@riwish |

Inverse Wishart random draws.

Syntax: @riwish(S, n)

@riwishc(S, n)

@riwishi(S, n)

@riwishic(S, n)

@riwish(X, S, n)

@riwishc(X, S, n)

@riwishi(X, S, n)

@riwishic(X, S, n)

X: (optional) sym,

S: sym, matrix,

n: number,

Return: sym

Draw a random symmetric inverse Wishart matrix using the density function.

The inverse Wishart density is given by

(18.8) |

where and are symmetric matrices, and .

There are four different forms of the function, corresponding to different ways of specifying . The forms are distinguished by different suffixes that are applied to the base “@rwish” command and how they change the interpretation of the S matrix argument:

@riwish | “” | Supply . |

@riwishc | “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). |

@riwishi | “i” | Supply . This form is more efficient than explicitly inverting to supply . |

@riwishic | “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 is follows a Wishart distribution:

Examples

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

returns a random draw from the distribution.

Cross-references