On Tue, Jul 5, 2011 at 10:33 AM, Ted To <rainexpec...@theo.to> wrote:
> On 07/05/2011 10:17 AM, josef.p...@gmail.com wrote:
>> On Mon, Jul 4, 2011 at 10:13 PM, Ted To <rainexpec...@theo.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
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