| rIW {MCMCglmm} | R Documentation |
Random Generation from the Conditional Inverse Wishart Distribution
Description
Samples from the inverse Wishart distribution, with the possibility of conditioning on a diagonal submatrix
Usage
rIW(V, nu, fix=NULL, n=1, CM=NULL)
Arguments
V |
Expected (co)varaince matrix as |
nu |
degrees of freedom |
fix |
optional integer indexing the partition to be conditioned on |
n |
integer: number of samples to be drawn |
CM |
matrix: optional matrix to condition on. If not given, and |
Details
If {\bf W^{-1}} is a draw from the inverse Wishart, fix indexes the diagonal element of {\bf W^{-1}} which partitions {\bf W^{-1}} into 4 submatrices. fix indexes the upper left corner of the lower
diagonal matrix and it is this matrix that is conditioned on.
For example partioning {\bf W^{-1}} such that
{\bf W^{-1}} = \left[
\begin{array}{cc}
{\bf W^{-1}}_{11}&{\bf W^{-1}}_{12}\\
{\bf W^{-1}}_{21}&{\bf W^{-1}}_{22}\\
\end{array}
\right]
fix indexes the upper left corner of {\bf W^{-1}}_{22}. If CM!=NULL then {\bf W^{-1}}_{22} is fixed at CM, otherwise {\bf W^{-1}}_{22} is fixed at \texttt{V}_{22}. For example, if dim(V)=4 and fix=2 then {\bf W^{-1}}_{11} is a 1X1 matrix and {\bf W^{-1}}_{22} is a 3X3 matrix.
Value
if n = 1 a matrix equal in dimension to V, if n>1 a
matrix of dimension n x length(V)
Note
In versions of MCMCglmm >1.10 the arguments to rIW have changed so that they are more intuitive in the context of MCMCglmm. Following the notation of Wikipedia (https://en.wikipedia.org/wiki/Inverse-Wishart_distribution) the inverse scale matrix {\bm \Psi}=(\texttt{V*nu}). In earlier versions of MCMCglmm (<1.11) {\bm \Psi} = \texttt{V}^{-1}. Although the old parameterisation is consistent with the riwish function in MCMCpack and the rwishart function in bayesm it is inconsistent with the prior definition for MCMCglmm. The following pieces of code are sampling from the same distributions:
riwish(nu, nu*V) | from MCMCpack |
rwishart(nu, solve(nu*V))$IW | from bayesm |
rIW(nu, solve(nu*V)) | from MCMCglmm <1.11 |
rIW(V, nu) | from MCMCglmm >=1.11 |
Author(s)
Jarrod Hadfield j.hadfield@ed.ac.uk
References
Korsgaard, I.R. et. al. 1999 Genetics Selection Evolution 31 (2) 177:181
See Also
Examples
nu<-10
V<-diag(4)
rIW(V, nu, fix=2)