Principles for Predictive
Optimality: Computational Examples
In many data gathering contexts, so little
physical modeling
information is available that a Statistician might default to a
predictive
optimality criterion. Even in such complicated settings, there
may be general principles that can be invoked to guide the
statistical modeling procedure.
In this talk three heuristic candidate statistical principles will be
stated
and explored in computational settings. They are: 1) A `principle
of
matching' between the model and the function space in a regression
context. 2) A generalized variance bias analysis to account for
model
uncertainty and mis-specification. 3) A data summarization principle
relating
the number of statistics sample size and cluster number in a short fat
data
context.
This is very much work in progress, so comments and discussion will be
truly
appreciated.