TITLE:
Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach
AUTHORS:
Georges Nguefack-Tsague, Walter Zucchini
KEYWORDS:
Model Selection Uncertainty, Model Uncertainty, Bayesian Model Selection, Bayesian Model Averaging, Bayesian Theory, Frequentist Performance
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.10,
June
22,
2016
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 proposed method, using Bayesian decision theory, is based on the
well known Bayesian model averaging (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.