A Monte Carlo strategy for data-based mathematical modeling

We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.