BAYESIAN INFERENCE IN THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

摘要

In his seminal paper (O'Hagan, A., BAYESIAN STATISTICS (1992) 4, pp. 345-363), O'Hagan introduced a framework that makes it possible to formulate many numerical problems in the language of Bayesian inference and Gaussian processes. This contribution extends O'Hagan's analysis to the field of ordinary differential equations and successfully deduces a Bayesian algorithm for making estimates to the solution of these equations. The Bayesian machinery adds some overhead in comparison to most classical methods. However, many of these methods can be formulated as limiting cases or as approximations within the proposed Bayesian framework. The Bayesian language also makes it easier to incorporate error estimates and automated decisions that calibrate the proposed algorithms. This contribution uses O'Hagan's framework and Bayesian experimental design in order to develop a few novel algorithms for integrating a system ordinary differential equations.