Marginal log-likelihood

[Isabella K]

Hi INLA experts,

Could someone please clarify what is the interpretation of the mlik output? I just wanted to be sure that it is actually giving me p(y) only (where y is data), integrating out everything else, hyperparameters, fixed effects etc. Any changes in how it's calculated when using a spde model, or is it done like described in Rue et al. (2009)?

Also, when using the zero fake data trick in more complicated state space models, is there any smart way of ignoring these artificial data in the mlik in INLA?

Any help is much appreciated. Thanks!

[Haakon Bakka]

Hi Isabella,

This is not so easy to know. See for example inla.doc(‘rw2’), the documentation says that the normalisation constant is not computed, and you have to add it to get the correct mlik. It also depends on whether all your priors are properly normalised.

Please provide the formulas of the models you want to compare.

Haakon

[INLA help]

Hi,


as Haakon says, with the exception of some intrinsic models for which
the normalizing constant is not computed, the result$mlik should be the
estimated log marginal likelihood, which is \pi(y)

H

On Mon, 2016-05-16 at 02:21 -0700, Haakon Bakka wrote:
> Hi Isabella,
>
> This is not so easy to know. See for example inla.doc(‘rw2’), the
> documentation says that the normalisation constant is not computed,
> and you have to add it to get the correct mlik. It also depends on
> whether all your priors are properly normalised.
>
> Please provide the formulas of the models you want to compare.
>
> Haakon
>

> > Hi INLA experts, 
> >
> > Could someone please clarify what is the interpretation of the mlik
> > output? I just wanted to be sure that it is actually giving me p(y)
> > only (where y is data), integrating out everything else,
> > hyperparameters, fixed effects etc. Any changes in how it's
> > calculated when using a spde model, or is it done like described in
> > Rue et al. (2009)?
> >
> > Also, when using the zero fake data trick in more complicated state
> > space models, is there any smart way of ignoring these artificial
> > data in the mlik in INLA? 
> >
> > Any help is much appreciated. Thanks!
> >
> >

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[Isabella K]

Thank you very much, Haakon and Dr. Rue. I appreciate the clarification.

Regarding the approximation method for the marginals of the latent field, could anyone clarify what is the default in inla()? There are 3 methods proposed in Rue (2009) paper, and I believe the Laplace approximation one is the default, but wanted to confirm. I couldn't find this information in the help files, and sorry if I missed it somewhere.

-I

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[Elias T Krainski]

Hi Isabela,

The default is 'simplified.laplace'. You can change to Laplace by
  control.inla=list(strategy='laplace')

See also the new correction in
http://arxiv.org/abs/1503.07307

Elias

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[Isabella K]

Much appreciated. Thanks, Elias!

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