Models, model lists, model spaces and predictive optimality
Seminar Room 1, Newton Institute
Sources of uncertainty related to model specification are often the single biggest factors in inference. In the predictive context, we demonstrate the effect of varying the model list used for averaging and varying the averaging strategy in computational examples. In addition, by varying the model space while using similar lists and averaging strategies, we demonstrate that the effect of the space itself computationally. Thus, it is reasonable to associate a concept of variance and bias not just to individual models but to other aspects of an overall modeling strategy. Moreover, although difficult to formalize, good prediction is seen to be associated with a sort of complexity matching between the space and the unknown function, and robustness. In some cases, the relationship among complexity, variance-bias, robustness and averaging strategy seems to be dependent on sample size. Taken together, these considerations can be formalized into an overview that may serve as a framework for more general inferential problems in Statistics
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