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

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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.

Original languageEnglish
Article number250
Pages (from-to)1-56
Number of pages56
JournalEntropy: international and interdisciplinary journal of entropy and information studies
Issue number6
Publication statusPublished - 2017


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

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