Sample uniformly from a simplex
- To: mathgroup at smc.vnet.net
- Subject: [mg94416] Sample uniformly from a simplex
- From: Andreas <aagas at ix.netcom.com>
- Date: Fri, 12 Dec 2008 06:56:02 -0500 (EST)
I need to develop Mathematica code to sample uniformly from a unit n-dimensional simplex. I came across a description of the problem at: http://geomblog.blogspot.com/2005/10/sampling-from-simplex.html Specifically, I would like a uniform sample from the set X = { (x1, x2, ..., xD) | 0 <= xi <= 1, x1 + x2 + ... + xD = 1}. D is the dimension of the simplex. So, the coordinates of any point on the simplex would sum to 1 and I need to sample points on the simplex. geomblog's solution suggested: Generating IID random samples from an exponential distribution by sampling X from [0,1] uniformly, and returning -log(X)). Take n samples, then normalize. This should result in a list of numbers which is a uniform sample from the simplex. I've searched extensively for a Mathematica implementation of something like this, to no avail. I keep trying different things but haven't made much headway. Any suggestions for how to develop this (or an equivelant) in Mathematica much appreciated A