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 — TypeAbstractNormalKernelAbstract type for representing Normal kernels.
MarkovKernels.NormalKernel — TypeNormalKernelStandard mean vector / covariance matrix parametrisation of Normal kernels.
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 caseConstructors
MarkovKernels.NormalKernel — MethodNormal(μ, Σ)Creates a Normal kernel with conditional mean and covariance parameters μ and Σ, respectively.
Methods
Statistics.mean — Methodmean(k::AbstractNormalKernel)Computes the conditonal mean function of the Normal kernel k. That is, the output is callable.
Statistics.cov — Methodcov(K::AbstractNormalKernel)Computes the conditonal covariance function of the Normal kernel K. That is, the output is callable.
MarkovKernels.covparam — Methodcovparam(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.
Base.rand — Methodrand([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.