I would like to perform a random walk on a J-dimensional simplex. However, since this is part of a metropolis-hastings algorithm application, my understanding is that the steps need to be drawn from a symmetric distribution (is this correct?)

I was wondering if there is a standard/established way to approach this.

Any help/pointers are greatly appreciated!



1 Answer 1


I think you're asking whether the MH proposal distribution has to be symmetric. No, it doesn't have to be symmetric, it just can't depend on the current state. For sampling on a constrained space it's perfectly valid just to use a Gaussian proposal distribution and reject any proposals that fall outside the space. However, this may not work well in practice, particularly if J is large or the mass is concentrated towards the corners of the simplex.

  • $\begingroup$ I take this as a correct answer as addressed my main question. Hats off to you for mentioning the fact that it should not depend on the current state. As you mentioned, the rejection/acceptance ratio can become impractical as the number of dimensions gets large. Searching some more, I came across the following links regarding uniform sampling from simplex and I am including them here for future reference:<br/> en.wikipedia.org/wiki/User:Skinnerd/Simplex_Point_Picking <br/>geomblog.blogspot.de/2005/10/sampling-from-simplex.html $\endgroup$ Commented Oct 31, 2013 at 18:16
  • $\begingroup$ Typically the proposal distribution depends on the current state. $\endgroup$ Commented Apr 9, 2016 at 18:11

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