Wishart distribution in Bayesian statistics
What is the Wishart distribution?
The Wishart distribution is a multivariate generalization of the univariate chi-squared distribution. It is used as the conjugate prior for the precision matrix in Bayesian statistics. The Wishart distribution is a family of distributions for symmetric positive definite matrices.In the context of the multivariate normal distribution, the Wishart distribution is the conjugate prior to the precision matrix Ω Σ^(-1). A Wishart random matrix with parameters n and Σ can be seen as a sum of outer products of independent multivariate normal random vectors having mean 0.
Applications of the Wishart distribution
The Wishart distribution is used in a variety of applications, including:- Bayesian inference for the mean and covariance matrix of a multivariate normal distribution
- Multivariate analysis of variance
- Random matrix theory
The Wishart distribution is a powerful tool for Bayesian inference and multivariate analysis. It is easy to sample from and has a number of useful properties.
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