In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and precision matrix (the inverse of the covariance matrix).
location (vector of real)|
scale matrix (pos. def.)
|Support||covariance matrix (pos. def.)|
has a Wishart distribution. Then has a normal-Wishart distribution, denoted as
Probability density function
Posterior distribution of the parameters
After making observations , the posterior distribution of the parameters is
Generating normal-Wishart random variates
Generation of random variates is straightforward:
- The normal-inverse Wishart distribution is essentially the same distribution parameterized by variance rather than precision.
- The normal-gamma distribution is the one-dimensional equivalent.
- The multivariate normal distribution and Wishart distribution are the component distributions out of which this distribution is made.
- Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning. Springer Science+Business Media. Page 690.
- Cross Validated, https://stats.stackexchange.com/q/324925
- Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning. Springer Science+Business Media.