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A model‐based initial guess for estimating parameters in systems of ordinary differential equations
Author(s) -
Dattner Itai
Publication year - 2015
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12348
Subject(s) - ordinary differential equation , focus (optics) , estimation theory , computer science , mathematics , inference , parameter space , process (computing) , mathematical optimization , inverse problem , function (biology) , statistical inference , dynamical systems theory , differential equation , algorithm , statistics , artificial intelligence , mathematical analysis , physics , evolutionary biology , optics , biology , operating system , quantum mechanics
Summary The inverse problem of parameter estimation from noisy observations is a major challenge in statistical inference for dynamical systems. Parameter estimation is usually carried out by optimizing some criterion function over the parameter space. Unless the optimization process starts with a good initial guess, the estimation may take an unreasonable amount of time, and may converge to local solutions, if at all. In this article, we introduce a novel technique for generating good initial guesses that can be used by any estimation method. We focus on the fairly general and often applied class of systems linear in the parameters. The new methodology bypasses numerical integration and can handle partially observed systems. We illustrate the performance of the method using simulations and apply it to real data.