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

摘要

The Buridan's ass paradox is characterized by perpetual indecision betweentwo states, which are never attained. When this problem is formulated as adynamical system, indecision is modeled by a discrete-state Markov processdetermined by the system's unknown parameters. Interest lies in estimatingthese parameters from a limited number of observations. We compare estimationmethods and examine how well each can be generalized to multi-dimensionalextensions of this system. By quantifying statistics such as mean, variance,frequency, and cumulative power, we construct both method of moments typeestimators and likelihood-based estimators. We show, however, why thesetechniques become intractable in higher dimensions, and thus develop ageometric approach to reveal the parameters underlying the Markov process. Wealso examine the robustness of this method to the presence of noise.