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grantbrown / inla

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Marginals for fitted values #18

Open GoogleCodeExporter opened 9 years ago

GoogleCodeExporter commented 9 years ago 
Currently the posterior marginals for the fitted values are computed from the 
posterior marginals of the linear predictor, using the inverse.link. 

As the postmarg for the lin.pred is a mixture, it would be more correct to 
transform each term in the mixture and then form the postmarg for the fitted 
values. 

When the inverse.link depends on the hyperarameters, then this becomes more 
important, but the post.margs for the fitted values, as each term in the 
mixture, can have an awkward shape, like having a spike near zero for a postive 
variable, hence the density-routines in inla will fail, as their design is not 
intended for that case. It is really really awkward. 

Therefore with hyperparameters in the link, then the mode-configuration is used 
to transform the postmarg for the linear predictor and this defines the 
postmarg for the fitted values. 

Quite a lot of work is needed to fix this properly

Original issue reported on code.google.com by havard.rue on 25 May 2013 at 12:35

GoogleCodeExporter commented 9 years ago 
The above explanation is unclear. When the link function is fixed, it is OK to 
compute the postmarg for the fitted values from the postmarg of the linear 
predictor, but not when the link function depends on hyperparameters.

Original comment by havard.rue on 26 May 2013 at 11:09