Quantitative conditioning criteria in bayesian automatic adaptive quadrature

Quantitative criteria enabling Bayesian inferences on the integrand conditioning over monotonicity intervals defined on integrand profiles obtained within the process of building the subrange binary tree associated to the numerical solution of a Riemann integral by automatic adaptive quadrature are derived. The theoretically obtained admissible relative variation bounds of the first order divided differences of the integrand around an abscissa belonging to the monotonicity interval put on firm ground previously reported empirical results.