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

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

van Erp, H.R.N. (TU Delft Safety and Security Science)
Linger, R.O. (TU Delft Safety and Security Science)
van Gelder, P.H.A.J.M. (TU Delft Safety and Security Science)

2017

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.

Akaike Information Criterion (AIC)
Bayesian
Bayesian Information Criterion (BIC)
Model selection
Non-linear
Proper uniform priors
Regression analysis
Regression coefficients
Splines

http://resolver.tudelft.nl/uuid:e6774049-9163-42aa-b115-d6cb4463cc72

https://doi.org/10.3390/e19060250

1099-4300

Entropy: international and interdisciplinary journal of entropy and information studies, 19 (6), 1-56

Institutional Repository

journal article

© 2017 H.R.N. van Erp, R.O. Linger, P.H.A.J.M. van Gelder