Re: multivariate gaussian distribution (Code)

[Emmanuel Benazera <ebenazer@email.arc.nasa.gov>]

Hi Przem,

> 1. Why did you (Emmanuel) use the Eigenvalue decomposition of the
> covariance matrix. This method is extremely inefficient with the gsl
> eigenvalues code. One shall (I do) use the Cholesky decomposition of the
> covariance matrix in order to compute the lower triangular matrix L of the
> form Cov = LL' This procedure is described in several books e.g.
> Harville's "Matrix Algebra from a Statistician's perspective".

As stated before, I read that eigenvalue decomposition was 'stablier' (...)
than Cholesky. However, I'll be interested implementing a faster 
algorithm. I don't have this book at hand. Could you describe this
procedure that uses the Cholesky decomposition ?

> 2. Why do you use this Box Mueller Algorithm? My point is: if you have a
> vector X of independent, normally distributed variables (Covariance matrix
> equals identity matrix) the product P = LX is always normally distributed
> with covariance matrix Cov, since (assuming E(X) = 0) E(PP') = E(LX(LX)')
> = E(LXX'L) = LIL' = Cov. Similar to this method one can simulate the whole
> family of elliptically countered distributions (like Bessel, generalized
> Lapalce, t-distributions).

Przem, I'm not sure I understand your point. The vector of independent variables 
needs to be generated at some point. Therefore the BM algorithm is used,
or the ratio method. Again, I'm not sure I got your point. I think the method
may be used for sampling from several other multi-dimensional distributions. Please
let me know your sources, I'll be happy to implement these algorithms.

Cheers,

Emmanuel

P.S.: Przem, please answer to me as well as to the list. Thanks.