Bayesian Computation with R

Name: Bayesian Computation with R
Availability: InStock
ISBN: 9780387922973

ISBN-10: 0387922970

ISBN-13: 9780387922973

Edition: 2nd 2009

Authors: Jim Albert

List price: $69.99

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Description:

There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry.Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter…

Book details

List price: $69.99
Edition: 2nd
Copyright year: 2009
Publisher: Springer New York
Publication date: 5/15/2009
Binding: Paperback
Pages: 300
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.276
Language: English




An Introduction to R



Overview



Exploring a Student Dataset



Introduction to the Dataset



Reading the Data into R



R Commands to Summarize and Graph a Single Batch



R Commands to Compare Batches



R Commands for Studying Relationships



Exploring the Robustness of the t Statistic



Introduction



Writing a Function to Compute the t Statistic



Programming a Monte Carlo Simulation



The Behavior of the True Significance Level Under Different Assumptions



Further Reading



Summary of R Functions



Exercises



Introduction to Bayesian Thinking



Introduction



Learning About the Proportion of Heavy Sleepers



Using a Discrete Prior



Using a Beta Prior



Using a Histogram Prior



Prediction



Further Reading



Summary of R Functions



Exercises



Single-Parameter Models



Introduction



Normal Distribution with Known Mean but Unknown Variance



Estimating a Heart Transplant Mortality Rate



An Illustration of Bayesian Robustness



Mixtures of Conjugate Priors



A Bayesian Test of the Fairness of a Coin



Further Reading



Summary of R Functions



Exercises



Multiparameter Models



Introduction



Normal Data with Both Parameters Unknown



A Multinomial Model



A Bioassay Experiment



Comparing Two Proportions



Further Reading



Summary of R Functions



Exercises



Introduction to Bayesian Computation



Introduction



Computing Integrals



Setting Up a Problem in R



A Beta-Binomial Model for Overdispersion



Approximations Based on Posterior Modes



The Example



Monte Carlo Method for Computing Integrals



Rejection Sampling



Importance Sampling



Introduction



Using a Multivariate t as a Proposal Density



Sampling Importance Resampling



Further Reading



Summary of R Functions



Exercises



Markov Chain Monte Carlo Methods



Introduction



Introduction to discrete Markov Chains



Metropolis-Hastings Algorithms



Gibbs Sampling



MCMC Output Analysis



A Strategy in Bayesian Computing



Learning About a Normal Population from Grouped Data



Example of Output Analysis



Modeling Data with Cauchy Errors



Analysis of the Stanford Heart Transplant Data



Further Reading



Summary of R Functions



Exercises



Hierarchical Modeling



Introduction



Three Examples



Individual and Combined Estimates



Equal Mortality Rates?



Modeling a Prior Belief of Exchangeability



Posterior Distribution



Simulating from the Posterior



Posterior Inferences



Shrinkage



Comparing Hospitals



Bayesian Sensitivity Analysis



Posterior Predictive Model Checking



Further Reading



Summary of R Functions



Exercises



Model Comparison



Introduction



Comparison of Hypotheses



A One-Sided Test of a Normal Mean



A Two-Sided Test of a Normal Mean



Comparing Two Models



Models for Soccer Goals



Is a Baseball Hitter Really Streaky?



A Test of Independence in a Two-Way Contingency Table



Further Reading



Summary of R Functions



Exercises



Regression Models



Introduction



Normal Linear Regression



The Model



The Posterior Distribution



Prediction of Future Observations



Computation



Model Checking



An Example



Model Selection Using Zellner's Prior



Survival Modeling



Further Reading



Summary of R Functions



Exercises



Gibbs Sampling



Introduction



Robust Modeling



Binary Response Regression with a Probit Link



Missing Data and Gibbs Sampling



Proper Priors and Model Selection



Estimating a Table of Means



Introduction



A Flat Prior Over the Restricted Space



A Hierarchical Regression Prior



Predicting the Success of Future Students



Further Reading



Summary of R Functions



Exercises



Using R to Interface with WinBUGS



Introduction to WinBUGS



An R Interface to WinBUGS



MCMC Diagnostics Using the coda Package



A Change-Point Model



A Robust Regression Model



Estimating Career Trajectories



Further Reading



Exercises


References


Index