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Title: Using stacking to combine Bayesian predictive distributions Authors:  Yuling Yao - Columbia University (United States) [presenting]
Abstract: A general challenge in statistics is the prediction in the presence of multiple candidate models or learning algorithms. Bayesian model averaging is flawed in the M-open setting in which the true data generating process is not one of the candidate models being fit. Equipped with a proper scoring rule, stacking is a better approach to combine Bayesian predictive distributions. It yields asymptotically optimal predictions for future data and is more desired than single model selection. Furthermore, stacking can be used to combine posterior draws of one model and give better predictive performance than full Bayesian inference under misspecified models. Finally, we present that stacking can be combined with hierarchical modeling in structured data.