A MONTE-CARLO STRATEGY FOR DATA-BASED MATHEMATICAL-MODELING

We establish the mathematical basis for building the MC-HARP data-proc essing environment. The MC-HARP strategy determines the functional str ucture 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 multiv ariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measu rable connected subdomains and builds a local approximation for the ma pping task. Fuzziness promotes continuity of the mapping constructed b y HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of r andom partitions reduces the localized disturbances among the fuzzy su bdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate th e procedure by applying it to a two-dimensional surface fitting proble m.