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Normal-Wishart distribution : ウィキペディア英語版
Normal-Wishart distribution

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).〔Bishop, Christopher M. (2006). ''Pattern Recognition and Machine Learning.'' Springer Science+Business Media. Page 690.〕
==Definition==
Suppose
: \boldsymbol\mu|\boldsymbol\mu_0,\lambda,\boldsymbol\Lambda \sim \mathcal(\boldsymbol\mu|\boldsymbol\mu_0,(\lambda\boldsymbol\Lambda)^)
has a multivariate normal distribution with mean \boldsymbol\mu_0 and covariance matrix (\lambda\boldsymbol\Lambda)^, where
:\boldsymbol\Lambda|\mathbf,\nu \sim \mathcal(\boldsymbol\Lambda|\mathbf,\nu)
has a Wishart distribution. Then (\boldsymbol\mu,\boldsymbol\Lambda)
has a normal-Wishart distribution, denoted as
: (\boldsymbol\mu,\boldsymbol\Lambda) \sim \mathrm(\boldsymbol\mu_0,\lambda,\mathbf,\nu) .


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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