NormalKernel

The Normal kernel is denoted by

\[k(y\mid x) = \mathcal{N}(y ; \mu(x) , \Sigma(x) ).\]

As with the Normal distributions, the explicit expression on the kernel depends on whether it is real or complex valued.

Types

Type aliases

const AffineNormalKernel{T} = NormalKernel{T,<:AbstractAffineMap,<:CovarianceParameter}

Constructors

MarkovKernels.NormalKernel — Method
NormalKernel(Φ::AbstractMatrix, Σ)

Creates a NormalKernel with a linear conditional mean function given by

x ↦ Φ * x,

and conditional covariance function parameter Σ. Σ is assumed to be callable and be of compatible eltype with Φ.

source
MarkovKernels.NormalKernel — Method
NormalKernel(Φ::AbstractMatrix, b::AbstractVector, Σ)

Creates a NormalKernel with an affine conditional mean function given by

x ↦ b + Φ * x,

and conditional covariance function parameter Σ. Σ is assumed to be callable and be of compatible eltype with Φ, b.

source
MarkovKernels.NormalKernel — Method
NormalKernel(Φ::AbstractMatrix, b::AbstractVector, c::AbstractVector, Σ)

Creates a NormalKernel with an affine corrector conditional mean function given by

x ↦ b + Φ * (x - c),

and conditional covariance function parameter Σ. Σ is assumed to be callable and be of compatible eltype with Φ, b, c.

source
MarkovKernels.NormalKernel — Method
NormalKernel(F::AbstractAffineMap, Σ::CovarianceParameter)

Creates a NormalKernel with conditional mean function F and a constant conditional covariance function parameterised by Σ.

source
MarkovKernels.NormalKernel — Method
NormalKernel(F::AbstractAffineMap, Σ::AbstractMatrix)

Creates a NormalKernel with conditional mean function F and a constant conditional covariance function Σ if Σ is Symmetric / Hermitian. Throws domain error otherwise.

source

Basics

Statistics.mean — Method
mean(K::AbstractNormalKernel)

Computes the conditonal mean function of the Normal kernel K. That is, the output is callable.

source
Statistics.cov — Method
mean(K::AbstractNormalKernel)

Computes the conditonal covariance matrix function of the Normal kernel K. That is, the output is callable.

source
MarkovKernels.covp — Method
covp(K::AbstractNormalKernel)

Returns the internal representation of the conditonal covariance matrix of the Normal kernel K. For computing the actual conditional covariance matrix, use cov.

source

Conditioning and sampling

Base.rand — Method
rand(RNG::AbstractRNG, K::AbstractNormalKernel, x::AbstractVector)

Computes a random vector conditionally on x with respect the the Normal kernel K using the random number generator RNG.

source
Base.rand — Method
rand(K::AbstractNormalKernel, x::AbstractVector)

Computes a random vector conditionally on x with respect the the Normal kernel K using the random number generator Random.GLOBAL_RNG.

source