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A comparison of approximation methods for the estimation of probability distributions on parameters. (English) Zbl 1115.65009

Summary: We compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods.

MSC:

65C50 Other computational problems in probability (MSC2010)
60H07 Stochastic calculus of variations and the Malliavin calculus
92D25 Population dynamics (general)
49J55 Existence of optimal solutions to problems involving randomness
49N45 Inverse problems in optimal control

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