On Tue, Jul 5, 2011 at 10:33 AM, Ted To

On 07/05/2011 10:17 AM, josef.pktd@gmail.com wrote:

On Mon, Jul 4, 2011 at 10:13 PM, Ted To

wrote: Hi,

Is there an easy way to make random draws from a conditional random variable? E.g., draw a random variable, x conditional on x>=\bar x.

If you mean here truncated distribution, then I asked a similar question on the scipy user list a month ago for the normal distribution.

The answer was use rejection sampling, Gibbs or MCMC.

I just sample from the original distribution and throw away those values that are not in the desired range. This works fine if there is only a small truncation, but not so well for distribution with support only in the tails. It's reasonably fast for distributions that numpy.random produces relatively fast.

(Having a bi- or multi-variate distribution and sampling y conditional on given x sounds more "fun".)

Yes, that is what I had been doing but in some cases my truncations moves into the upper tail and it takes an extraordinary amount of time. I found that I could use scipy.stats.truncnorm but I haven't yet figured out how to use it for a joint distribution. E.g., I have 2 normal rv's X and Y from which I would like to draw X and Y where X+Y>= U.

Any suggestions?

If you only need to sample the sum Z=X+Y, then it would be just a univariate normal again (in Z). For the general case, I'm at least a month away from being able to sample from a generic multivariate distribution. There is an integral transform that does recursive conditioning y|x. (like F^{-1} transform for multivariate distributions, used for example for copulas) For example sample x>=U and then sample y>=u-x. That's two univariate normal samples. Another trick I used for the tail is to take the absolute value around the mean, because of symmetry you get twice as many valid samples. I also never tried importance sampling and the other biased sampling procedures. If you find something, then I'm also interested in a solution. Cheers, Josef

Cheers, Ted To _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion