Bayesian Model Averaging and Model Search Strategies (original) (raw)
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arXiv: Computation, 2016
In this paper we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior elicitation, summaries of the posterior distribution and computational strategies. We then examine and compare various publicly available {\tt R}-packages for its practical implementation summarizing and explaining the differences between packages and giving recommendations for applied users. We find that all packages reviewed lead to very similar results, but there are potentially important differences in flexibility and efficiency of the packages.
Methods and Tools for Bayesian Variable Selection and Model Averaging in Normal Linear Regression
International Statistical Review, 2018
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Bayesian Model Selection and Model Averaging
Journal of Mathematical Psychology, 2000
This paper reviews the Bayesian approach to model selection and model averaging. In this review, I emphasize objective Bayesian methods based on noninformative priors. I will also discuss implementation details, approximations, and relationships to other methods.
Bayesian model selection and averaging via mixture model estimation
2018
A new approach for Bayesian model averaging (BMA) and selection is proposed, based on the mixture model approach for hypothesis testing in [12]. Inheriting from the good properties of this approach, it extends BMA to cases where improper priors are chosen for parameters that are common to all candidate models. From an algorithmic point of view, our approach consists in sampling from the posterior distribution of the single-datum mixture of all candidate models, weighted by their prior probabilities. We show that this posterior distribution is equal to the ‘Bayesian-model averaged’ posterior distribution over all candidate models, weighted by their posterior probability. From this BMA posterior sample, a simple Monte-Carlo estimate of each model’s posterior probability is derived, as well as importance sampling estimates for expectations under each model’s posterior distribution.
Adaptive MC^ 3 and Gibbs algorithms for Bayesian Model Averaging in Linear Regression Models
The MC 3 (Madigan and and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each iteration using uniform selection probabilities and then propose to update that variable. This may be computationally inefficient if the number of variables is large and many variables are redundant. In this work, we introduce adaptive versions of these samplers that retain their simplicity in implementation and reduce the selection probabilities of the many redundant variables. The improvements in efficiency for the adaptive samplers are illustrated in real and simulated datasets.
Bayesian Model Selection in High-Dimensional Settings
Journal of the American Statistical Association, 2012
Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariates p is bounded by the number of observations n, a property that has not been extended to other model selection procedures. In addition to consistently identifying the true model, the proposed procedures provide accurate estimates of the posterior probability that each identified model is correct. Through simulation studies, we demonstrate that these model selection procedures perform as well or better than commonly used penalized likelihood methods in a range of simulation settings. Proofs of the primary theorems are provided in the Supplementary Material that is available online.
Mixtures of g-priors for Bayesian model averaging with economic applications
2010
This paper examines the issue of variable selection in linear regression modeling, where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. The main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. The authors combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, they assign a hyperprior to g, as the choice of g has been found to have a large impact on the . The authors may be contacted at M.F.Steel@stats.warwick.ac.uk and eley@worldbank.org .
Bayesian model averaging via mixture model estimation
arXiv: Methodology, 2017
A new approach for Bayesian model averaging (BMA) and selection is proposed, based on the mixture model approach for hypothesis testing in Kaniav et al., 2014. Inheriting from the good properties of this approach, it extends BMA to cases where improper priors are chosen for parameters that are common to all candidate models. From an algorithmic point of view, our approach consists in sampling from the posterior distribution of the single-datum mixture of all candidate models, weighted by their prior probabilities. We show that this posterior distribution is equal to the 'Bayesian-model averaged' posterior distribution over all candidate models, weighted by their posterior probability. From this BMA posterior sample, a simple Monte-Carlo estimate of each model's posterior probability is derived, as well as importance sampling estimates for expectations under each model's posterior distribution.
Mixtures of -priors for Bayesian model averaging with economic applications
Journal of Econometrics, 2012
This paper examines the issue of variable selection in linear regression modeling, where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. The main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. The authors combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, they assign a hyperprior to g, as the choice of g has been found to have a large impact on the . The authors may be contacted at M.F.Steel@stats.warwick.ac.uk and eley@worldbank.org .
Clustered Bayesian Model Averaging
Bayesian Analysis, 2013
It is sometimes preferable to conduct statistical analyses based on the combination of several models rather than on the selection of a single model, thus taking into account the uncertainty about the true model. Models are usually combined using constant weights that do not distinguish between different regions of the covariate space. However, a procedure that performs well in a given situation may not do so in another situation. In this paper, we propose the concept of local Bayes factors, where we calculate the Bayes factors by restricting the models to regions of the covariate space. The covariate space is split in such a way that the relative model efficiencies of the various Bayesian models are about the same in the same region while differing in different regions. An algorithm for clustered Bayes averaging is then proposed for model combination, where local Bayes factors are used to guide the weighting of the Bayesian models. Simulations and real data studies show that clustered Bayesian averaging results in better predictive performance compared to a single Bayesian model or Bayesian model averaging where models are combined using the same weights over the entire covariate space.