Gaussian likelihood model with fixed precision

[Zhe Sha]

Hi,

I want to estimate and predict a Gaussian likelihood model with spde latent field and I want to fix the error term in the Gaussian likelihood model with given values. 

Suppose my data frame looks like this

ID   ydata   std 

1    y1        s1

2    y2        s2

3    y3        s3

...  ...         ...

I want to use the value in the column "std" to be the Gaussian likelihood errors, so I fix the precision to be 1 and use 1/std for scale. Below are my codes.

st.est <- inla.stack(data = list(y=ydata), A = list(Ay), 

                     effects = list(spde = 1:n.spde), tag = "est")

st.pred <- inla.stack(data = list(y=NA), A = list(Ay), 

                      effects = list(spde=1:n.spde), tag = "pred")

st <- inla.stack(st.est, st.pred)

## Fix the sigma_e^2 to be 1 and scale them according to the data in inla(...,scale = scale)

## Default uses log(1/sigma_e^2) to be loggamma distribution with intial value = 0.

hyper <- list(prec = list(fixed = TRUE, initial = 0))

formula = y ~ -1 + f(spde, model = my_spde)

prec_scale <- rep(1/std, 2)

res_inla <- inla(formula, data = inla.stack.data(st, spde = spde), family = "gaussian", 

                      scale = prec,_scale, control.family = list(hyper = hyper),

                      control.predictor=list(A=inla.stack.A(st), compute =TRUE))

Just wondering if I have done it correctly in INLA, especially about setting up the scale. Is the resulted variance 1/(scale*prec) or 1/(scale*prec)^2? 

i.e Should I use scale = 1/std or scale = 1/std^2 ?

Also, when I want to predict at the data location, should I also provide the scale or just leave them to be one?

i.e Should I use scale = rep(1/std, 2) or  scale = c(1/std, rep(1, length(ydata)) ?

Thanks for your attention and help!

Zhe

[Elias T Krainski]

Hi Zha,

If you want the predictions at the data locations, there is no need for a new stack as such predictions will be already computed if asked, just set compute=TRUE in control.predictor().

The 'scale' is the scale for the precision, which is the inverse of the squared standard deviation.

Best,

Elias

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