scores: Generic Function: Scores for a Covariance Kernel Object

In kergp: Gaussian Process Laboratory

Generic Function: Scores for a Covariance Kernel Object

Description

Generic function returning the scores for a covariance kernel object.

Usage

scores(object, ...)

Arguments

object	A covariance object.
...	Other arguments passed to methods.

Details

Compute the derivatives \partial_{\theta_k}\ell for the (possibly concentrated) log-likelihood \ell := \log L of a covariance object with parameter vector \boldsymbol{\theta}. The score for \theta_k is obtained as a matrix scalar product

\partial_{\theta_k} \ell = \textrm{trace}(\mathbf{W} \mathbf{D})

where \mathbf{D} := \partial_{\theta_k} \mathbf{C} and where \mathbf{W} is the matrix \mathbf{W} := \mathbf{e}\mathbf{e}^\top - \mathbf{C}^{-1} . The vector \mathbf{e} is the vector of residuals and the matrix \mathbf{C} is the covariance computed for the design \mathbf{X}.

Value

A numeric vector of length npar(object) containing the scores.

Note

The scores can be efficiently computed when the matrix \mathbf{W} has already been pre-computed.

kergp documentation built on April 4, 2025, 2:29 a.m.