[R] riwish() problem

[Kevin Quinn]

Dear Ed,

I think the discrepancy you are seeing is due to a change in 
parameterization of the inverse Wishart distribution in MCMCpack from 
MCMCpack version 0.6-1 to 0.6-2 and later. Starting in 0.6-2 we've 
parameterized the inverse Wishart in the same way as in Appendix A of 
Gelman, Carlin, Stern, and Rubin, _Bayesian Data Analyis_. In 
particular, under this parameterization if W ~ InvWIsh(nu, S) then the 
expected value of W is S * (1/(nu-p-1)) where S is a p by p matrix. 
This is in the MCMCpack documentation.

In your example below, I think that simply using the inverse of lam in 
the call to the new version of riwish() will give you the result you 
were expecting.

Hope this helps.

Best,
KQ


> From: Ed Merkle <merkle.14 at osu.edu>
> Date: April 28, 2005 11:39:26 AM CDT
> To: r-help at stat.math.ethz.ch
> Subject: [R] riwish() problem
>
> R users-
>
> In moving from R 2.0.0 to R 2.1.0 in Windows, I have encountered a 
> problem with the "riwish" command in the package "MCMCpack".  I've 
> searched the documentation and can't seem to figure it out.  For 
> example:
>
> Define a matrix:
> > lam <- matrix(c(.00233,-.00057,-.00057,.00190),2,2)
>
> and then use the riwish command to generate a random inverse-Wishart 
> variate:
> > riwish(72,lam)
>
> In version 2.1.0, the result is a matrix of very small numbers like:
>               [,1]          [,2]
> [1,]  3.323499e-05 -3.417600e-06
> [2,] -3.417600e-06  2.283511e-05
>
> In version 2.0.0, the result is a matrix of larger numbers like:
>          [,1]     [,2]
> [1,] 9.707082 2.228333
> [2,] 2.228333 9.037631
>
> This result is consistent across random variates, so I don't think 
> that random variability is the culprit.  I suspect that the version 
> 2.0.0 result is correct because my larger program worked under 2.0.0 
> and did not work under 2.1.0.  I have loaded the coda package and VR 
> bundle in each case.  I appreciate any and all help/tips.
>
> -Ed Merkle
>
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------------------------------------------------------
Kevin Quinn
Assistant Professor
Department of Government and
The Institute for Quantitative Social Science
34 Kirkland Street
Harvard University
Cambridge, MA  02138