Testing RNG for Multivariate Distributions

[Peter Li]

Hi,

Does anyone know if there is an easy way to test RNG for multi normal distribution or dirichlet? (i.e. what to compare the alleged RNG distributions to)


Thanks,
Peter

[Ben Goodrich]

On Wednesday, March 6, 2013 8:45:56 PM UTC-5, Peter Li wrote:

Does anyone know if there is an easy way to test RNG for multi normal distribution or dirichlet? (i.e. what to compare the alleged RNG distributions to)

 
One problem is that there are dozens of MVN tests, see

http://scholar.google.com/scholar?cluster=17172775488998657703&hl=en&as_sdt=5,33&sciodt=0,33

and in principle you can do Pearson-like tests, but I don't know of any test that is both simple to compute, deterministic, and applies to any multivariate distribution.

Ben

[Jiqiang Guo]

But at least we can test the marginal of MVN and linear combination of MVN, both of which are normal.  For dirichlet, we can also test the marginal, which is the beta.

--

Jiqiang 

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[Ben Goodrich]

Hi Peter,

On Wednesday, March 6, 2013 8:45:56 PM UTC-5, Peter Li wrote:

Does anyone know if there is an easy way to test RNG for multi normal distribution or dirichlet? (i.e. what to compare the alleged RNG distributions to)

In b01cac1782c3edba7354d900758d53ca89d23cd4, you would want to use Eigen's Cholesky decomposition and use a VectorXd rather than a Matrix<double,Dynamic,Dynamic> when the number of columns is one. So, something like

Eigen::VectorXd z(Sigma.cols());
for(int i = 0; i < sigma.cols(); i++)
  z(i) = std_normal_rng();
return mu + Sigma.llt().matrixL() * z;

Same with multi_student_t.

Ben

[Peter Li]

Ah. I didn't realize there was already a method implemented for Cholesky decomp, so I used the formula on wiki, but I fixed it now and used VectorXd in multi norm and multi student-t.

Thanks,

Peter