Award Abstract # 1463642
FRG: Collaborative Proposal: Extreme Theory Value Theory for Spatially Indexed Functional Data

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: THE REGENTS OF THE UNIV. OF COLORADO
Initial Amendment Date: July 24, 2015
Latest Amendment Date: July 8, 2017
Award Number: 1463642
Award Instrument: Continuing Grant
Program Manager: Gabor Szekely
DMS
 Division Of Mathematical Sciences
MPS
 Directorate for Mathematical and Physical Sciences
Start Date: August 1, 2015
End Date: July 31, 2019 (Estimated)
Total Intended Award Amount: $129,326.00
Total Awarded Amount to Date: $129,326.00
Funds Obligated to Date: FY 2015 = $37,558.00
FY 2016 = $39,619.00

FY 2017 = $52,149.00
History of Investigator:
  • Joshua French (Principal Investigator)
    joshua.french@ucdenver.edu
Recipient Sponsored Research Office: University of Colorado at Denver
13001 E 17TH PL STE F428
AURORA
CO  US  80045-2571
(303)724-0090
Sponsor Congressional District: 06
Primary Place of Performance: University of Colorado at Denver
1201 Larimer Street, Suite 4000
Denver
CO  US  80217-3364
Primary Place of Performance
Congressional District:
01
Unique Entity Identifier (UEI): MW8JHK6ZYEX8
Parent UEI: MW8JHK6ZYEX8
NSF Program(s): STATISTICS
Primary Program Source: 01001516DB NSF RESEARCH & RELATED ACTIVIT
01001617DB NSF RESEARCH & RELATED ACTIVIT

01001718DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 1616, 1303
Program Element Code(s): 126900
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

This project focuses on the development of statistical tools to model the spatial and temporal structure of environmental and climate extreme events. Most climate and environmental data sets can be viewed as collections of curves, one curve per year, available at several locations within a region. For example, temperature at a specific location has an annual pattern. The shapes of such annual curves change from year to year, and from location to location. Extreme departures from a typical pattern over a sizeable region can impact agricultural production and public health. The economic impacts are considerable, particularly, if they occur at unexpected times and locations. An unusual timing of a heat wave over a large area may cause significant economic damage due to crop failure and forest fires, and also affect the level of preparedness of public health services. Similarly, long spells of cold, storm-free winter time weather often lead to an increase in particulate pollution levels in densely populated mountain valleys. It is important that public officials are well-informed about the possible range and impact of such extreme events. This project will contribute toward a rigorous and objective understanding of the risks involved, and provide quantitative tools for researchers and decision makers in the fields of agriculture, public health, actuarial science, climatology and ecology.

The project seeks to develop a statistical framework for a quantitative assessment of possible extremal departures from the usual annual pattern over a region, i.e. departures of the form that have not been observed in historical records, but can occur with a positive probability. The primary focus of the project is the creation of a mathematical framework, and implementation through the development of statistical software. Building on recent advances in functional data analysis, extreme value theory and spatio-temporal statistics, methodology for modeling the extremal distributions of curves observed at spatial locations will be developed. Extreme curves will be determined by functionals defined on a function space in which the curves live. The work will be guided and validated by the analysis of several historical, derived, and computer data sets. Exploratory analysis will reveal the most prominent properties of extremal shapes. This will be followed by model building and the development of asymptotic theory needed to evaluate probabilities of events not previously observed. The models will reveal extremal features of the spatially indexed functional data that are not apparent from the exploratory analysis. Procedures for the construction of confidence regions, where extremal departures may occur with prescribed probability, will be obtained. Exploratory and inferential tools for the assessment of trends in the extremal shapes and regions over which they occur will also be derived.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Ettie M. Lipner, David Knox, Joshua French, Jordan Rudman, Michael Strong, James L. Crooks, "A geospatial epidemiologic analysis of nontuberculous mycobacterial infection: an ecological study in Colorado" Annals of the American Thoracic Society , 2017
French, Joshua P. and Kokoszka, Piotr S. "A sandwich smoother for spatio-temporal functional data" Spatial Statistics , 2020 https://doi.org/10.1016/j.spasta.2020.100413 Citation Details
Joshua P. French "autoimage: Multiple Heat Maps for Projected Coordinates" R Journal , 2017
Joshua P. French, Piotr Kokoszka, and Stilian Stoev, Lauren Hall "Quantifying the risk of extreme heat waves over North America using climate model forecasts" Journal of the Royal Statistical Society , v.131 , 2019 10.1016/j.csda.2018.07.004
Joshua P. French, Seth McGinnis, Armin Schwartzman "Comparing and contrasting the NARCCAP climate models using spatial confidence regions" Advances in Statistical Climatology, Meteorology and Oceanography , 2017
Lauren M Hall and Joshua P French "A modified CUSUM test to control post-outbreak false alarms" Statistics in Medicine , v.31 , 2019 10.1002/sim.8088
Lipner, Ettie M. and French, Joshua and Bern, Carleton R. and Walton-Day, Katherine and Knox, David and Strong, Michael and Prevots, D. Rebecca and Crooks, James L. "Nontuberculous Mycobacterial Disease and Molybdenum in Colorado Watersheds" International Journal of Environmental Research and Public Health , v.17 , 2020 10.3390/ijerph17113854 Citation Details
Pansing, E.R., Tomback, D.F., Wunder, M.B., French, J.P., and Wagner, A.C. "Microsite and elevation zone effects on seed pilferage, germination, and seedling survivalduring early whitebark pine recruitment." Ecology and Evolution , v.7 , 2018 , p.9027

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

This project used advances in functional data analysis, extreme value theory and spatio-temporal statistics to develop methodology for modeling extreme behavior in spatio-temporal data. Advances were made in formally defining extreme features of spatio-temporal functional data with respect to amplitude, duration, and spatial extent and developing risk quantification measures for such characteristics using extreme value theory. Methodology was also developed for constructing confidence regions where departures from expected behavior may occur with prescribed probability. Procedures were developed for correctly identifying the starting and ending times of extreme events observed over time, as well as identifying their spatial extent. New methodology for was developed for describing massive spatio-temporal data sets as functions, which is critical for more detailed examination of their characteristics.

 Extreme events related to climate and health can have considerable economic impacts.  An unusual timing of a heat wave or cold spell over a large area can have significant impacts on crop production, risk of forest fire, public safety, and energy production.  This in turn affects consumer food prices, insurance premia, health services availability, etc. This project applied developed methodology in quantifying extreme climate risk, assessing the similarity in future climate predictions, and identifying the duration and spatial extent of disease outbreak, all of which are useful in helping scientists, researchers, and public officials make well-informed decisions about the possible range and impact of extreme events affecting the public. Free, user-friendly software was created for this project to allow capable parties to apply and extend these methods for further examination of important topics. Several students were trained and supported under this research, increasing the availability of data scientists well-equipped to study and address important scientific and societal issues.


Last Modified: 11/22/2019
Modified by: Joshua French

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