Inverted Wishart density from the inverse.

Computes the density of an Inverted Wishart (df, Sigma) in X, by supplying (X^(-1), df, Sigma) rather than (X, df, Sigma). Avoids a matrix inversion.

diwishart_inverse_R(X.inv, df, Sigma, log = FALSE, is.chol = FALSE)

Arguments

X.inv	inverse of X (the observation)
df	degrees of freedom
Sigma	scale matrix
log	if TRUE, return the log-density
is.chol	if TRUE, Sigma and X.inv are the upper Cholesky factors of Sigma and X.inv

Value

the density in X

Details

Computes the pdf p_X(x) by knowing x^(-1)

Inverted Wishart parametrization (Press)

Uses (Press 2012) parametrization.

$$X \sim IW(\nu, S)$$ with \(S\) is a \(p \times p\) matrix, \(\nu > 2p\) (the degrees of freedom).

Then: $$E[X] = \frac{S}{\nu - 2(p + 1)}$$

References

Press SJ (2012). Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. Courier Corporation.

See also

diwishart_inverse, diwishart

Other R functions: diwishart(), dwishart(), riwish_Press()

Other statistical functions: diwishart_inverse(), diwishart(), dmvnorm(), dwishart(), riwish_Press(), rmvnorm(), rwish()

Other Wishart functions: diwishart_inverse(), diwishart(), dwishart(), get_minimum_nw_IW(), riwish_Press(), rwish()