
108 Current Trends in Bayesian Methodology with Applications
The hyper-parameter τ appearing above is given a Wishart distribution in
this hierarchical structure.
τ ∼ W ishart (I
N×N
, N) .
In the above framework, the spatial dependence within a given block of
(latitude, longitude, depth)-level is captured by commo n parameters, while
between-block dependencies a re captured by shared hyper-parameters. Tem-
poral dependencies are captured by the built-in dependence structure for e ach
longitude and depth block in the precision matrices Θ
i
’s, and in the share d
dependencies in the η
i
’s. Note that it is guaranteed that we have a proper pos-
terior distribution, ...