A Bayesian Approach for Nonlinear Regression Models with Continuous Errors

References

• Arnold , L. 1971 . Stochastics Differential Equations: Theory and Applications New York : Wiley .
   Google Scholar
• Bennett , J. E. , Racine-Poon , A. and Wakefield , J. C. 1996 . “ MCMC for nonlinear hierarchical models ” . In Markov Chain Monte Carlo in Practice Edited by: Gilks , W. R. , Richardson , S. and Spiegelhalter , D. J. pp. 339 – 358 . Chapman and Hall .
   Google Scholar
• Best , N. G. , Cowles , M. K. and Vines , S. K. 1995 . CODA: Convergence Diagnosis and Output Analysis Software for Gibbs sampling output, Version 0.3 Cambridge : MRC Biostatistics Unit .
   Google Scholar
• Brockwell , P. J. , Hyndman , R. J. and Grunwald , G. K. 1991 . Continuous time threshold autoregressive models . Statistica Sinica , 1 : 401 – 410 .
   Web of Science ®Google Scholar
• Broemeling , L. D. and Cook , P. 1997 . A Bayesian Analysis of Regression Models with Continuous Errors with Application to Longitudinal Studies . Statistics in Medicine , 16 : 321 – 332 .
   PubMed Web of Science ®Google Scholar
• Davidian , M. and Giltinan , D. M. 1996 . Nonlinear Models for Repeated Measurement Data London : Chapman and Hall .
   Google Scholar
• De la Cruz-Mesía , R. 1999 . A Bayesian Analysis of Nonlinear Random Effects Models with Continuous Errors Catholic University of Chile . Master's Thesis. Department of Statistics
   Google Scholar
• Dey , D. , Chen , M.-H. and Chang , H. 1997 . Bayesian approach for the nonlinear random effects models . Biometrics , 53 : 15 – 28 .
   Web of Science ®Google Scholar
• Diggle , P. J. and Liang , Kung-Yee, Zeger, S. L. 1994 . Analysis of Longitudinal Data Oxford : Oxford University Press .
   Google Scholar
• Gelfand , A. and Smith , A. 1990 . Sampling based approaches to calculating marginal densities . J. Amer. Statist. Assoc. , 85 : 398 – 409 .
   Web of Science ®Google Scholar
• Geweke , J. 1995 . “ Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments ” . In Bayesian Statistics 4 Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. pp. 169 – 194 . Oxford University Press .
   Google Scholar
• Gibaldi , M. and Perrier , D. 1993 . Drugs and the Pharmaceutical Sciences. Volume 1: Pharamacokinetics New York : Marcel Dekker Inc. .
   Google Scholar
• Heidelberger , P. and Welch , P. 1983 . Simulation run length control in the presence of an initial transient . Operations Research , 31 : 1109 – 1144 .
   Web of Science ®Google Scholar
• Jones , R. H. 1993 . Longitudinal Data With Serial Correlations: A State Space Approach London : Chapman & Hall .
   Google Scholar
• Pinheiro , J. C. , Bates , D. M. and Lindstrom , M. Nonlinear mixed effects classes and methods for S , Technical Report 931 . Department of Statistics, University of Wisconsin. 1994
   Google Scholar
• Racine , A. , Grieve , A. P. , Flühler , H. and Smith , A. F. M. 1986 . Bayesian methods in practice: experiences in the pharmaceutical industry . Appl. Statist. , 35 : 93 – 150 .
   Web of Science ®Google Scholar
• Racine-Poon , A. and Moppert , J. 1985 . Oxprenolol: concentration effect relationship. A retrospective study . Br. J. Clin. Pharmac. , 19 : 143S – 149S .
   Web of Science ®Google Scholar
• Smith , A. F. M. and Roberts , G. O. 1993 . Bayesian Computation via the Gibbs sampler and related Markov chain Monte Carlos methods . J. R. Statist. Soc. B , 55 : 3 – 23 .
   Google Scholar
• Tanner , M. A. 1993 . Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions. , 2nd ed. New York : Springer-Verlag .
   Google Scholar
• Tierney , L. 1994 . Markov chains for exploring posterior distributions . The Annals of Statistics , 22 : 1701 – 1728 .
   Web of Science ®Google Scholar
• Wakefield , J. C. 1996 . Bayesian Analysis of Population Pharmacokinetic Models . J. Amer. Statist. Assoc. , 91 : 62 – 75 .
   Web of Science ®Google Scholar
• Wakefield , J. C. , Smith , A. F. M. , Racine-Poon , A. and Gelfand , A. E. 1994 . Bayesian Analysis of Linear and Non-linear Population Models by using the Gibbs Sampler . Appl. Statist. , 43 : 201 – 221 .
   Web of Science ®Google Scholar