Introduction To Probability Simulation And Gibbs Sampling With R

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Introduction To Probability Simulation And Gibbs Sampling With R

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Author : Eric A. Suess
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-15

Introduction To Probability Simulation And Gibbs Sampling With R written by Eric A. Suess and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-15 with Mathematics categories.

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.

Introducing Monte Carlo Methods With R

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Author : Christian Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2010

Introducing Monte Carlo Methods With R written by Christian Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.

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.

An Introduction To Statistical Computing

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Author : Jochen Voss
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-28

An Introduction To Statistical Computing written by Jochen Voss and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.

A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course.

Probability And Bayesian Modeling

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Author : Jim Albert
language : en
Publisher: CRC Press
Release Date : 2019-12-06

Probability And Bayesian Modeling written by Jim Albert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.

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.

Bayesian Computation With R

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Author : Jim Albert
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-20

Bayesian Computation With R written by Jim Albert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Mathematics categories.

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).

Probability With R

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Author : Jane M. Horgan
language : en
Publisher: John Wiley & Sons
Release Date : 2019-12-18

Probability With R written by Jane M. Horgan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-18 with Mathematics categories.

Provides a comprehensive introduction to probability with an emphasis on computing-related applications This self-contained new and extended edition outlines a first course in probability applied to computer-related disciplines. As in the first edition, experimentation and simulation are favoured over mathematical proofs. The freely down-loadable statistical programming language R is used throughout the text, not only as a tool for calculation and data analysis, but also to illustrate concepts of probability and to simulate distributions. The examples in Probability with R: An Introduction with Computer Science Applications, Second Edition cover a wide range of computer science applications, including: testing program performance; measuring response time and CPU time; estimating the reliability of components and systems; evaluating algorithms and queuing systems. Chapters cover: The R language; summarizing statistical data; graphical displays; the fundamentals of probability; reliability; discrete and continuous distributions; and more. This second edition includes: improved R code throughout the text, as well as new procedures, packages and interfaces; updated and additional examples, exercises and projects covering recent developments of computing; an introduction to bivariate discrete distributions together with the R functions used to handle large matrices of conditional probabilities, which are often needed in machine translation; an introduction to linear regression with particular emphasis on its application to machine learning using testing and training data; a new section on spam filtering using Bayes theorem to develop the filters; an extended range of Poisson applications such as network failures, website hits, virus attacks and accessing the cloud; use of new allocation functions in R to deal with hash table collision, server overload and the general allocation problem. The book is supplemented with a Wiley Book Companion Site featuring data and solutions to exercises within the book. Primarily addressed to students of computer science and related areas, Probability with R: An Introduction with Computer Science Applications, Second Edition is also an excellent text for students of engineering and the general sciences. Computing professionals who need to understand the relevance of probability in their areas of practice will find it useful.

Simulation

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Author : Sheldon M. Ross
language : en
Publisher: Academic Press
Release Date : 2022-06-14

Simulation written by Sheldon M. Ross and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-14 with Mathematics categories.

Simulation, Sixth Edition continues to introduce aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers will learn to apply the results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions. By explaining how a computer can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time, this book presents the statistics needed to analyze simulated data and validate simulation models. Includes updated content throughout Offers a wealth of practice exercises as well as applied use of free software package R Features the author’s well-known, award-winning and accessible approach to complex information

Introduction To Probability With R

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Author : Kenneth Baclawski
language : en
Publisher: CRC Press
Release Date : 2008-01-24

Introduction To Probability With R written by Kenneth Baclawski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-24 with Mathematics categories.

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.

Markov Chain Monte Carlo

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Author : Dani Gamerman
language : en
Publisher: CRC Press
Release Date : 2006-05-10

Markov Chain Monte Carlo written by Dani Gamerman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-10 with Mathematics categories.

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.

Introduction To Scientific Programming And Simulation Using R

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Author : Owen Jones
language : en
Publisher: CRC Press
Release Date : 2014-06-12

Introduction To Scientific Programming And Simulation Using R written by Owen Jones and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.

Learn How to Program Stochastic ModelsHighly recommended, the best-selling first edition of Introduction to Scientific Programming and Simulation Using R was lauded as an excellent, easy-to-read introduction with extensive examples and exercises. This second edition continues to introduce scientific programming and stochastic modelling in a clear,