Abstract
We discuss the problem of constructing a suitable regression model from a nonparametric Bayesian viewpoint. For this purpose, we consider the case when the error terms have symmetric and unimodal densities. By the Khintchine and Shepp theorem, the density of response variable can be written as a scale mixture of uniform densities. The mixing distribution is assumed to have a Dirichlet process prior. We further consider appropriate prior distributions for other parameters as the components of the predictive device. Among the possible submodels, we select the one which has the highest posterior probability. An example is given to illustrate the approach.
Similar content being viewed by others
References
Brunner LJ (1995) Bayesian linear regression with error terms that have symmetric unimodal densities. J Nonparametr Stat 4:335–348
Feller W (1971) An introduction to probability theory and its applications, vol 2. Wiley, New York, p 158
Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Statist 1:209–230
Gutierrez-Pena E, Walker SG (2001) A Bayesian predictive approach to model selection. J Stat Plan Inference 93:259–276
Hoeting JA, Ibrahim JG (1998) Bayesian predictive simultaneous variable and transformation selection in the linear model. J Comput Stat Data Analy 28:87–103
Ibrahim JG, Laud PW (1994) A predictive approach to the analysis of designed experiments. J Am Stat Assoc 89:309–319
Laud PW, Ibrahim JG (1995) Predictive model selection. J R Stat Soc B 57:247–262
Lo AY (1984) On a class of Bayesian nonparametric estimates: I. Density estimates. Ann Statist 12:351–357
Mitchell TJ, Beauchamp JJ (1988) Bayesian variable selection in linear regression, (with discussion). J Am Stat Assoc 83:1023–1036
Neter J, Wasserman W, Kutner MH (1985) Applied linear statistical models, regression, analysis of variance, and experimental designs, 2nd edn. Richard D. Irwin, IL, p 420
Smith M, Kohn R (1996) Nonparametric regression using bayesian variable selection. J Econ 75:317–367
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mostofi, A.G., Behboodian, J. On model selection in Bayesian regression. Metrika 66, 259–268 (2007). https://doi.org/10.1007/s00184-006-0109-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0109-0