Confidence sets for variable selection

Speaker: Dr Davide Ferrari (The University of Melbourne)
Time & Date: 1.00 pm EST; Friday 13 September 2013
Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus.

Abstract: We introduce the notion of variable selection confidence set (VSCS) for linear regression based on F-testing. The VSCS extends the usual notion of confidence intervals to the variable selection problem: A VSCS is a set of regression models that contains the true model with a given level of confidence. For noisy data, distinguishing among competing models is usually very difficult and the VSCS will contain many models; if the data are really informative, the VSCS will contain a much smaller number of useful models. We advocate special attention to the set of lower boundary models (LBMs), which are the most parsimonious models that are not statistically significantly inferior to the full model at a given confidence level. Based on the LBMs, variable importance and measures of co-appearance importance of predictors can be naturally defined.

Up to date, an almost exclusive emphasis has been on selecting a single model or two. In the presence of a number of predictors, especially when the number of predictors is comparable to (or even larger than) the sample size, the hope of identifying the true or the unique best model is often unrealistic. Consequently, a better approach is to select a relatively small set of models that all can more or less adequately explain the data at the given confidence level. This strategy identifies the most important variables in a principled way that goes beyond simply trusting the single lucky winner based on a model selection criterion.

Seminar Convenor: Dr Andriy Olenko (a.olenko@latrobe.edu.au)
AGR IT support: Dr Darren Condon (d.condon@latrobe.edu.au)

If you (and your colleagues) wish to participate, please

1. book your own AGR (or university/APAC etc. AGR that you otherwise are able to use), and ask your AGR technical people to contact Darren in advance of the seminar date; and
2. inform Andriy of your intention to participate.

This notice is available on the AMSI website: Events > AGR Events