What is the entropy of the Inverse-Wishart distribution? I need just a reference, but derivation (e.g. using inverse property) would be interesting too.


Wishart and Inverse Wishart Distributions

The Wishart and inverse Wishart distributions are arguably the most popular distributions for modeling random positive definite matrices. Moreover, if a random variable has a Gaussian distribution, then its sample covariance is drawn from a Wishart distribution. The relative entropy between Wishart distributions may be a useful way to measure the dissimilarity between collections of covariance matrices or Gram (inner product) matrices.

A new Bayesian entropy estimator is proposed using an inverted Wishart distribution and a data-dependent prior that handles the small-sample case.

Inverse Wishart Differential Entropy and Relative Entropy

The above link explains the derivation of the entropy of Inverse-Wishart distribution

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