Fitting coefficients of differential systems with Monte Carlo methods

• Main Authors: Chan Shio, Christian, Diener, Francine
• Format: text
• Published: Archīum Ateneo 2015
• Subjects: Coefficient fitting; differential system; Monte Carlo method; sequential rejection sampling; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/6; https://hal.inria.fr/hal-01320623
• Institution: Ateneo De Manila University

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