Deriving proper uniform priors for regression coefficients, Parts I, II, and III

Journal article (2017)

Authors

H.R.N. van Erp Safety and Security Science - TPM
R.O. Linger Safety and Security Science - TPM
P.H.A.J.M. van Gelder Safety and Security Science - TPM
Research Group
Safety and Security Science (TPM) (TU Delft)
Copyright: © 2017 H.R.N. van Erp, R.O. Linger, P.H.A.J.M. van Gelder
DOI: https://doi.org/10.3390/e19060250
Bayesian Model selection Splines Non-linear Regression analysis Regression coefficients Akaike Information Criterion (AIC) Bayesian Information Criterion (BIC) Proper uniform priors
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Published Date

2017

Language

English

Faculty

Technology, Policy and Management

Department

Values Technology and Innovation

Research Group

Safety and Security Science

Abstract

It is a relatively well-known fact that in problems of Bayesian model selection, improper priors should, in general, be avoided. In this paper we will derive and discuss a collection of four proper uniform priors which lie on an ascending scale of informativeness. It will turn out that these priors lead us to evidences that are closely associated with the implied evidence of the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). All the discussed evidences are then used in two small Monte Carlo studies, wherein for different sample sizes and noise levels the evidences are used to select between competing C-spline regression models. Also, there is given, for illustrative purposes, an outline on how to construct simple trivariate C-spline regression models. In regards to the length of this paper, only one half of this paper consists of theory and derivations, the other half consists of graphs and outputs of the two Monte Carlo studies.