INLA SPDE Kernel usage

[Alokesh Manna]

Hello INLA Group,

 We considered the model:
\[
y_{nt} \sim\text{Pois}(\lambda_{nt}),\\
\lambda_{nt}= \exp(\beta_{0} + \sum_{i=1}^{13} \sum_{j=1}^{13} \beta_{ij} X_{nij} + \beta_{n}),
\]
where $n=1,\cdots,3939$ and $t=1,\cdots,300$. Here we consider $\beta_{0}$ as fixed effect, $\beta_{n} \sim N(0, \frac{1}{\tau})$ as random effect. We also considered the image location-specific effect as a random effect, which we considered as an SPDE kernel; i.e. (\beta_{ij}) as a vector follows SPDE kernel. 

Q1. Is there any inla formulation that can handle SPDE accordingly?

Q2: What if we make the model a little more complicated to be spatio-temporal? Instead of \beta_{ij} we want \beta_{ijt}. Is there any formulation that can work?

Ultimately, the goal is to work as 

formula <- y ~ 1 +
  f(rep_id, model = "iid") +
  f(spatial_field, model = spde)..

[Håvard Rue]

so the log-mean is like a local weighted average?

> --
> You received this message because you are subscribed to the Google Groups "R-
> inla discussion group" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to r-inla-discussion...@googlegroups.com.
> To view this discussion, visit
> https://groups.google.com/d/msgid/r-inla-discussion-group/1601d4e9-53c8-448c-a9d9-167498a31dd1n%40googlegroups.com
> .

--
Håvard Rue
hr...@r-inla.org

[Alokesh Manna]

Yes. If we have 3*3 instead of 13*13, simulated data is given in the screenshot.

We want to model as;

\[\lambda_{nt}= \exp(\beta_{0} + \sum_{i=1}^{3} \sum_{j=1}^{3} \beta_{ij} X_{nij} + \beta_{n}),\],

where \lambda_{nt} is the average of n the rep_id and t th time_bin_num.

[Helpdesk (Haavard Rue)]

This is most easy done using this new feature (which I think is going to stick
and not change, but I cannot be 100% sure, but it has not changed for a long,
measured in developer years, time.

test on easy examples to make sure you get it right...

Best
Havard

he...@r-inla.org