1 Model Search, Selection, and Averaging.

Although some model selection procedures boil down to testing hypotheses about parameters and choosing the best parameter or a subset of parameters, model selection is a broader inferential task. It can be nonparametric, for example. Model selection sometimes can be interpreted as an estimation problem. If the competing models are indexed by i ∈ {1, 2, . . . , m}, getting the posterior distribution of an index i would lead to the choice of best model, for example, the model that maximizes posterior probability of i.