Christian Chan Shio ; Francine Diener - Fitting coefficients of differential systems with Monte Carlo methods

arima:1988 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, October 16, 2015, Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît - https://doi.org/10.46298/arima.1988
Fitting coefficients of differential systems with Monte Carlo methods

Authors: Christian Chan Shio ; Francine Diener

We consider the problem of estimating the coefficients in a system of differential equations when a trajectory of the system is known at a set of times. To do this, we use a simple Monte Carlo sampling method, known as the rejection sampling algorithm. Unlike deterministic methods, it does not provide a point estimate of the coefficients directly, but rather a collection of values that "fits" the known data well. An examination of the properties of the method allows us not only to better understand how to choose the different parameters when implementing the method, but also to introduce a more efficient method by using a new two-step approach which we call sequential rejection sampling. Several examples are presented to illustrate the performance of both the original and the new methods.


Volume: Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît
Published on: October 16, 2015
Submitted on: March 18, 2015
Keywords: Coefficient fitting, differential system, Monte Carlo method, sequential rejection sampling.,Ajustement de coefficients, systèmes différentiels, méthode de Monte Carlo, méthode de rejet séquentielle.,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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