Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. In many real-world integration problems, the analytical solution is either unavailable or difficult to... Show moreAutomatic cubatures approximate multidimensional integrals to user-specified error tolerances. In many real-world integration problems, the analytical solution is either unavailable or difficult to compute. To overcome this, one can use numerical algorithms that approximately estimate the value of the integral. For high dimensional integrals, quasi-Monte Carlo (QMC) methods are very popular. QMC methods are equal-weight quadrature rules where the quadrature points are chosen deterministically, unlike Monte Carlo (MC) methods where the points are chosen randomly. The families of integration lattice nodes and digital nets are the most popular quadrature points used. These methods consider the integrand to be a deterministic function. An alternate approach, called Bayesian cubature, postulates the integrand to be an instance of a Gaussian stochastic process. Show less
