Bayesian inference for dynamical systems

Bayesian inference is a common method for conducting parameter estimation for dynamical systems. Despite the prevalent use of Bayesian inference for performing parameter estimation for dynamical systems, there is a need for a formalized and detailed methodology. This paper presents a comprehensive methodology for dynamical system parameter estimation using Bayesian inference and it covers utilizing different distributions, Markov Chain Monte Carlo (MCMC) sampling, obtaining credible intervals for parameters, and prediction intervals for solutions. A logistic growth example is given to illustrate the methodology.