[R] question about AIC

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Nov 16 10:33:54 CET 2004

On Tue, 16 Nov 2004 dlavecchia at tiscali.it wrote:

> we are a pool of phd students and we have a question about AIC. We are interested
> in calculating the AIC for a mixture model on galaxies data. So far we have
> found AIC works only for regression models, whereas we need AIC for a mixture
> of Normal with mean, sd and weights given by our  EM algorithm.

What is the problem?  The concept AIC or the function AIC()?  If the 
concept, it was originally developed in the area of AR(p) time series 
models, using asymptotic theory for MLEs, and you need to check that the 
concepts apply to your situation (the original papers do not).

Note there are some fundamental problems here: the likelihood for a 
mixture of normals is unbounded, the MLE corresponding to degenerate 
(zero-variance) components.  And AIC is about maximized likelihoods, with 
maxima in the interior of the space.  So you need to take some 
professional statistical advice about the concepts.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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