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Document Type
Article
Date of this Version
2017
Citation
2017 International Society for Bayesian Analysis
Abstract
In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model averaging procedure that gives a composite predictor by combining individual predictors from a list of models using weights that optimize a cross validation criterion. We show that the stacking weights also asymptotically minimize a posterior expected loss. Hence we formally provide a Bayesian justification for cross-validation. Often the weights are constrained to be positive and sum to one. For greater generality, we omit the positivity constraint and relax the ‘sum to one’ constraint.
Comments
Bayesian Analysis (2017) 12, Number 3, pp. 807–829