Normal-WishartNotation |
 |
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Parameters |
location (vector of real)
(real)
scale matrix (pos. def.)
(real) |
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Support |
covariance matrix (pos. def.) |
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PDF |
 |
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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).[1]
Definition
Suppose

has a multivariate normal distribution with mean
and covariance matrix
, where

has a Wishart distribution. Then
has a normal-Wishart distribution, denoted as

Posterior distribution of the parameters
After making
observations
, the posterior distribution of the parameters is

where



[2]