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Re: multivariate gaussian distribution (Code)
- From: Emmanuel Benazera <ebenazer at email dot arc dot nasa dot gov>
- To: sliwa at euv-frankfurt-o dot de
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Mon, 29 Dec 2003 09:13:22 -0800
- Subject: Re: multivariate gaussian distribution (Code)
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.