NormalInverseChisq(μ, σ2, κ, ν)

A Normal-χ^-2 distribution is a conjugate prior for a Normal distribution with unknown mean and variance. It has parameters:

  • μ: expected mean
  • σ2 > 0: expected variance
  • κ ≥ 0: mean confidence
  • ν ≥ 0: variance confidence

The parameters have a natural interpretation when used as a prior for a Normal distribution with unknown mean and variance: μ and σ2 are the expected mean and variance, while κ and ν are the respective degrees of confidence (expressed in "pseudocounts"). When interpretable parameters are important, this makes it a slightly more convenient parametrization of the conjugate prior.

Equivalent to a NormalInverseGamma distribution with parameters:

  • m0 = μ
  • v0 = 1/κ
  • shape = ν/2
  • scale = νσ2/2

Based on Murphy "Conjugate Bayesian analysis of the Gaussian distribution".


The parameters are

  • μ::AbstractVector{T<:Real} the expected mean vector
  • Λchol::Cholesky{T<:Real} the Cholesky decomposition of the scale matrix
  • κ::T<:Real prior pseudocount for the mean
  • ν::T<:Real prior pseudocount for the covariance