Bayesian spatial models in INLA

The linear predictor (latent Gaussian random field) is the model of a parameter of the likelihood distribution, transformed with the link function.

E.g. using log link for parameter \(\mu_i\):

\[\eta_i = ln(\mu_i) = X_i \cdot \beta + Z_i\]

E.g. using logit link for parameter \(\pi_i\):

\[\eta_i = ln(\frac{\pi_i}{1 - \pi_i}) = X_i \cdot \beta + Z_i\]