covTS | R Documentation |
covTS
Objects
Creator function for covTS
objects representing a Tensor Sum
covariance kernel.
covTS(inputs = paste("x", 1:d, sep = ""),
d = length(inputs), kernel = "k1Matern5_2",
dep = NULL, value = NULL, var = 1, ...)
inputs |
Character vector giving the names of the inputs used as arguments of
|
d |
Integer specifying the spatial dimension (equal to the number of
inputs). Optional if |
kernel |
Character, name of the one-dimensional kernel. |
dep |
Character vector with elements |
value |
Named numeric vector. The names must correspond to the 1d kernel parameters. |
var |
Numeric vector giving the variances |
... |
Not used at this stage. |
A covTS
object represents a d
-dimensional kernel object
K
of the form
K(\mathbf{x}, \mathbf{x}';
\boldsymbol{\theta}) = \sum_{i=1}^d k(x_i,
x_i';\boldsymbol{\theta}_{\mathbf{s}_i})
where k
is
the covariance kernel for a Gaussian Process Y_x
indexed by a scalar
x
. The d
numbers x_i
stand for the components of the
d
-dimensional location vector \mathbf{x}
. The length
p
of all the vectors \mathbf{s}_i
is the number of
parameters of the one-dimensional kernel k
, i.e. 2 or 3 for
classical covariance kernels.
The package comes with the following covariance kernels which can
be given as kernel
argument.
name | description | p | par. names |
k1Exp | exponential | 2 | range ,
var |
k1Matern3_2 | Matérn \nu = 3/2 | 2 |
range , var |
k1Matern5_2 | Matérn \nu = 5/2 | 2 |
range , var |
k1PowExp | power exponential | 3 | range ,
shape , var |
k1Gauss | gaussian or "square exponential" | 2 |
range , var |
Note that the exponential kernel of k1Exp
is identical to the
Matérn kernel for \nu = 1/2
, and that the three Matérns kernels
provided here for \nu = 1/2
, \nu = 3/2
and \nu = 5/2
are special cases of Continuous AutoRegressive (CAR) process
covariances, with respective order 1
, 2
and 3
.
An object with S4 class "covTS"
.
The 1d
kernel k
as given in kernel
is always
assumed to have a variance parameter with name var
. This
assumption may be relaxed in future versions.
Most arguments receive default values or are recycled if necessary.
Y. Deville, O. Roustant D. Ginsbourger
N. Durrande, D. Ginsbourger, and O. Roustant (2012) Additive "Covariance kernels for high-dimensional Gaussian Process modeling", Annales de la Faculté des Sciences de Toulouse 21(3), pp. 481–499.
myCov1 <- covTS(kernel = "k1Exp", inputs = c("v1", "v2", "v3"),
dep = c(range = "input"))
coef(myCov1) <- c(range = c(0.3, 0.7, 0.9), sigma2 = c(2, 2, 8))
myCov1
coef(myCov1)
coef(myCov1, as = "matrix")
coef(myCov1, as = "list")
coef(myCov1, as = "matrix", type = "range")
# with a common range parameter
myCov2 <- covTS(kernel = "k1Exp", inputs = c("v1", "v2", "v3"),
dep = c(range = "cst"), value = c(range = 0.7),
var = c(2, 2, 8))
myCov2
myCov3 <- covTS(d = 3, kernel = "k1PowExp",
dep = c(range = "cst", shape = "cst"),
value = c(shape = 1.8, range = 1.1),
var = c(2, 2, 8))
myCov3
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