Gilles,
I think it will be difficult (for me, at least) to provide a general method for testing sampling
across all multivariate distributions. I imagine it can be done, but I would prefer for now
just to make it an abstract method and expect the writers of future multivariate distribution
classes to provide ways to verify their sampling works. I am new here, though, so that may
not be your preference. I do think a general statistical test such as TestUtils ChiSquared
as applied in RealDistributionAbstractTest may be difficult to apply in general to all multivariate
distributions.
Unless someone has a better idea, I would suggest that for the time being multivariate sampling
unit tests be implemented in their own classes, and the base class method remain abstract.
Jared
Original Message
From: Gilles Sadowski [mailto:gilles@harfang.homelinux.org]
Sent: Wednesday, July 25, 2012 4:37 AM
To: dev@commons.apache.org
Subject: Re: [math] Unit Tests for Multivariate Distribution Sampling
Hi Jared.
>
> I am working on submitting code for multivariate normal distributions,
> including sampling and unit tests (issue Math815). 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 (ChiSquared) 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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