Inverse Modeling of Dynamical Systems: Multi-Dimensional Extensions of a Stochastic Switching Problem

Rachel Gettinger, Erik Bates, Blake Chamberlain

Publication date: 17 August 2012

Abstract: The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision is modeled by a discrete-state Markov process determined by the system's unknown parameters. Interest lies in estimating these parameters from a limited number of observations. We compare estimation methods and examine how well each can be generalized to multi-dimensional extensions of this system. By quantifying statistics such as mean, variance, frequency, and cumulative power, we construct both method of moments type estimators and likelihood-based estimators. We show, however, why these techniques become intractable in higher dimensions, and thus develop a geometric approach to reveal the parameters underlying the Markov process. We also examine the robustness of this method to the presence of noise.

Mathematics Subject Classification ID

Inference from stochastic processes and fuzziness (62M86)

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