Myriads of model selection criteria (Bayesian and frequentist) have been proposed in the literature aiming at selecting a single model regardless of its intended use. An honorable exception in the frequentist perspective is the “focused information criterion” (FIC) aiming at selecting a model based on the parameter of interest (focus). This paper takes the same view in the Bayesian context; that is, a model may be good for one estimand but bad for another. The proposed method exploits the Bayesian model averaging (BMA) machinery to obtain a new criterion, the focused Bayesian model averaging (FoBMA), for which the best model is the one whose estimate is closest to the BMA estimate. In particular, for two models, this criterion reduces to the classical Bayesian model selection scheme of choosing the model with the highest posterior probability. The new method is applied in linear regression, logistic regression, and survival analysis. This criterion is specially important in epidemiological studies in which the objective is often to determine a risk factor (focus) for a disease, adjusting for potential confounding factors. 1. Introduction A variety of model selection criteria (Bayesian or frequentist) have been proposed in the literature; most of them aim at selecting a single model for any purposes. For an overview of model selection criteria, see the studies by Leeb and Poetscher [1] and Zucchini [2]; for inference after model selection, see the studies by Nguefack-Tsague [3], Nguefack-Tsague and Zucchini [4], Zucchini et al. [5], Behl et al. [6], and Nguefack-Tsague [7–9]. Allen [10], within the context of Mallows’ [11], developed a criterion that depends on a given prediction. In a frequentist approach, Claeskens and Hjort [12] developed a focused information criterion (FIC) for model selection which, unlike common model selection criteria that lead to a single model for all purposes, selects different models for different purposes. Thus Allen’s criterion can be considered as an early precursor of FIC. So far the FIC is gaining in popularity as evidenced by its applications in various fields and specific models. Some of these applications include missing response (Sun et al. [13]), energy substitution (Behl et al. [6]), economic applications (Behl et al. [14]), Tobit model (Zhang et al. [15]), additive partial models (Zhang and Liang [16]), volatility forecasting (Brownlees and Gallo [17]), and Cox proportional hazard regression models (Hjort and Claeskens [18]). Focused information criterion and model averaging can be found in the studies by Sueishi
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