"Principles of the Bayesian automatic adaptive quadrature"

"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