Parametric stationary covariance models¶
The multivariate exponential model
This model defines the covariance function by:
(1)¶
where is a
correlation matrix,
is defined by:
(2)¶
and is defined by:
(3)¶
with and
for any
.
We call the amplitude vector and
the scale vector.
The expression of
is the combination of:
the matrix
that models the spatial correlation between the components of the process
at any vertex
(since the process is stationary):
(4)¶
the matrix
that models the correlation between the marginal random variables
and
:
the matrix
that models the variance of each marginal random variable:
This model is such that:
(5)¶
It is possible to define the exponential model from the spatial
covariance matrix rather than the correlation
matrix
:
(6)¶
API:
See
ExponentialModel
See
MaternModel
Examples: