What is wishart distribution?

The Wishart distribution is a probability distribution that is commonly used in statistics to model the covariance matrix of multivariate normal distributions. It is named after John Wishart, a British statistician who introduced the distribution in 1928.

The Wishart distribution is parameterized by a positive definite matrix ( \Sigma ) and a degrees of freedom parameter ( \nu ). The distribution represents the set of positive semi-definite matrices that result from multiplying a matrix by its transpose, where the original matrix is drawn from a multivariate normal distribution with covariance matrix ( \Sigma ). The degrees of freedom parameter ( \nu ) determines the concentration of the distribution around ( \Sigma ).

In practice, the Wishart distribution is commonly used in Bayesian statistics for modeling the covariance matrix of multivariate normal distributions, particularly in applications such as factor analysis, Bayesian inference, and image processing.

The properties of the Wishart distribution make it a versatile tool in statistical analysis and inference, particularly when dealing with multivariate data that exhibit complex relationships and dependencies between variables.