2015/03/24 by Yuki Kawakubo, Kawakubo, Yuki, Tatsuya Kubokawa +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1503.07102
openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (2002).