author: Peter Dalgaard

Publisher: Springer Science & Business Media

ISBN: 0387790543

Category: Mathematics

Page: 364

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This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets. All examples are directly runnable and all graphics in the text are generated from the examples. The statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one-and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis.

Probability for Statistics and Machine Learning

Fundamentals and Advanced Topics

Author: Anirban DasGupta

Publisher: Springer Science & Business Media

ISBN: 9781441996343

Category: Mathematics

Page: 784

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This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

Computational Electromagnetics

Author: Thomas Rylander,Pär Ingelström,Anders Bondeson

Publisher: Springer Science & Business Media

ISBN: 1461453518

Category: Computers

Page: 288

View: 5419

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Computational Electromagnetics is a young and growing discipline, expanding as a result of the steadily increasing demand for software for the design and analysis of electrical devices. This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element method and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell's equations, using, for example, "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. To reach this goal, convergence analysis, extrapolation, von Neumann stability analysis, and dispersion analysis are introduced and used frequently throughout the book. Another major goal of the book is to provide students with enough practical understanding of the methods so they are able to write simple programs on their own. To achieve this, the book contains several MATLAB programs and detailed description of practical issues such as assembly of finite element matrices and handling of unstructured meshes. Finally, the book aims at making the students well-aware of the strengths and weaknesses of the different methods, so they can decide which method is best for each problem. In this second edition, extensive computer projects are added as well as new material throughout. Reviews of previous edition: "The well-written monograph is devoted to students at the undergraduate level, but is also useful for practising engineers." (Zentralblatt MATH, 2007)

The Bayesian Choice

A Decision-Theoretic Motivation

Author: Christian Robert

Publisher: Springer Science & Business Media

ISBN: 1475743149

Category: Mathematics

Page: 437

View: 1976

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This graduate-level textbook covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics, such as complete class theorems, the Stein effect, hierarchical and empirical Bayes modelling, Monte Carlo integration, and Gibbs sampling. In translating the book from the original French, the author has taken the opportunity to add and update material, and to include many problems and exercises for students.