Hi Jared.

> 
> I am working on submitting code for multivariate normal distributions, 
> including sampling and unit tests (issue Math-815).  It is my first 
> submission, and it has had some issues with style and other guidelines. 
> Gilles has given me some useful feedback about several pieces, but I
> thought I would also ask a question this list.
> 
> I need to have a unit test pass deterministically even though the
> sampling algorithm is inherently stochastic.  I assumed that resetting
> the seed before sampling would be sufficient to test a few values to
> within a specified tolerance.  It has worked so far for me.  Gilles
> suggested, though, that I use the testSampling method in
> RealDistributionAbstractTest.java as a model.  But it uses a
> statistical test (Chi-Squared) in addition to resetting the seed.
> Aside from the added difficulty of hypothesis testing in more
> dimensions, is it actually necessary?  Wouldn't resetting the seed
> give you the same values each time when you sample in the unit test?
> Doesn't that make it essentially a deterministic test, eliminating the
> need for a hypothesis test of the samples?

There are 2 things:
1. Having a test that sometimes fail just because of one "bad" draw.
   This is indeed solved by selecting a seed.
2. Test that the "sample" of the distribution provides the expected
   result. The "testSampling" referred to is nice because it is set up
   independently of the actual distribution: The expected result of an
   infinite number of draws is known and the statistical test (of the test
   result) checks that the set of actual draws is close enough to the the
   one theoretically expected.

As you say, adapting the hypothesis testing is not necessarily obvious (I
don't know), but people here might be able explain what to do...


Thanks,
Gilles

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