Performance Bounds for Dispersion Analysis: A Comparison Between Monte Carlo and Perron-Frobenius Operator Approach
نویسندگان
چکیده
We compare computational cost and accuracy between two different approaches of dispersion analysis. One is the conventional Monte Carlo method and the other being the Perron-Frobenius operator approach, that directly propagates the joint probability density function using Liouville equation. It is shown that with same computational budget, Perron-Frobenius operator approach rewards better accuracy than MonteCarlo based dispersion analysis. In particular, we show that propagation of uncertainty through the PerronFrobenius operator is exact in the sense that the joint density computation incurs no more than the path integration error. On contrary, the rate of approximation from Monte Carlo simulation, has fractional decay. We also establish performance guarantees for approximating marginals from the joint density and obtain the optimal approximation algorithm for piecewise constant approximating class. These results justify why Perron-Frobenius operator outperforms Monte Carlo, as observed numerically in uncertainty propagation setting [Halder and Bhattacharya, 2011] and in nonlinear filtering setting [Dutta and Bhattacharya, 2011].
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