Non-Standard Semiparametric Regression via BRugs

We provide several illustrations of Bayesian semiparametric regression analyses in the BRugs package. BRugs facilitates use of the BUGS inference engine from the R computing environment and allows analyses to be managed using scripts. The examples are chosen to represent an array of non-standard situations, for which mixed model software is not viable. The situations include: the response variable being outside of the one-parameter exponential family, data subject to missingness, data subject to measurement error and parameters entering the model via an index.

[1]  J LunnDavid,et al.  WinBUGS A Bayesian modelling framework , 2000 .

[2]  Walter R. Gilks,et al.  BUGS - Bayesian inference Using Gibbs Sampling Version 0.50 , 1995 .

[3]  Jeremy MG Taylor,et al.  Robust Statistical Modeling Using the t Distribution , 1989 .

[4]  Andrew Gelman,et al.  R2WinBUGS: A Package for Running WinBUGS from R , 2005 .

[5]  R. Rigby,et al.  Generalized Additive Models for Location Scale and Shape (GAMLSS) in R , 2007 .

[6]  Ciprian M. Crainiceanu,et al.  Bayesian Analysis for Penalized Spline Regression Using WinBUGS , 2005 .

[7]  B. Ripley,et al.  Semiparametric Regression: Preface , 2003 .

[8]  L. Wasserman,et al.  Bayesian analysis of outlier problems using the Gibbs sampler , 1991 .

[9]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[10]  M. Wand,et al.  Smoothing with Mixed Model Software , 2004 .

[11]  M. Wand,et al.  General design Bayesian generalized linear mixed models , 2006, math/0606491.

[12]  M P Wand,et al.  Negative Binomial Additive Models , 2000, Biometrics.

[13]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[14]  T. Kneib,et al.  BayesX: Analyzing Bayesian Structural Additive Regression Models , 2005 .

[15]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[16]  Andreas Brezger,et al.  Generalized structured additive regression based on Bayesian P-splines , 2006, Comput. Stat. Data Anal..

[17]  M P Wand,et al.  Robustness for general design mixed models using the t-distribution , 2009 .

[18]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[19]  ohn,et al.  Additive models with predictors subject to measurement error , 2004 .

[20]  Jianqing Fan,et al.  Generalized Partially Linear Single-Index Models , 1997 .

[21]  Martyn Plummer,et al.  JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling , 2003 .

[22]  Martin L Hazelton,et al.  Tutorial in biostatistics: spline smoothing with linear mixed models , 2005, Statistics in medicine.

[23]  R. Tibshirani,et al.  Linear Smoothers and Additive Models , 1989 .

[24]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[25]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[26]  Scott M. Berry,et al.  Bayesian Smoothing and Regression Splines for Measurement Error Problems , 2002 .

[27]  M. P. Wand,et al.  Corrigendum: ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALISED SPLINES , 2010 .

[28]  E. Mark,et al.  Early age at smoking initiation and tobacco carcinogen DNA damage in the lung. , 1999, Journal of the National Cancer Institute.

[29]  M. Wand.  SEMIPARAMETRIC REGRESSION AND GRAPHICAL MODELS , 2009 .