[R] integration over a simplex

[Robin Hankin]

Hello

The excellent adapt package integrates over multi-dimensional
hypercubes.

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  
tetrahedron.
It is the convex hull of (n+1) points in an n-dimensional Euclidean  
space.

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