Bayesian Computation with R

Abstract

), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) 2009926660 PrefaceThere 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, and the extensive number of applications of Bayesian articles in applied disciplines such as science and engineering.One reason for the dramatic growth in Bayesian modeling is the availability of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern computers, it is now possible to use the Bayesian paradigm to fit very complex models that cannot be fit by alternative frequentist methods.To fit Bayesian models, one needs a statistical computing environment. This environment should be such that one can:• write short scripts to define 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 displays. 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 Comprehensive R Archive Network (CRAN).The purpose of this book is to illustrate Bayesian modeling by computations using the R language. At Bowling Green State University, I have taught an introductory Bayesian inference class to students in masters and doctoral programs in statistics for which this book would be appropriate. This book would serve as a useful companion to the introductory Bayesian texts by Gelman et al. (2003), Carlin and Louis (2009), Press (2003), Gill (2008), or Lee (2004. The book would also be valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. Chapters 2, 3, and 4 illustrate the use of R for Bayesian inference for standard one-and two-parameter problems. These chapters discuss the use of different types of priors, the use of the posterior distribution to perform different types of inferences, and the use of the predictive distribution. The base package of R provides functions to simulate from all of the standard probabi...

Bayes in biological anthropology

“…At that time, one of the chief impediments to teaching about Bayesian inference was the general lack of suitable textbooks and readily available software, with Albert's (1996) and Berry's (1996) introductory texts being about the only options. Since then Kruschke (2010a) has written an excellent introductory Bayesian text that incorporates the use of both R and BUGS, and there are now more advanced texts that focus on Bayesian inference and MCMC (Albert, 2009;Link and Barker, 2010;Christensen et al, 2011;Lesaffre and Lawson, 2012;Cowles, 2013). Examples in these more advanced texts do sometimes run to the anthropological, such as in Christensen et al's (2011, p 4) use of data on Ache armadillo hunting practices.…”

Volatility modeling for IDR exchange rate through APARCH model with student-t distribution

“…In this case, the mean and the variance are found using the method which is based on the behavior of the density about its mode (see [20]). Denoting the posterior mode of by , the mode is provided by which can be approximated using bisection's method.…”

A non-linear forecast combination procedure for binary outcomes

“…The details can be found in Koop (2003). The value of c is determined in such a way that the resulting acceptance rate is about 25%, as suggested by Albert (2009). The first 10, 000 draws are discarded to remove the impact of the initial value.…”