  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.
