Comments on: A general science-based framework for dynamical spatio-temporal models

Abstract

My congratulations to Dr. Wikle and Dr. Hooten for their excellent article on physically-informed dynamical spatio-temporal models. This article nicely unifies a large and important body of work on scientifically motivated dynamical models, and it adds to it their generalized quadratic model. The authors (and their collaborators) have demonstrated the utility of these approaches in a variety of applications, which span the last 15 years; I am sure we will see more in the future. A key feature of this work is the use of physical modeling concepts to inform about the structure of the statistical model, while leaving a number of parameters within that structure free to be estimated by the physical observations. This general strategy of using the science to constrain the model form, but not necessarily the exact parameter values, has proven fruitful in a number of physical science applications we have worked with at Los Alamos National Laboratory. I think it is an excellent way to incorporate scientific judgement into statistical analyses. A good portion of all statistics addresses the question of how one combines scientific information (theories, models, judgement, etc.) and physical observations to make inferences. The approach taken in this article encodes physical rules and principles into a dynamic spatio-temporal model (DSTM) which is amenable to Bayesian computation. In contrast, the recent work in computer model calibration takes a different tact (see Kennedy and O’Hagan 2001; Higdon et al. 2004 or Sanso et al. 2008, for example). In these applications the scientific information is encoded in a large scale computer model. This computational model is basically embedded as a “black box” within the statistical model. Below I contrast these two basic approaches.