On May 1st at 10AM, Dr. Vrugt will give a seminar on:
The iterative research cycle – On detection of model structural errors
In the past decades, Bayesian methods have found widespread application and use in environmental systems modeling. Bayes theorem states that the posterior probability, P(H|D) of a hypothesis, H is proportional to the product of the prior probability, P(H) of this hypothesis and the likelihood, L(H|D) of the same hypothesis given the new/incoming observations, D, or P(H|D) is proportional to the product of P(H) and L(H|D). In science and engineering, H often constitutes some numerical simulation model, D = F(x) which summarizes using algebraic, empirical, and differential equations, state variables and fluxes, all our theoretical and/or practical knowledge of the system of interest, and x = \{ x_1,…,x_d } are the d unknown parameters which are subject to inference using some data, D of the observed system response. The Bayesian approach is intimately related to the scientific method and uses an iterative cycle of hypothesis formulation (model), experimentation and data collection, and theory/hypothesis refinement to elucidate the rules that govern the natural world. Unfortunately, model refinement has proven to be very difficult in large part because of the poor diagnostic power of residual based likelihood functions. In this talk I will introduce the elements of a diagnostic approach to model evaluation and improvement.
This diagnostic approach uses signature behaviors and patterns observed in the input-output data to illuminate to what degree a representation of the real world has been adequately achieved and how the model should be improved for the purpose of learning and scientific discovery. Several case studies are used to illustrate the proposed methodology.
Dr. Vrugt is an assistant professor at the Civil & Environmental Engineering department that leads a research group that combines numerical modeling (deterministic, stochastic) and/or analytic solutions with small and large-scale measurement (direct and indirect observations), and inverse modeling (parameter estimation, data assimilation, model averaging, etc.) to improve theory, understanding and predictability of complex Earth systems. We engage in all aspects of the iterative research cycle and regularly develop new numerical, computational, statistical, and optimization approaches to reconcile complex system models with observations for the purpose of learning and scientific discovery and, thereby, enhancing the growth of environmental knowledge. We use distributed computing to permit inference of CPU-intensive forward models.
For more information, please visit http://faculty.sites.uci.edu/jasper/