Is 'Which model ...' the right question?
This paper presents a critique of the standard two-stage approach in
which a well-fitting model is identified first, and then applied in
one or several subsequent inferences.
Although deeply ingrained in practice, this approach is deficient
because the possibility of an erroneous decision in the model
selection (model uncertainty) is discounted.
The criticism applies to all model selection procedures,
equally in the frequentist and Bayesian perspectives.
We describe an approach based on synthetic estimation, in which
the estimators based on the candidate models are linearly combined.
Its properties are explored in the setting of an experiment from