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Recursive integration methodologies with statistical applications

Institution:	1. McMaster University, Hamilton, Canada;2. University of Illinois at Chicago, USA;1. Instituto de Física (IFLP-CCT-Conicet), Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina;2. Comision de Investigaciones Científicas (CIC), Argentina;3. Argentina’s National Research Council (CONICET), Argentina;1. Université Paul Sabatier de Toulouse, 31062 Toulouse, France;2. Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraíba, Brazil;1. Mechanical Engineering, University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072, USA;2. Institute for Computational Mechanics and Its Applications, Northwestern Polytechnical University, Xi׳an, Shaanxi 710072, China;1. Departamento de Física, Universidade Estadual de Maringá - Maringá, PR 87020-900, Brazil;2. Departamento de Física, Universidade Tecnológica Federal do Paraná - Apucarana, PR 86812-460, Brazil;3. Departamento de Física, Universidade Estadual de Ponta Grossa - Ponta Grossa, PR 87030-900, Brazil;4. National Institute of Science and Technology for Complex Systems, CNPq - Rio de Janeiro, RJ 22290-180, Brazil

Abstract:	This paper shows how recursive integration methodologies can be used to evaluate high-dimensional integral expressions. This has applications to many areas of statistical inference where probability calculations and critical point evaluations often require such high-dimensional integral evaluations. Recursive integration can allow an integral expression of a given dimension to be evaluated by a series of calculations of a smaller dimension. This significantly reduces the computation time. The application of the recursive integration methodology is illustrated with several examples.

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