Inf in the posterior mean prediction and converge time

[何博文]

Hi,

I want to fit a spatial Poisson model to predict the mean values on the finer grids from the coarser block areal. My posterior mean prediction for the finer grids has some unexpected larger values and some Infs that are definitely not appropriate. I am wondering what could be the potential reason for the Inf prediction from the model?

Also, when I increase the resolution of the finer grids, the number of prediction locations increases significantly and the model fitting process seems to need a significant amount of more time to converge. How can I manage the model fitting time so that I can control the resolution of the grids so that the model can converge in a reasonable amount of time (progress bar or control parameter)?

Thanks,

Bowen

[Helpdesk]

this depends on details of the model, but with finer and finer
resolution you introduce singuarities in the model and numerical
singularities even before that.

also when increasing the resolution, you have to make sure the prior(s)
are changed accordingly, otherwise you are using a different model every
time

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Håvard Rue
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[何博文]

Thanks for the reply! 

Just to want to clarify why the prior(s) have to be changed accordingly with the increasing resolution if I only have non-informative priors? The increasing resolution of the prediction grids doesn't change the model's hyperparameter structure and why not the non-informative priors can be used across those different resolution model?

The verbose=TRUE indicates the following and never changes. Is it because the singularity problem?

Optimise using DEFAULT METHOD

Smart optimise part I: estimate gradient using forward differences

Thanks,

Bowen

[Finn Lindgren]

The resolution vs prior issue is for some models, but not all. For
spde models, the mesh maps to a continuous domain, keeping the range
parameter interpretation intact when the mesh resolution is changed,
but for graph based models (bym2 etc), the "distance" unit is always
1, so finer resolution changes the real world interpretation of the
range parameters.

Finn

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Finn Lindgren
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