Wishart ClassInfer.NET Documentation
Microsoft Research, Cambridge
A Wishart distribution on positive definite matrices.
Inheritance Hierarchy

OnlineSystem Object
  MicrosoftResearch.Infer.Distributions Wishart

Namespace: MicrosoftResearch.Infer.Distributions
Assembly: Infer.Runtime (in Infer.Runtime.dll) Version: 2.5.30417.0 (2.5.30417.0)


In the matrix case, the distribution is p(X) = |X|^(a-(d+1)/2)*exp(-tr(X*B))*|B|^a/Gamma_d(a). In this code, the a parameter is called the "Shape" and the B parameter is called the "Rate". The mean of the distribution is a/B and the diagonal variance is var(X_ii) = a*C_ii^2 where C=inv(B). The non-diagonal variances are var(X_ij) = a*0.5*(C_ij^2 + C_ii*C_jj) where C=inv(B).

The distribution is represented by a one-dimensional Vector for a and a PositiveDefiniteMatrix for B. Because both are Cursors, any Wishart instance can be used as a cursor.

See Also