covMat: Calculate a covariance matrix

In GPFDA: Gaussian Process for Functional Data Analysis

Calculate a covariance matrix

Description

Evaluates one of the following covariance functions at input vectors t and t':

• Powered exponential

• Rational quadratic

• Matern

• Linear

Usage

cov.pow.ex(hyper, input, inputNew = NULL, gamma = 2)

cov.rat.qu(hyper, input, inputNew = NULL)

cov.matern(hyper, input, inputNew = NULL, nu)

cov.linear(hyper, input, inputNew = NULL)

Arguments

hyper	The hyperparameters. It must be a list with certain names. See details.
input	The covariate t. It must be either a matrix, where each column represents a covariate, or a vector if there is only one covariate.
inputNew	The covariate t'. It also must be a vector or a matrix. If NULL (default), 'inputNew' will be set to be equal to ‘input’ and the function will return a squared, symmetric covariance matrix.
gamma	Power parameter used in powered exponential kernel function. It must be 0<gamma<=2. Default to 2, which gives the squared exponential covariance function.
nu	Smoothness parameter of the Matern class. It must be a positive value.

Details

The names for the hyperparameters should be:

• "pow.ex.v" and "pow.ex.w" (powered exponential);

• "rat.qu.v", "rat.qu.w" and "rat.qu.a" (rational quadratic);

• "matern.v" and "matern.w" (Matern);

• "linear.i" and "linear.a" (linear);

• "vv" (Gaussian white noise).

Value

A covariance matrix

References

Shi, J. Q., and Choi, T. (2011), “Gaussian Process Regression Analysis for Functional input”, CRC Press.

GPFDA documentation built on Sept. 11, 2023, 1:08 a.m.