[R] integration over a simplex

Robin Hankin r.hankin at noc.soton.ac.uk
Tue Jul 10 12:57:25 CEST 2007


The excellent adapt package integrates over multi-dimensional

I want to integrate over a multidimensional simplex.  Has anyone
implemented such a thing in R?

I can transform an n-simplex to a hyperrectangle
but the Jacobian is a rapidly-varying (and very lopsided)
function and this is making adapt() slow.

A \dfn{simplex} is an n-dimensional analogue of a triangle or  
It is the convex hull of (n+1) points in an n-dimensional Euclidean  

My application is a variant of the Dirichlet distribution:
With p~D(a), if length(p) = n+1 then the requirement that
all(p>0) and sum(p)=1 mean that the support of the
Dirichlet distribution is an n-simplex.

Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

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