Control decisions in the Bayesian automatic adaptive quadrature

Two topics in the Bayesian automatic adaptive quadrature are addressed. First, it is shown that the accuracy specifications controlling the error tolerance of the derived output need a twofold scrutiny: check of the input accuracy reliability and check for the need of integrand dependent accuracy bounds. Second, a criterion is proposed for the definition of the separation boundary between macroscopic and mesoscopic integration domain length which singles out the first ones as being free of cancellation by subtraction at the computation of the integration domain lengths.