Bayesian equation selection on sparse data for discovery of stochastic dynamical systems

Abstract

Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential equations under assumptions that align with real-life scenarios, including the availability of relatively sparse data. Further, we discuss computational strategies that are critical in teasing out the important details about the dynamical system and algorithmic innovations to solve for acute parameter interdependence in the absence of rich data. This gives a complete Bayesian pathway for model identification via a variable selection paradigm and parameter estimation of the corresponding model using only the observed data. We present detailed computations and analysis of the Lorenz-96, Lorenz-63, and the Orstein-Uhlenbeck system using the Bayesian framework we propose.

References in corpus (7)

• Spike and slab variable selection: Frequentist and Bayesian strategies
• Bayesian variable selection with shrinking and diffusing priors
• Monte Carlo maximum likelihood estimation for discretely observed diffusion processes
• Approximate Bayes learning of stochastic differential equations
• Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems
• A probabilistic scheme for joint parameter estimation and state prediction in complex dynamical systems
• Bayesian estimation in differential equation models