Bayesian Automatic Adaptive Quadrature: An Overview

The progress obtained within the Bayesian approach to the automatic adaptive quadrature is reviewed. It is shown that the derivation of reliable Bayesian inferences, both as it concerns the construction of the subrange binary tree with its associated priority queue and the a priori validation of the input to the local quadrature rules, can be done provided the well-conditioning criteria for the integrand profile check are implemented taking into account the hardware and software environments at hand.