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In this article, we present a selective overview of some recent developments in Bayesian model and variable selection methods for high dimensional linear models. While most of the reviews in literature are based on conventional methods, we focus on recently developed methods, which have proven to be successful in dealing with high dimensional variable selection. First, we give a brief overview of the traditional model selection methods (viz. Mallow's Cp, AIC, BIC, DIC), followed by a discussion on some recently developed methods (viz. EBIC, regularization), which have occupied the minds of many statisticians. Then, we review high dimensional Bayesian methods with a particular emphasis on Bayesian regularization methods, which have been used extensively in recent years. We conclude by briefly addressing the asymptotic behaviors of Bayesian variable selection methods for high dimensional linear models under different regularity conditions.
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PMID:Bayesian Methods for High Dimensional Linear Models. 2451 33

Evidence accumulations models (EAMs) have become the dominant modeling framework within rapid decision-making, using choice response time distributions to make inferences about the underlying decision process. These models are often applied to empirical data as "measurement tools", with different theoretical accounts being contrasted within the framework of the model. Some method is then needed to decide between these competing theoretical accounts, as only assessing the models on their ability to fit trends in the empirical data ignores model flexibility, and therefore, creates a bias towards more flexible models. However, there is no objectively optimal method to select between models, with methods varying in both their computational tractability and theoretical basis. I provide a systematic comparison between nine different model selection methods using a popular EAM-the linear ballistic accumulator (LBA; Brown & Heathcote, Cognitive Psychology 57(3), 153-178 2008)-in a large-scale simulation study and the empirical data of Dutilh et al. (Psychonomic Bulletin and Review, 1-19 2018). I find that the "predictive accuracy" class of methods (i.e., the Akaike Information Criterion [AIC], the Deviance Information Criterion [DIC], and the Widely Applicable Information Criterion [WAIC]) make different inferences to the "Bayes factor" class of methods (i.e., the Bayesian Information Criterion [BIC], and Bayes factors) in many, but not all, instances, and that the simpler methods (i.e., AIC and BIC) make inferences that are highly consistent with their more complex counterparts. These findings suggest that researchers should be able to use simpler "parameter counting" methods when applying the LBA and be confident in their inferences, but that researchers need to carefully consider and justify the general class of model selection method that they use, as different classes of methods often result in different inferences.
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PMID:Assessing the practical differences between model selection methods in inferences about choice response time tasks. 3078 96

In practice, the capital asset pricing model (CAPM) using the parametric estimator is almost certainly being used to estimate a firm's systematic risk (beta) and cost of equity as in Eq. (1). However, the parametric estimators, even when data is normal, may not yield better performance compared with the non-parametric estimators when outliers existed. This research argued for the non-parametric Bayes estimator to be employed in the CAPM by applying both advance and basic evaluation criteria such as hypotheses/confidence intervals of the AIC/DIC, model variance, fit, and error, alpha, and beta and its standard deviation. Using all the S&P 500 stocks having monthly data from 07/2007-05/2019 (450 stocks) and the Bayesian inference, we showed the non-parametric Bayes estimator yielded less number of zeroed betas and smaller alpha compared with the parametric Bayes estimator. More importantly, this non-parametric Bayes yielded the statistically significantly smaller AIC/DIC, model variance, and beta standard deviation and higher model fit compared with the parametric Bayes estimator. These findings indicate the CAPM using the non-parametric Bayes estimator is superior compared with the parametric Bayes estimator, a contrast of common practice. Hence, the non-parametric estimator is recommended to be employed in asset pricing work.
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PMID:The systematic risk estimation models: A different perspective. 3207 58