BayesianNonparametrics.GammaNormalMethod

GammaNormal(; μ0 = 0.0, λ0 = 1.0, α0 = 1.0, β0 = 1.0)

Normal-Gamma distribution

A Normal-Gamma distribution is the conjugate prior of a Normal distribution with unknown mean and precision.

Paramters

• μ0: location
• λ0 > 0: number of pseudo-observations
• α0 > 0
• β0 > 0

Example:

d = GammaNormal()
BayesianNonparametrics.WishartGaussianMethod

WishartGaussian(μ0, κ0, ν0, Σ0)

Gaussian-inverse-Wishart distribution

A Gaussian-inverse-Wishart distribution is the conjugate prior of a multivariate normal distribution with unknown mean and covariance matrix.

Parameters

• μ0, Dx1: location
• κ0 > 0: number of pseudo-observations
• ν0 > D-1: degrees of freedom
• Σ0 > 0, DxD: scale matrix

Example

julia> (N, D) = size(X)
julia> μ0 = mean(X, dims = 1)
julia> d = WishartGaussian(μ0, 1.0, 2*D, cov(x)) 
BayesianNonparametrics.pointestimateMethod
point_estimate(psm::Array{Float64, 2})

Find optimal partition which minimizes the lower bound to the Variation of Information obtain from Jensen's inequality where the expectation and log are reversed.

BayesianNonparametrics.point_estimate_hclustMethod
point_estimate_avg(psm::Array{Float64, 2})