scores {kergp}R Documentation

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

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

where D:=θkC\mathbf{D} := \partial_{\theta_k} \mathbf{C} and where W\mathbf{W} is the matrix W:=eeC1 \mathbf{W} := \mathbf{e}\mathbf{e}^\top - \mathbf{C}^{-1} . The vector e\mathbf{e} is the vector of residuals and the matrix C\mathbf{C} is the covariance computed for the design X\mathbf{X}.

Value

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

Note

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


[Package kergp version 0.5.7 Index]