Wishart distribution
(30 minutes to learn)
Summary
The Wishart distribution is a distribution over positive semidefinite matrices. It is most often used as the conjugate prior for the precision matrix of a multivariate Gaussian.
Context
This concept has the prerequisites:
- gamma distribution (The Wishart distribution is a multivariate generalization of the gamma distribution.)
- positive definite matrices (The Wishart distribution is a distribution over positive definite matrices.)
- expectation and variance (We would like to derive the mean of the distribution.)
- determinant (The probability density function includes a determinant.)
- matrix inverse (The probability density function includes a matrix inverse.)
Core resources (read/watch one of the following)
-Paid-
→ Machine Learning: a Probabilistic Perspective
A very comprehensive graudate-level machine learning textbook.
Location:
Section 4.5, pages 125-127
See also
- sampling from a Wishart distribution
- math tricks for Wishart distributions