AltDistributions

# AltDistributions

``````AltMvNormal(?, μ, L)
``````

Inner constructor used internally, for specifying `L` directly when the first argument is `Val{:L}`.

You don't want to use this unless you obtain `L` directly. Use a `Cholesky` factorization instead.

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``````AltMvNormal(μ, Σ)
``````

Multivariate normal distribution with mean `μ` and covariance matrix `Σ`, which can be an abstract matrix (eg a factorization) or `I`. If `Σ` is not symetric because of numerical error, wrap in `LinearAlgebra.Symmetric`.

Use the `AltMvNormal(Val(:L), μ, L)` constructor for using `LL'=Σ` directly.

Also, see `StdCorrFactor` for formulating `L` from standard deviations and a Cholesky factor of a correlation matrix:

``AltMvNormal(μ, StdCorrFactor(σ, S))``
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``````StdCorrFactor(σ, F)
``````

A factor `L` of a covariance matrix `Σ = LL'` given as `L = Diagonal(σ) * F`. Can be used in place of `L`, without performing the multiplication.

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``````LKJL(η)
``````

The LKJ distribution (Lewandowski et al 2009) for the Cholesky factor L of correlation matrices.

A correlation matrix \$Ω=LL'\$ has the density \$|Ω|^{η-1}\$. However, it is usually not necessary to construct \$Ω\$, so this distribution is formulated for the Cholesky decomposition `L*L'`, and takes `L` directly.

Note that the methods does not check if `L` yields a valid correlation matrix.

Valid values are \$η > 0\$. When \$η > 1\$, the distribution is unimodal at `Ω=I`, while \$0 < η < 1\$ has a trough. \$η = 2\$ is recommended as a vague prior.

When \$η = 1\$, the density is uniform in `Ω`, but not in `L`, because of the Jacobian correction of the transformation.

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