Applied Mathematics, 2016, 7, 1103-1115 Published Online June 2016 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2016.710098 How to cite this paper: Nguefack-Tsague, G. and Zucchini, W. (2016) Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach. Applied Mathematics, 7, 1103-1115. http://dx.doi.org/10.4236/am.2016.710098 Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach Georges Nguefack-Tsague 1 , Walter Zucchini 2 1 Biostatistics Unit, Department of Public Health, Faculty of Medicine and Biomedical Sciences, University of Yaounde 1, Yaounde, Cameroon 2 Institute for Statistics and Econometrics, University of Goettingen, Goettingen, Germany Received 15 April 2016; accepted 19 June 2016; published 22 June 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance; i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The pro- posed method, using Bayesian decision theory, is based on the well known Bayesian model aver- aging (BMA)’s machinery; and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials. Keywords Model Selection Uncertainty, Model Uncertainty, Bayesian Model Selection, Bayesian Model Averaging, Bayesian Theory, Frequentist Performance 1. Introduction Statistical modeling usually deals with situation in which some quantity of interest is to be estimated from a sample of observations that can be regarded as realizations of some unknown probability distribution. In order to do so, it is necessary to specify a model for the distribution. There are usually many alternative plausible models