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

MarkovKernels.AbstractNormalKernel — Type

AbstractNormalKernel

Abstract type for representing Normal kernels.

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MarkovKernels.NormalKernel — Type

NormalKernel

Standard mean vector / covariance matrix parametrisation of Normal kernels.

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Type aliases

const HomoskedasticNormalKernel{TM,TC} = NormalKernel{<:Homoskedastic,TM,TC} where {TM,TC} # constant conditional covariance
const AffineHomoskedasticNormalKernel{TM,TC} =
    NormalKernel{<:Homoskedastic,TM,TC} where {TM<:AbstractAffineMap,TC} # affine conditional mean, constant conditional covariance
const AffineHeteroskedasticNormalKernel{TM,TC} =
    NormalKernel{<:Heteroskedastic,TM,TC} where {TM<:AbstractAffineMap,TC} # affine conditional mean, non-constant covariance
const NonlinearNormalKernel{TM,TC} = NormalKernel{<:Heteroskedastic,TM,TC} where {TM,TC} # the general, nonlinear case

Constructors

MarkovKernels.NormalKernel — Method

Normal(μ, Σ)

Creates a Normal kernel with conditional mean and covariance parameters μ and Σ, respectively.

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Methods

Statistics.mean — Method

mean(K::AbstractNormalKernel)

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

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Statistics.cov — Method

cov(K::AbstractNormalKernel)

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

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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.

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Base.rand — Method

rand([rng::AbstractRNG], K::AbstractNormalKernel, x::AbstractVector)

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

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