Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach

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.

A Mixture-Based Bayesian Model Averaging Method

Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.

Bayesian Rayleigh wave inversion with an unknown number of layers

Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.

Power-expected-posterior prior Bayes factor consistency for nested linear models with increasing dimensions

The power-expected-posterior prior is used in this paper for comparing nested linear models.The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior.Focus is given on the consistency of the Bayes factor of comparing the full model M_(p) versus a generic submodel M_(l).In each case,we allow the true generating model to be either M_(p) or M_(l) and we keep the dimension of M_(l) fixed,while the dimension of M_(p) can be either fixed or(grow as)O(n),with n denoting the sample size.