Groupe d’études et de recherche en analyse des décisions

Models, Model Lists, Model Spaces, and Predictive Optimality

Bertrand Clarke

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. In some cases, the relationship among complexity, variance-bias, and averaging strategy seem to be dependent on sample size.