Spatially-varying stochastic differential equations, with application to the biological sciences

(July 7,2015 - July 10,2015 )

Organizers


Peter Craigmile
Department of Statistics, The Ohio State University
Radu Herbei
Department of Statistics, The Ohio State University

In biology, ecology, and public health there has been a growth in the use of stochastic differential equations (SDEs) to model scientific phenomena over time. SDEs have the ability to simultaneously capture he known deterministic dynamics of the variable of interest (e.g., chemical levels within a cell, the chemical or physical characteristics of a river, the presence, absence and spread of a disease), while enabling a modeler to capture the unknown dynamics or measurement processes in a stochastic setting.

In this four-day workshop, participants will learn about the use of SDEs to model physical phenomena in the biological sciences. Students will learn how to define and manipulate SDEs, and will understand the difficulties in performing statistical inference on the parameters of SDEs using data. They will relate the modeling of SDEs to the theory of spatial and temporal data analysis, and will carry out a small group project to discover and investigate how to model data from various disciplines within the biological sciences.

The lectures will be taught by a selection of external and internal speakers, each of which have a different experience in different aspects of modeling using SDEs, as well as in spatial and temporal data analysis. Students will learn the material through practical exercises.

Students should come to the workshop with two years of graduate experience in Statistics or equivalent. They should be comfortable with statistical models and theory, likelihood inference, and have some exposure to Monte Carlo techniques. Students should have taken a course in linear models, and have knowledge of the statistical software package called R (http://www.r-project.org). Some exposure to time series analysis and spatial statistics is helpful, but not essential. Students should bring a laptop to the workshop, preloaded with R. Online material (including videos and exercises) useful for this course will be made available at least a week before the workshop begins.

Partial support is available for students to attend this workshop.

Additional workshop support is being provided by STATMOS, a NSF-funded Research Network for Statistical Methods for Atmospheric and Oceanic Sciences.

Accepted Speakers

Veronica Berrocal
Department of Biostatistics, University of Michigan
Catherine Calder
Department of Statistics, The Ohio State University
Peter Craigmile
Department of Statistics, The Ohio State University
Murali Haran
Statistics, Penn State University
Radu Herbei
Department of Statistics, The Ohio State University
Laura Kubatko
Statistics/EEOB, The Ohio State University
Finn Lindgren
Mathematical Sciences, University of Bath
Christopher Wikle
Department of Statistics, University of Missouri
Tuesday, July 7, 2015
Time Session
09:00 AM
09:30 AM

Opening Remarks

09:30 AM
11:30 AM

Radu Herbei - Introduction to SDEs

11:30 AM
12:30 PM

Introduction to the student projects

12:30 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM

Radu Herbei - Inference for SDEs

04:00 PM
05:00 PM

Question and answer session

05:00 PM
07:00 PM

Opening mixer

Wednesday, July 8, 2015
Time Session
09:00 AM
12:00 PM
Peter Craigmile - Time series modeling, with application to SDEs and the biological sciences

No abstract has been provided.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
04:30 PM
Veronica Berrocal - Geostatistical and hierarchical modeling of spatial data

No abstract has been provided.

04:30 PM
06:00 PM

Student work time (faculty circulate)

Thursday, July 9, 2015
Time Session
09:00 AM
12:00 PM
Christopher Wikle - An Introduction to Spatio-Temporal Dynamical Models

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially explicit processes that evolve over time. Although descriptive models that approach this problem from the second-order (covariance) perspective are important, many real-world processes are dynamic, and it can be more efficient in such cases to characterize the associated spatio-temporal dependence by the use of dynamical models. One of the goals of this tutorial talk is to establish connections between these approaches and to discuss how a hierarchical modeling perspective adds significant flexibility to the dynamical approach. The challenge with the specification of dynamical spatio-temporal models has been related to the curse of dimensionality and the specification of realistic dependence structures. Even in fairly simple linear/Gaussian settings, spatio-temporal statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters and science-based parameterizations. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models, yet these are the processes that govern environmental and physical science. Relevant examples will be presented from the environmental sciences.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
04:30 PM
Finn Lindgren - Stochastic PDEs and Markov random fields with ecological applications

No abstract has been provided.

04:30 PM
06:00 PM

Student work time (faculty circulate)

Friday, July 10, 2015
Time Session
09:00 AM
09:40 AM
Laura Kubatko - Diffusion Models in Population Genetics

No abstract has been submitted.

09:40 AM
10:20 AM
Catherine Calder - Nonstationary Spatial Modeling

No abstract has been provided.

10:20 AM
10:50 AM
Murali Haran - Statistical Methods for Complex Computer Models

Complex computer models for physical phenomenon play an important role in science and engineering problems. Analyzing these complex models, which are often large systems of differential equations used to model the dynamics of a system, is a non-trivial problem. Statistical inference for parameters of these models and analyses of their behavior may be complicated because the models may only be studied by actually running the computer code at various settings. Also, the output from these models as well as actual observations of the physical system may be complicated and high-dimensional. I will outline some recent methodological developments for addressing these problems, and discuss both statistical and computational issues.

11:00 AM
12:00 PM

Student work time (faculty circulate)

12:00 PM
01:30 PM

Lunch Break

01:30 PM
03:30 PM

Students presentations

Name Email Affiliation
Bernstein, Jason jib5317@psu.edu Statistics, The Pennsylvania State University
Berrocal, Veronica berrocal@umich.edu Department of Biostatistics, University of Michigan
Calder, Catherine calder@stat.osu.edu Department of Statistics, The Ohio State University
Craigmile, Peter pfc@stat.osu.edu Department of Statistics, The Ohio State University
Ganguly, Shreyan ganguly.28@osu.edu Statistics, The Ohio State University
Goldwyn, Joshua jhgoldwyn@gmail.com Mathematics, Ohio State University
Haran, Murali muh10@psu.edu Statistics, Penn State University
Hefley, Trevor Trevor.Hefley@colostate.edu Department of Fish, Wildlife, and Conservation Biology, Colorado State University
Herbei, Radu herbei@stat.osu.edu Department of Statistics, The Ohio State University
Keshavarz, Hossein hksh@umich.edu Statistics, University of Michigan
Kubatko, Laura lkubatko@stat.osu.edu Statistics/EEOB, The Ohio State University
Lila, Eardi eardi.lila@gmail.com Department of Mathematics, Politecnico di Milano
Lindgren, Finn f.lindgren@bath.ac.uk Mathematical Sciences, University of Bath
Ma, Pulong mapn@mail.uc.edu Department of Mathematical Sciences, University of Cincinnati
Manlove, Kezia krm17@psu.edu Biology, Pennsylvania State University
Matthews, Michael matthews.306@buckeyemail.osu.edu Statistics, The Ohio State University
Pereira, Paula paula.pereira@estsetubal.ips.pt Department of Mathematics, School of Technology of Setúbal, Polytechnic Institute of Setúbal
Russell, James jcr264@psu.edu Statistics, Pennsylvania State University
Safikhani, Abolfazl safikhan@stt.msu.edu Statistics and Probability, Michigan State University
Shand, Lyndsay lshand2@illinois.edu Statistics, University of Illinois Urbana Champaign
Wang, Xin xinwang@iastate.edu Department of Statistics, Iowa State University
Wikle, Christopher wiklec@missouri.edu Department of Statistics, University of Missouri
Woroszylo, Casper cw20@rice.edu Statistics, Rice University
Yamazaki, Kazuo kyamazaki@math.wsu.edu Mathematics, Washington State University
Yang, Lei Lei.Yang@colostate.edu Department of Statistics, Colorado State University
Yoon, Nara nxy47@case.edu Mathematics, Case Western Reserve University
Zhou, Yuzhen zhouyuzh@msu.edu Department of Statistics and Probability, Michigan State Univerisity
Zimmerman, Aaron azimmer@uw.edu Statistics, University of Washington
Geostatistical and hierarchical modeling of spatial data

No abstract has been provided.

Nonstationary Spatial Modeling

No abstract has been provided.

Time series modeling, with application to SDEs and the biological sciences

No abstract has been provided.

Statistical Methods for Complex Computer Models

Complex computer models for physical phenomenon play an important role in science and engineering problems. Analyzing these complex models, which are often large systems of differential equations used to model the dynamics of a system, is a non-trivial problem. Statistical inference for parameters of these models and analyses of their behavior may be complicated because the models may only be studied by actually running the computer code at various settings. Also, the output from these models as well as actual observations of the physical system may be complicated and high-dimensional. I will outline some recent methodological developments for addressing these problems, and discuss both statistical and computational issues.

Diffusion Models in Population Genetics

No abstract has been submitted.

Stochastic PDEs and Markov random fields with ecological applications

No abstract has been provided.

An Introduction to Spatio-Temporal Dynamical Models

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially explicit processes that evolve over time. Although descriptive models that approach this problem from the second-order (covariance) perspective are important, many real-world processes are dynamic, and it can be more efficient in such cases to characterize the associated spatio-temporal dependence by the use of dynamical models. One of the goals of this tutorial talk is to establish connections between these approaches and to discuss how a hierarchical modeling perspective adds significant flexibility to the dynamical approach. The challenge with the specification of dynamical spatio-temporal models has been related to the curse of dimensionality and the specification of realistic dependence structures. Even in fairly simple linear/Gaussian settings, spatio-temporal statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters and science-based parameterizations. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models, yet these are the processes that govern environmental and physical science. Relevant examples will be presented from the environmental sciences.