Question about Rue et al. 2009 INLA paper

[Guillermina Senn]

Hi Håvard and team.

In Section 1.3 in the INLA paper the authors define a LGM. They write the density of the latent field x conditional to a hyperparameter vector Theta1, and the density of y conditional to a hyperparameter vector Theta2. Later they join Theta1 and Theta2 into one unique hyperparameter vector Theta.

I'm new to the topic and I'm not sure I understand correctly the logic behind this formulation. Could you give an example of a hyperparameter that could go into Theta2?

Thank you 

Guillermina

[Elias T. Krainski]

Example,

  y_i | x_i ~ N(x_i, a^2)

x_i ~ N(x_{i-1}, b^2)

so, x depends on b and y conditional on x depends on a, where a and b are hyperparameters. Generally speaking, one is the parameters of x (the latent field parameters -> hyperparameters) and the other of y conditional on y (the likelihood hyperparameters).

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[Elias T. Krainski]

... of y conditional on x (the likelihood hyperparameters).

[Guillermina Senn]

Understood. Thank you Elias!