[SciPy-User] Conditional bivariate normal

[Ted To]

On 07/18/2011 05:01 PM, Ted To wrote:
> Hi All,
> 
> I have a puzzle that I'm having trouble figuring out.  Suppose U=X+Y
> where X and Y are independent normals.  Sampling X and Y conditional on
> U>=\bar U takes an inordinate amount of time since at times \bar U can
> be fairly large so I've been thinking about how to shorten the time.  I
> thought I came upon a solution by using scipy.stats.truncnorm.rvs to
> first draw U=u and then draw an X=x conditional on U=u.  Using U=u and
> X=x, Y=y=u-x.
> 
> I'm getting the correct means and the correct standard deviation for U
> but the standard deviations for X and Y are too small.  Is there
> something wrong with my logic or have I incorrectly derived the sd for
> X|U=u?

Gah!  Never mind.  I forgot to take the square root of the variance...