Bayesian Statistics and Markov Chain Monte Carlo Method in Data Assimilation

Data assimilation is an effective way to integrate observations into models. We will demonstrate how parameters in a model may be estimated by data assimilation in such a way that model simulations best fit observations. Data assimilation based on Bayesian inversion is used to retrieve posterior distributions of model parameters from observations. The Markov Chain Monte Carlo (MCMC) method is applied as a numerical method to home in on the parameter set that maximizes goodness of fit between model outputs and measurements.