D2 {GPFDA}

Second derivative of the likelihood

Description

Calculate the second derivative of the likelihood function with respect to one of the hyperparameters, given the first and second derivative of the kernel with respect to that hyperparameter.

Usage

D2(d1, d2, inv.Q, Alpha.Q)

Arguments

d1

First derivative of the kernel function with respect to the required hyperparameter.

d2

Second derivative of the kernel function with respect to the required hyperparameter.

inv.Q

Inverse of covariance matrix Q.

Alpha.Q

This is alpha * alpha'- invQ, where invQ is the inverse of the covariance matrix Q, and alpha = invQ * Y, where Y is the response.

Details

The function calculates the second derivative of the log-likelihood, using the first and second derivative of the kernel functions.

Value

A number.

References

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

Examples

## This function is used in the vignette 'co2':
# vignette("co2", package = "GPFDA")