From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 1457 invoked by alias); 29 Dec 2003 17:54:40 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 12853 invoked from network); 29 Dec 2003 17:13:47 -0000 Date: Mon, 29 Dec 2003 17:54:00 -0000 From: Emmanuel Benazera To: sliwa@euv-frankfurt-o.de Cc: gsl-discuss@sources.redhat.com Subject: Re: multivariate gaussian distribution (Code) Message-ID: <20031229171322.GB5259@wow.arc.nasa.gov> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.4.1i X-SW-Source: 2003-q4/txt/msg00160.txt.bz2 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.