Cubature rules and expected value of some complex functions

TL;DR

This paper develops a theoretical framework for computing the expected value of complex-valued random vectors using cubature rules and designed experiments, with specific results for discrete and Gaussian cases.

Contribution

It introduces a general theory linking algebraic statistics with cubature rules to evaluate expectations of complex random vectors, including precision analysis.

Findings

Derived formulas for finite discrete random vectors

Results for Gaussian random vectors

Determined the precision space of certain cubature rules

Abstract

The expected value of some complex valued random vectors is computed by means of the indicator function of a designed experiment as known in algebraic statistics. The general theory is set-up and results are obtained for finite discrete random vectors and the Gaussian random vector. The precision space of some cubature rules/designed experiments are determined.