Model Selection and Accounting for Uncertainty
Abstract
Statistical modeling is about finding general laws from observed data, which amounts to extracting information from the data. We are to admit no more causes of natural things (as we are told by Newton) than such as are both true and sufficient to explain their appearances. This central theme is basic to the pursuit of science, and goes back to the principle known as Occam's razor: `if presented with a choice between indifferent alternatives, then one ought to select the simplest one.' Reliable inferences allow one to make good predictions and decisions regarding the data under a much wider variety of assumptions than unreliable inferences do. It will allow us to establish in what way we can, and in what way we cannot, use overly simple models. In general, we will be interested in what can be reliably predicted - and what not - from a model that is only partially correct. We describe a new procedure called entropification. With an entropified model, if given enough data, we can find the model with the smallest expected prediction error. This model will provide a correct estimate of the average prediction error that it will achieve; hence the model gives a good impression of `how good it really is.'
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 2005
- Accession Number
- ADA451610
Entities
People
- C. V. Van Wijk
- H. W. Naus