Introduction To Probability Simulation And Gibbs Sampling With R

Author : Eric A. Suess
Publisher : Springer Science & Business Media
ISBN 13 : 038740273X
Total Pages : 317 pages
Book Rating : 4.34/5 ( download)

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Download or read book Introduction to Probability Simulation and Gibbs Sampling with R written by Eric A. Suess and published by Springer Science & Business Media. This book was released on 2010-06-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels.

Author : Christian Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1441915753
Total Pages : 297 pages
Book Rating : 4.57/5 ( download)

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Download or read book Introducing Monte Carlo Methods with R written by Christian Robert and published by Springer Science & Business Media. This book was released on 2010 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jim Albert
Publisher : Springer Science & Business Media
ISBN 13 : 0387922989
Total Pages : 304 pages
Book Rating : 4.80/5 ( download)

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Download or read book Bayesian Computation with R written by Jim Albert and published by Springer Science & Business Media. This book was released on 2009-04-20 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Author : Jim Albert
Publisher : CRC Press
ISBN 13 : 1351030124
Total Pages : 511 pages
Book Rating : 4.20/5 ( download)

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Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Author : Christian Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1475741456
Total Pages : 670 pages
Book Rating : 4.52/5 ( download)

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Download or read book Monte Carlo Statistical Methods written by Christian Robert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

Author : Laura M. Chihara
Publisher : John Wiley & Sons
ISBN 13 : 1118518950
Total Pages : 432 pages
Book Rating : 4.53/5 ( download)

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Download or read book Mathematical Statistics with Resampling and R written by Laura M. Chihara and published by John Wiley & Sons. This book was released on 2012-09-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques. The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as: Exploratory data analysis Calculation of sampling distributions The Central Limit Theorem Monte Carlo sampling Maximum likelihood estimation and properties of estimators Confidence intervals and hypothesis tests Regression Bayesian methods Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints. Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work.

Author : Maria Dolores Ugarte
Publisher : CRC Press
ISBN 13 : 1466504404
Total Pages : 967 pages
Book Rating : 4.00/5 ( download)

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Download or read book Probability and Statistics with R written by Maria Dolores Ugarte and published by CRC Press. This book was released on 2015-07-21 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohesively Incorporates Statistical Theory with R ImplementationSince the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and Statistics with R, Second Edition explores how some o

Author : Roe Goodman
Publisher : Courier Corporation
ISBN 13 : 0486450376
Total Pages : 370 pages
Book Rating : 4.77/5 ( download)

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Download or read book Introduction to Stochastic Models written by Roe Goodman and published by Courier Corporation. This book was released on 2006-01-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state probabilities, general queuing systems, and renewal processes. Each section features worked examples, and exercises appear at the end of each chapter, with numerical solutions at the back of the book. Suggestions for further reading in stochastic processes, simulation, and various applications also appear at the end.

Author : Dani Gamerman
Publisher : CRC Press
ISBN 13 : 9781584885870
Total Pages : 352 pages
Book Rating : 4.74/5 ( download)

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Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 2006-05-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Prabhanjan N. Tattar
Publisher : John Wiley & Sons
ISBN 13 : 1119152720
Total Pages : 693 pages
Book Rating : 4.29/5 ( download)

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Download or read book A Course in Statistics with R written by Prabhanjan N. Tattar and published by John Wiley & Sons. This book was released on 2016-05-02 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical concepts Provides graphical presentations inclusive of mathematical expressions Aids understanding of limit theorems of probability with and without the simulation approach Presents detailed algorithmic development of statistical models from scratch Includes practical applications with over 50 data sets