Replicated Spatial-Temporal Correlation – inlabru

[Brian Tavernia]

Using the INLA package, one can specify a replicated spatial-temporal correlation by including a term that includes the spde model (‘spde’), spde index (‘w’), and a vector of replications (‘w.repl’):

f(w, model = spde, replicate = w.repl)

How does one create the same type of correlation using a bru formula?  Are there multiple ways to do this?

In an August 22 post on this forum, Tim Meehan created a replicated spatial-temporal correlation by passing the model = ‘iid’ argument to his field_residuals component in the model formula.

However, when looking at the available arguments for a bru component, I see a replicate argument, and this suggest to me that it might also be possible to specify a replicated spatial-temporal correlation by passing the replicate argument to a bru component?  

Am I correct about the potential use of the replicate argument in the bru component?

Thanks!

[Finn Lindgren]

Hi,

The basic use of replicate in inlabru works the same way as for non-SPDE models. The odd one out is actually the inla() SPDE models, where one needs to construct the A matrix first, which is why the w.repl construction is needed there. In inlabru, you would instead supply the replicate information directly in the component definition, e.g. like

+ field(geometry, model=spde, replicate=time)

(Assuming that replications across “time” are desired; replace it with your own variable of choice…)

One can also optionally use a custom mapper for the replicates, which for example would allow interpolation between replicates (this can make sense in some models, but usually it does not; it is more commonly useful for some “group” models).

Finn

On 10 Sep 2024, at 21:37, Brian Tavernia <btav...@gmail.com> wrote:



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[Brian Tavernia]

Thanks, Finn. 

[Courtney Taylor]

Hi Finn, 

I see this question has been closed for some time but I was wondering if it would it be possible to see the code for what such a custom mapper might look like? For example, if observations were non-uniformly sampled over time and we wanted to attempt to also account for the potential associated temporal autocorrelation.

Thanks very much. 

[Finn Lindgren]

Hi,

an easy case is if one wants to e.g. have 2nd degree B-spline basis functions such that the coefficients follow an ar1 process (via "group"), or independent (via "replicate"):

# mapper

b_spline_2_mapper <- bm_fmesher(fm_mesh_1d(temporal_knots, degree = 2, boundary = "free")))
# independent basis coefficients

field(geometry, model=spde, replicate=time, replicate_mapper = b_spline_2_mapper)
# ar1-dependent coefficients:
field(geometry, model=spde, group=time, group_mapper = b_spline_2_mapper, control.group=list(model="ar1"))

You could then choose the temporal_knots to have uniform spacing, linking the model to unevenly spaced observations (in geometry and time).

Finn 

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Finn Lindgren
email: finn.l...@gmail.com