R help - Jul 2003 - Conditional Distribution of MVN variates

Hi Folks,

Given k RVs with MVN distribution N(mu,S) (S a kxk covariance matrix),
let (w.l.o.g.) X1 denote the first r of them, and X2 the last (k-r).
Likewise, let mu1 and mu2 denote their respective expectations.

Then, of course, the expectation of X2 given X1=x1 is

  mu2 + S21*inv(S22)*(x1 - mu1)

and the covariance matrix of X2 given X1=x2 is

  S22 - S21*inv(X11)*S12

where Sij is the matrix derived from S by taking the rows corresponding
to the indices of Xi and the columns corresponding to the indices of Xj,
and these define the MVN conditional distribution of X2 given X1=x1.

While these are not difficult to write one's own functions for in R,
I feel almost sure that they already exist somewhere, if only I could
find them!

So, are there standard functions for this in R? If so, in what library?

With thanks,
Ted.


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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 06-Jul-03                                       Time: 17:37:57
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On 06-Jul-03 Ted Harding wrote:
> Given k RVs with MVN distribution N(mu,S) (S a kxk covariance matrix),
> let (w.l.o.g.) X1 denote the first r of them, and X2 the last (k-r).
> Likewise, let mu1 and mu2 denote their respective expectations.
> 
> Then, of course, the expectation of X2 given X1=x1 is
OOPS!! Typos:
>*** mu2 + S21*inv(S22)*(x1 - mu1)
should of course be

     mu2 + S21*inv(S11)*(x1 - mu1)
> and the covariance matrix of X2 given X1=x2 is
> 
>*** S22 - S21*inv(X11)*S12
should be

     S22 - S21*inv(S11)*S12
> [...]
> So, are there standard functions for this in R? If so, in what library?
> 
> With thanks,
> Ted.
Sorry about the typos.

Anyway, can R say "here's one I prepared earlier"?

Thanks again,
Ted.


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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 07-Jul-03                                       Time: 12:36:33
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