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Entropy 2017, 19(6), 250; doi:10.3390/e19060250

Deriving Proper Uniform Priors for Regression Coefficients, Parts I, II, and III

1
Safety and Security Science Group, TU Delft, Delft 2628 BX, The Netherlands
2
Safety and Security Institute, TU Delft, Delft 2628 BX, The Netherlands
This is an extended version of the original MaxEnt 2016 conference paper: Deriving Proper Uniform Priors forRegression Coefficients, Part II, in which the main result of the first part of this research has been integratedand to which new theoretical insights and more extensive Monte Carlo study outputs have been added.
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Author to whom correspondence should be addressed.
Received: 24 February 2017 / Revised: 7 April 2017 / Accepted: 27 April 2017 / Published: 30 May 2017
(This article belongs to the Special Issue Selected Papers from MaxEnt 2016)

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. View Full-Text
Keywords: proper uniform priors; regression coefficients; Bayesian; model selection; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); non-linear; regression analysis; splines proper uniform priors; regression coefficients; Bayesian; model selection; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); non-linear; regression analysis; splines
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Erp, H.N.; Linger, R.O.; Gelder, P.H. Deriving Proper Uniform Priors for Regression Coefficients, Parts I, II, and III . Entropy 2017, 19, 250.

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