A Variant of AIC Based on the Bayesian Marginal Likelihood

Yuki Kawakubo (), Tatsuya Kubokawa () and Muni S. Srivastava ()
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Yuki Kawakubo: Chiba University
Tatsuya Kubokawa: University of Tokyo
Muni S. Srivastava: University of Toronto

Sankhya B: The Indian Journal of Statistics, 2018, vol. 80, issue 1, No 4, 60-84

Abstract: Abstract We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models, assuming a prior distribution of the regression coefficients. Then, we discuss the relationship between the proposed criteria and related criteria. There are three advantages of our method. First, this is a compromise between the frequentist and Bayesian standpoints because it evaluates the frequentist’s risk of the Bayesian model. Thus, it is less influenced by a prior misspecification. Second, the criteria exhibits consistency when selecting the true model. Third, when a uniform prior is assumed for the regression coefficients, the resulting criterion is equivalent to the residual information criterion (RIC) of Shi and Tsai (J. R. Stat. Soc. Ser. B 64, 237–252 2002).

Keywords: AIC; BIC; Consistency; Kullback–Leibler divergence; Linear regression model; Residual information criterion; Variable selection; Primary 62J05; Secondary 62F12 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13571-018-0152-7

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