Matrix-variate Distributions

Matrix-variate Distributions

Matrix-variate distributions are the distributions whose variate forms are Matrixvariate (i.e each sample is a matrix). Abstract types for matrix-variate distributions:

Common Interface

Both distributions implement the same set of methods:

Base.sizeMethod.
size(d::MatrixDistribution)

Return the size of each sample from distribution d.

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Base.lengthMethod.
length(d::MatrixDistribution)

The length (i.e number of elements) of each sample from the distribution d.

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Statistics.meanMethod.
mean(d::MatrixDistribution)

Return the mean matrix of d.

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Distributions.pdfMethod.
pdf(d::MatrixDistribution, x::AbstractArray)

Compute the probability density at the input matrix x.

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logpdf(d::MatrixDistribution, AbstractMatrix)

Compute the logarithm of the probability density at the input matrix x.

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Base.randMethod.
rand(d::MatrixDistribution, n)

Draw a sample matrix from the distribution d.

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Distributions

Wishart(nu, S)

The Wishart distribution is a multidimensional generalization of the Chi-square distribution, which is characterized by a degree of freedom ν, and a base matrix S.

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InverseWishart(nu, P)

The Inverse Wishart distribution is usually used as the conjugate prior for the covariance matrix of a multivariate normal distribution, which is characterized by a degree of freedom ν, and a base matrix Φ.

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Internal Methods (for creating your own matrix-variate distributions)

_logpdf(d::MatrixDistribution, x::AbstractArray)

Evaluate logarithm of pdf value for a given sample x. This function need not perform dimension checking.

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