A comparative study of randomized algorithms for multidimensional integration

This paper presents a comparative study of randomized algorithms for computation of a class of high dimensional Gaussian weighted integrals. The work is an extension of past research by Keister et al. and later by Papageorgiou et al. who used non-product (grid-less) multidimensional quadrature rules and Quasi Monte Carlo respectively for integration in up to 100 dimensions. In the present paper, the same integrals are computed using Markov chain Monte Carlo (MCMC) and a comparison is made. It is shown that the MCMC technique is significantly more accurate for the problem of interest and is also robust in implementation. Moreover, by virtue of its information-centric approach, MCMC can be adapted to efficiently compute integrals weighted by general weight functions (besides Gaussian weights).