kernel {dgpsi}

Initialize a Gaussian process node

Description

This function constructs a kernel object to represent properties of a Gaussian process node.

Usage

kernel(
  length,
  scale = 1,
  nugget = 1e-06,
  name = "sexp",
  prior_name = "ga",
  prior_coef = NULL,
  bounds = NULL,
  nugget_est = FALSE,
  scale_est = FALSE,
  input_dim = NULL,
  connect = NULL
)

Arguments

length

a vector of lengthscales. The length of the vector equals to:

1. either one if the lengthscales in the kernel function are assumed same across input dimensions; or

2. the total number of input dimensions, which is the sum of the number of feeding GP nodes in the last layer (defined by the argument input_dim) and the number of connected global input dimensions (defined by the argument connect), if the lengthscales in the kernel function are assumed different across input dimensions.

scale

the variance of a GP node. Defaults to 1.

nugget

the nugget term of a GP node. Defaults to 1e-6.

name

kernel function to be used. Either "sexp" for squared exponential kernel or "matern2.5" for Matérn-2.5 kernel. Defaults to "sexp".

prior_name

prior options for the lengthscales and nugget term: gamma prior ("ga"), inverse gamma prior ("inv_ga"), or jointly robust prior ("ref") for the lengthscales and nugget term. Set NULL to disable the prior. Defaults to "ga".

prior_coef

a vector that contains the coefficients for different priors:

• for the gamma prior, it is a vector of two values specifying the shape and rate parameters of the gamma distribution. Set to NULL for the default value c(1.6,0.3).

• for the inverse gamma prior, it is a vector of two values specifying the shape and scale parameters of the inverse gamma distribution. Set to NULL for the default value c(1.6,0.3).

• for the jointly robust prior, it is a vector of a single value specifying the a parameter in the prior. Set to NULL for the default value c(0.2). See the reference below for the jointly robust prior.

Defaults to NULL.

bounds

a vector of length two that gives the lower bound (the first element of the vector) and the upper bound (the second element of the vector) of all lengthscales of the GP node. Defaults to NULL where no bounds are specified for the lengthscales.

nugget_est

set to TRUE to estimate the nugget term or to FALSE to fix the nugget term as specified by the argument nugget. If set to TRUE, the value set to the argument nugget is used as the initial value. Defaults to FALSE.

scale_est

set to TRUE to estimate the variance (i.e., scale) or to FALSE to fix the variance (i.e., scale) as specified by the argument scale. Defaults to FALSE.

input_dim

a vector that contains either

1. the indices of GP nodes in the feeding layer whose outputs feed into this GP node; or

2. the indices of global input dimensions that are linked to the outputs of some feeding emulators, if this GP node is in the first layer of a GP or DGP, which will be used for the linked emulation.

When set to NULL,

1. all outputs from the GP nodes in the feeding layer feed into this GP node; or

2. all global input dimensions feed into this GP node.

Defaults to NULL.

connect

a vector that contains the indices of dimensions in the global input connecting to this GP node as additional input dimensions. When set to NULL, no global input connection is implemented. Defaults to NULL. When this GP node is in the first layer of a GP or DGP emulator, which will consequently be used for linked emulation, connect gives the indices of global input dimensions that are not connected to some feeding emulators. In such a case, set input_dim to a vector of indices of the remaining input dimensions that are connected to the feeding emulators.

Details

See further examples and tutorials at https://mingdeyu.github.io/dgpsi-R/.

Value

A 'python' object to represent a GP node.

References

Gu, M. (2019). Jointly robust prior for Gaussian stochastic process in emulation, calibration and variable selection. Bayesian Analysis, 14(3), 857-885.

Examples

## Not run: 

# Check https://mingdeyu.github.io/dgpsi-R/ for examples
# on how to customize DGP structures using kernel().

## End(Not run)