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Command Reference : Function Reference : Function Reference: D

@diwish

Element Functions

Inverse Wishart probability density.

Syntax: @diwish(X, S, n)

@diwishc(X, S, n)

@diwishi(X, S, n)

@diwishic(X, S, n)

X: sym,

S: sym, matrix,

n: number,

Return: number

Evaluate the inverse Wishart distribution

density function for sym values of X, and

The inverse Wishart density is given by

where

and

are symmetric

matrices, and

There are four different forms of the density evaluation function, corresponding to different ways of specifying

. The forms are distinguished by different suffixes that are applied to the base “@dwish” command and how they change the interpretation of the S matrix argument:

@diwish	“”	Supply .
@diwishc	“c”	Supply the Cholesky decomposition of . This form is more efficient when performing multiple draws from the same distribution (compute the Cholesky once, but sample many times).
@diwishi	“i”	Supply . This form is more efficient than explicitly inverting to supply .
@diwishic	“ic”	Supply the Cholesky decomposition of . This form combines the efficiencies of the Cholesky and inverse forms.

Note that if

is an inverse Wishart random variable, then

follows a Wishart distribution:

Examples

= @diwish(@identity(3), @identity(3), 5)

returns 0.00018....

Cross-references