varKernel: Compute the kernel of the Variance Kovariance operator

In DistributionalDDA: Distributional Data Analysis in Bayes Spaces

Compute the kernel of the Variance Kovariance operator

Description

Variance in Bayes spaces can be expressed in various forms. The variance kernel is essentially the covariance function of the clr-transform of a random variable:

Usage

varKernel(X, ...)

## S3 method for class 'BDataSplines'
varKernel(X, ...)

## S3 method for class 'BData'
varKernel(X, ...)

## S3 method for class ''function''
varKernel(X, basis = getBayesSpaceBasis(X), ...)

## S3 method for class 'varKernel'
varKernel(X, basis = getBayesSpaceBasis(X), ...)

Arguments

X	a dataset of BData objects
...	further parameters detailing computation
basis	the BayesSpaceBasis for which this covariance kernel is valid

Details

c(x,y) = cov( clr(X)(x),clr(X)(y))

Value

a function of two arguments with a basis attribute representing the BayesSpaceBasis, and varKernel class.

Methods (by class)

• varKernel(BDataSplines): method for BDataSplines uses the covariance of the spline coefficients to compute

• varKernel(BData): default method for BData computes implicitly using clr transforms.

• varKernel(`function`): constructor

• varKernel(varKernel): method for varKernel, keeps the kernel, possibly overwrites the basis.

See Also

plot.varKernel, variationKernel

Examples

data(DTD)
X = BDataPDFs(DTD$shapePDF,basis=B2Unif01Basis5)
C = varKernel(X)
C
plot(C)

K = BDataSplines(matrix(rnorm(10*5),ncol=5),basis=B2Unif01Basis5)
var(K)
C2 = varKernel(K)
C2
plot(C2)

DistributionalDDA documentation built on Oct. 20, 2026, 5:06 p.m.