"Principles of the Bayesian automatic adaptive quadrature"
Adam Gh., Adam S.

The addition of Bayesian inference to the automatic adaptive quadrature scheme developed in QUADPACK} (R. Piessens, E. deDoncker-Kapenga, C.W. Uberhuber, and D.K. Kahaner, QUADPACK, a quadrature package for automatic integration, Springer, Berlin, 1983) significantly increases the output reliability under the lack of a priori knowledge on the behavior of the function over the integration domain. In the present paper, we review the progress obtained until now along these lines.

Keywords: numerical integration, automatic adaptive quadrature, integrand profile analysis, reliability, Bayesian inference

Adam Gh., Professor, e-mail: adamg@jinr.ru; Adam S., Professor, e-mail: adams@jinr.ru - Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia and Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele, Bucharest, 077125, Romania