Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Bayesian Model Selection for Nonlinear Regression under Noninformative Prior

  • Na, Jonghwa (Dept. of Information and Statistics, Chungbuk National University) ;
  • Kim, Jeongsuk (Dept. of Information and Statistics, Chungbuk National University)
  • Published : 2003.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

We propose a Bayesian model selection procedure for nonlinear regression models under noninformative prior. For informative prior, Na and Kim (2002) suggested the Bayesian model selection procedure through MCMC techniques. We extend this method to the case of noninformative prior. The difficulty with the use of noninformative prior is that it is typically improper and hence is defined only up to arbitrary constant. The methods, such as Intrinsic Bayes Factor(IBF) and Fractional Bayes Factor(FBF), are used as a resolution to the problem. We showed the detailed model selection procedure through the specific real data set.

Keywords

References

  1. Biometrika v.65 Posterior Probabilities for Choosing a Regression Model Atkinson,A.C. https://doi.org/10.1093/biomet/65.1.39
  2. Nonlinear Regression Analysis and its Applications Bates,D.M.;Watts,D.G.
  3. Journal of the American Statistical Association v.91 The Intrinsic Bayes Factor for Model Selection and Prediction Berger,J.O.;Pericchi,L.R. https://doi.org/10.2307/2291387
  4. Research Report 93-006, University of Minnesota Bayesian Model Choice via Marcov Vhain Monte Carlo Carlin,B.P.;Chib,S.
  5. Sankhya v.38 Bayes Factors for Behrens-Fisher Problems Dayal,H.H.;Dickey,J.M.
  6. Biometrika v.70 no.2 On Bayesian nonlinear regression with an enzyme example Eaves,D.M. https://doi.org/10.1093/biomet/70.2.373
  7. Theory of Probability (3rd ed.) Jeffreys,H.
  8. Journal of the American Statistical Association v.90 Bayes factors Kass,R.E.;Raftery,A.E.
  9. Technical Report 279, University of Washington The Laplace-Metropolis Estimator for Bayes Factors via Posterior Simulation Lewis,S.M.;Raftery,A.E.
  10. M.S. Thesis, University of Wisconsin-Madison Biochemical Oxygen Demand Data Interpretation Using Sum of Squares Surface Marske, Donald
  11. The Korean Journal of Applied Statistics v.15 no.1 Bayesian Model Selection and Diagnostics for Nonlinear Regression Model via MCMC Na,J.H.;Kim,J.S. https://doi.org/10.5351/KJAS.2002.15.1.139
  12. Journal of the Royal Statistical Society, Ser. B v.57 Fractional Bayes Factors for Model Comparisons O'Hagan,A.
  13. Journal of the Royal Statistical Society. Ser. B v.44 Bayes Factors for Linear and Log-Linear Models with Vague Prior Information Spiegelhalter,D.J.;Smith,A.F.M.