Integral of a polynomial over a simplex with 'spray' (not an issue)

[stla]

Hi,

I wrote this blog post which involves spray. Maybe you would like to link it in the README (or include the function in the package?).

[RobinHankin]

hello Stéphane: great to hear from you! I've been enjoying that blog post very much, and would be delighted to cite it in the spray package. Do you have a preferred citation format for the work? I got very interested in integration over simplexes a few years ago, but I didn't know about the work by Lasserre. I guess it is quite recent which is why I missed it. Actually my main use for integrating over a simplex would be in the hyper2 package which includes a vignette that discusses generalizations of the Dirichlet distribution (you need to integrate over a simplex to get the normalization constant). But the method is clunky and slow and inefficient, I wonder if I could use or adapt Lasserre's work?

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-- Robin K. S. Hankin Associate Professor, computational statistics

On Tue, Dec 6, 2022 at 1:22 AM stla ***@***.***> wrote: Hi, I wrote this blog post <https://laustep.github.io/stlahblog/posts/integratePolynomialOnSimplex.html> which involves *spray*. Maybe you would like to link it in the *README* (or include the function in the package?). — Reply to this email directly, view it on GitHub <#37>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ADFFZUUMK2WSAL5AOBVGK2DWLXM7BANCNFSM6AAAAAASUGTJYA> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[stla]

Hi Robin,

Are you aware of the SimplicialCubature package? It is good. It implements adaptive integration on simplices.

I don't have a preferred citation format for the blog post.

Actually I'm wondering whether Lasserre's results are really new. Because everything is derived from the formula for the integral of a monomial over the unit simplex, and I'm not sure this is new.

[stla]

Ah but for a Dirichlet distribution the support is the boundary of a simplex, like x_1 + ... + x_n = 1. This is not the simplex x_1 + ... + x_n <= 1. So the SimplicialCubature package does not help here.

[stla]

Hi Robin,

I've just done qspray, a GMP version of spray. It allows to get the value of the integral as an exact rational number.