Challenges in the Statistical Modeling of Stochastic Processes for the Natural Sciences (17w5107)

Arriving in Banff, Alberta Sunday, July 9 and departing Friday July 14, 2017

Organizers

(The Ohio State University)

(Simon Fraser University)

(University of California, Santa Barbara)

(University of Washington)

(Oregon State University)

Paul Sampson (University of Washington)

Objectives

In recent years there have been a number of statistics workshops focused on a particular application area in the Natural Sciences. Here is a small sampling: Frontiers in the Detection and Attribution of Climate Change (BIRS, May 2012); The role of oceans in climate uncertainty (BIRS, Oct 2013); Big Data in Environmental Science workshop (University of British Columbia, Canada, May 2015); Spatially-varying stochastic differential equations with application to the biological sciences (Math Biosciences Institute workshop, Columbus, Ohio, Jul 2015); Program on Uncertainties in Computational Hemodynamics (Statistical and Applied Mathematical Sciences Institute, SAMSI, Summer 2015); Probabilistic modeling in genomics (Cold Spring Harbor Laboratory, Oct 2015).



These workshops can focus easily on the issues in each scientific area [see also, e.g., the articles 2, 3, 4 and 5], but do not allow statisticians to look at the bigger picture of developing more general statistical tools that can be applied to the analysis of stochastic processes in varied scientific fields. While there are a number of biological, physical science and environmental statistics conferences (e.g., organized by the International Biometric Society, the American Statistical Association, and The International Environmetrics Society), larger conferences can be more limited in providing an opportunity for researchers to come together to talk about general statistical solutions that can be used to understand how different scientific processes behave in the natural sciences.



Meanwhile, many practitioners in the natural sciences are still using simple statistical methods, such as linear models, to infer scientific relationships. While scientists understand the need for more involved inferences, they are limited by the statistical tools available to them. Statistical modeling using stochastic processes provides a way to represent coherently what is known, postulated, or unknown in a given scientific problem. For example in climate change, we can use stochastic processes to more accurately represent the climate forcing that drives change, rather than just modeling linear associations [4]. In assessing flood risk, we can model the stochastic processes that drive the hydrologic systems, rather than using deterministic systems modeling [6].



There is a need to better communicate the use of statistical methods for modeling stochastic processes in these areas. We need to understand not only how to describe complicated datasets that we observe in varied fields, but to understand what common challenges the data provide. This has only become more critical as researchers, companies, and, crucially, granting agencies are looking to solve more complicated problems which lie at the interfaces of many areas (e.g., the food/water nexus; examining the factors underlying environmental hazards; modeling interacting ecological systems).



This workshop will bring together statisticians studying a wide range of applications in the natural sciences. In preparation for this proposal potential attendees were asked to highlight issues in modeling and inference for stochastic processes in their particular application areas. Several cross-cutting themes emerged: space-time modeling for random fields; space-time modeling for point processes; hierarchical statistical modeling; multi-scale modeling; non-Gaussian random fields; excursion/exceedance modeling for extreme values for stochastic processes; and ensemble models among others. Across these modeling strategies a number of inference challenges emerged in many guises: model selection; model validation; model verification; data assimilation; forecasting uncertainty. In all these inference areas there is a need for tools and tactics which make full use of the stochastic process structure.



Part of our focus will be to understand these commonalities between the stochastic processes, and the statistical methods used to fit models to these processes based on data. For example, in many applications, the use of hierarchical spatio-temporal modeling has become a critical tool in understanding change over varied spatial and temporal changes. State-of-the-art spatio-temporal stochastic models can capture the known deterministic features of systems (for example, weather, climate, hydrological discharge, or animal movement), while allowing for uncertainty. Since scientific areas are challenged by the complexity of the interaction between different systems, and ever-expanding data sources, this workshop will seek to explore how to develop general statistical methods to facilitate inference about processes in these cases. Statistical computation for massive data, multiscale approaches, change-of-support (e.g., statistical up- and downscaling), and data assimilation are natural topics to discuss in this arena.



The workshop will focus on cross-pollination, encouraging statisticians with an expertise in a given scientific field (e.g., biology, climate, ecology, geophysics, hydrology) to learn about the exciting problems in other scientific fields. Earlier days in the workshop will contain a mix of talks, a poster session, and roundtable discussions in assorted fields. Researchers with different skill sets in the statistical modeling of stochastic processes will have an opportunity to draw parallels to problems in their own areas. By the end of the workshop the focus will be on sessions that allow the attendees to investigate and outline the common problems that need to be solved in the future as we develop general statistical methodology for the analysis of stochastic processes in the Natural Sciences.



We will strive to invite researchers from all walks of life, making sure to include graduate and junior researchers in the program. As part of striving to better communicate the use of statistical methods for stochastic processes in science, the discussion and results of the workshop will be made widely available. For example, we are currently discussing the possibility of having a special issue of a statistics journal dedicated to this topic.



References:



[1] P. Guttorp (1995), Stochastic Modeling of Scientific Data, Chapman & Hall.



[2] M. Tingley, P. F. Craigmile, M. Haran, B. Li, E. Mannshardt, and B. Rajaratnam (2012). Piecing together the past: Statistical insights into paleoclimatic reconstructions. Quaternary Science Reviews, 35, 1-22.



[3] S. Ditlevsen and A. Samson (2013). Introduction to stochastic models in biology. In M. Bachar, J. Batzel, and S. Ditlevsen, editors, Stochastic Biomathematical Models, Springer.



[4] R. W. Katz, P. F. Craigmile, P. Guttorp, M. Haran, B. Sanso, and M. L. Stein (2013). Uncertainty analysis in climate change assessments. Nature Climate Change, 3, 769-771.



[5] O. Gimenez, S. T. Buckland, B. J. Morgan, N. Bez, S. Bertrand, R. Choquet, S. Dray, M.-P. Etienne, R. Fewster, and F. Gosselin (2014). Statistical ecology comes of age. Biology Letters, 10:20140698.



[6] NRC Committee on Challenges and Opportunities in the Hydrologic Sciences (2012), National Research Council. Challenges and Opportunities in the Hydrologic Sciences. Washington, DC: The National Academies Press.