1 Colorado State University’s Colorado State University’s EPA-FUNDED PROGRAM ON EPA-FUNDED PROGRAM ON SPACE-TIME AQUATIC RESOURCE SPACE-TIME AQUATIC RESOURCE MODELING and ANALYSIS PROGRAM MODELING and ANALYSIS PROGRAM (STARMAP) (STARMAP) Jennifer A. Hoeting and N. Scott Urquhart Associate Professor and Senior Research Scientist Department of Statistics Colorado State University Fort Collins, CO 80523-1877
39
Embed
1 Colorado State University’s EPA-FUNDED PROGRAM ON SPACE-TIME AQUATIC RESOURCE MODELING and ANALYSIS PROGRAM (STARMAP) Jennifer A. Hoeting and N. Scott.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Colorado State University’s Colorado State University’s EPA-FUNDED PROGRAM ONEPA-FUNDED PROGRAM ON
SPACE-TIME AQUATIC RESOURCESPACE-TIME AQUATIC RESOURCEMODELING and ANALYSIS PROGRAMMODELING and ANALYSIS PROGRAM
(STARMAP) (STARMAP)
Colorado State University’s Colorado State University’s EPA-FUNDED PROGRAM ONEPA-FUNDED PROGRAM ON
SPACE-TIME AQUATIC RESOURCESPACE-TIME AQUATIC RESOURCEMODELING and ANALYSIS PROGRAMMODELING and ANALYSIS PROGRAM
(STARMAP) (STARMAP)
Jennifer A. Hoeting and N. Scott Urquhart
Associate Professor and Senior Research ScientistDepartment of Statistics
Colorado State UniversityFort Collins, CO 80523-1877
2
STARMAP FUNDINGSTARMAP FUNDINGSpace-Time Aquatic Resources Modeling and Analysis ProgramSpace-Time Aquatic Resources Modeling and Analysis Program
STARMAP FUNDINGSTARMAP FUNDINGSpace-Time Aquatic Resources Modeling and Analysis ProgramSpace-Time Aquatic Resources Modeling and Analysis Program
The work reported here today was developed under the STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by EPA. The views expressed here are solely those of presenters and STARMAP, the Program they represent. EPA does not endorse any products or commercial services mentioned in these presentation.
This research is funded by
U.S.EPA – Science To AchieveResults (STAR) ProgramCooperativeAgreement
# CR - 829095
3
Overview of PresentationOverview of PresentationOverview of PresentationOverview of Presentation
1. EPA’s Request for Applications (RFA)
2. CSU’s Response = STARMAP
3. A summary of some of the goals and recent accomplishments of the four STARMAP projects
4. Opportunities for Cooperation
4
EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA)(RFA)
EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA)(RFA)
Content Requirements• Research in Statistics
Directed toward using, in part, data gathered by probability surveys of the “EMAP-sort.”
• Training of “future generations” of environmental statisticians
• Outreach to the states and tribes
5
EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA) (RFA) - continued- continued
EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA) (RFA) - continued- continued
• Major Administrative Requirement “… each of the two programs established will involve
collaborative research at multiple, geographically diverse sites.”
• Two Programs:1. Oregon State University: Design-based/model assisted survey methodology2. Colorado State University:
Spatial and temporal modeling, incorporating hierarchical survey design, data analysis, modeling
6
RESPONSE to RFA from CSURESPONSE to RFA from CSURESPONSE to RFA from CSURESPONSE to RFA from CSU
• Institutions: Colorado State University
o Department of Statistics o Natural Resources Ecology Lab
Oregon State University
Including work at o Iowa State Universityo University of Alaska, Fairbankso University of Washington o Southern California Coastal Water Research Project (SCCWRP)o Water Quality Technology, Inc
• Most statistical techniques taught in graduate statistics classes assume that the observations are uncorrelated
• Reality: aquatic resources that are nearby in space are typically more similar than those far apart
• STARMAP aims to1. Develop sampling methods to enhance EMAP designs2. Develop statistical methods which make the best use of
the all available current data
9
STARMAPSTARMAPTypes of available dataTypes of available data
STARMAPSTARMAPTypes of available dataTypes of available data
• A response of interest A probability sample in a region, e.g., 305(b) Some purposefully chosen points in the region Spatially “intensive” points near some of the observation
locations Response may be multivariate
• Predictors Some at observation locations only Some at whatever density desired from GIS
STARMAP PROJECT 1: STARMAP PROJECT 1: COMBINING ENVIRONMENTAL DATA SETSCOMBINING ENVIRONMENTAL DATA SETS
STARMAP PROJECT 1: STARMAP PROJECT 1: COMBINING ENVIRONMENTAL DATA SETSCOMBINING ENVIRONMENTAL DATA SETS
Project leader: Jennifer Hoeting, CSU Department of Statistics
Two of the goals of the project: 1. Develop models and methodology for modeling
aquatic resource data 2. Enhance EMAP designs
12
STARMAP PROJECT 1: STARMAP PROJECT 1: A closer look at one of the projectsA closer look at one of the projects
STARMAP PROJECT 1: STARMAP PROJECT 1: A closer look at one of the projectsA closer look at one of the projects
Goal 1: Develop models and methodology for modeling aquatic resource data
• Challenges: Spatially explicit, but incomplete coverage over space Form of the response
• Example: Compositional data What proportion of the species of fish at a sample location are in
three pollution (or thermal) tolerance categories: intolerant, intermediate, and tolerant?
Can we relate multiple compositions to environmental covariates in a scientifically meaningful way?
13
Modeling compositional data:Modeling compositional data:Motivating ProblemMotivating Problem
Modeling compositional data:Modeling compositional data:Motivating ProblemMotivating Problem
• Stream sites in the Mid-Atlantic region of the United States were visited Response: For each site, each observed fish species was
cross categorized according to several traits Predictors: Environmental variables are also measured at
each site (e.g. precipitation, chloride concentration,…)
• How can we determine if collected environmental variables affect species trait compositions (which ones)?
14
Modeling compositional data:Modeling compositional data:Sampling locations for Sampling locations for
Mid-Atlantic Highlands Region Mid-Atlantic Highlands Region
Modeling compositional data:Modeling compositional data:Sampling locations for Sampling locations for
Mid-Atlantic Highlands Region Mid-Atlantic Highlands Region
15
Modeling compositional data:Modeling compositional data:Discrete Compositions and Probability ModelsDiscrete Compositions and Probability Models
Modeling compositional data:Modeling compositional data:Discrete Compositions and Probability ModelsDiscrete Compositions and Probability Models
• Compositional data are multivariate observations
Z = (Z1,…,ZD) subject to the constraints that iZi = 1 and Zi 0.
• Compositional data are usually modeled with the Logistic-Normal distribution (Aitchison 1986). LN model defined for positive compositions only, Zi > 0
• Problem: With discrete counts one has a non-trivial probability of observing 0 individuals in a particular category
• Mathematical graphs are used to illustrate complex dependence relationships in a multivariate distribution
• A random vector is represented as a set of vertices, V .
• Pairs of vertices are connected by directed or undirected edges depending on the nature of each pair’s association
19
Modeling compositional data: Fish Species Modeling compositional data: Fish Species Richness in the Mid-Atlantic HighlandsRichness in the Mid-Atlantic Highlands
Modeling compositional data: Fish Species Modeling compositional data: Fish Species Richness in the Mid-Atlantic HighlandsRichness in the Mid-Atlantic Highlands
• 91 stream sites in the Mid Atlantic region of the United States were visited in an EPA EMAP study
• Response composition: Observed fish species were cross-categorized according to 2 discrete variables:
Modeling compositional data: Modeling compositional data: Fish Species Functional GroupsFish Species Functional GroupsModeling compositional data: Modeling compositional data:
Fish Species Functional GroupsFish Species Functional Groups
Edge exclusion determined from 95% HPD intervals for parameters and off-diagonal elements of Ø
Posterior suggested chain graph for independence model (lowest DIC model)
Tolerance
Precipitation
Chloride
Elevation
Turbidity
Area
SulfateHabit
22
Modeling compositional data:Modeling compositional data:A summary A summary
Modeling compositional data:Modeling compositional data:A summary A summary
The Random Effects Discrete Regression Model
• Allows for multivariate composition response• Provides a statistically defensible graphical model
interpretation• Offers measures of uncertainty and inferences not
available using other techniques for species trait and related analyses
• Allows for predictions at unobserved locations
23
STARMAP PROJECT 1: STARMAP PROJECT 1: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 1: STARMAP PROJECT 1: Some Recent Accomplishments Some Recent Accomplishments
Goal 1: Develop models and methodology for modeling aquatic resource data
Other projects aimed at goal 1:• Models for radio telemetry habitat association data
Radio-tagged fish are monitored over time Goal: extend existing models to account for seasonal changes in fish
habitat types
• Model selection for geo-statistical models When predicting a continuous response , which covariates are best? Does spatial correlation affect model selection (YES!)
24
STARMAP PROJECT 1: STARMAP PROJECT 1: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 1: STARMAP PROJECT 1: Some Recent Accomplishments Some Recent Accomplishments
Goal 2: Enhance EMAP designs • How should EMAP-type sampling be intensified to
estimate spatial correlation? Current context – City of San Diego and Southern
California Coastal Water Research Project (SCCWRP)o Accurate maps of environmental measures around San Diego’s
oceanic sewage outfall
• How to Get From 305(b) Survey Results to Identify 303(d) Sites? STARMAP organized a morning of talks on this topic at
the recent EMAP Conference
25
STARMAP PROJECT 2: STARMAP PROJECT 2: Local Inferences from Aquatic StudiesLocal Inferences from Aquatic Studies
STARMAP PROJECT 2: STARMAP PROJECT 2: Local Inferences from Aquatic StudiesLocal Inferences from Aquatic Studies
Project leader: Jay Breidt, CSU Department of Statistics
Goals: 1. Develop techniques for small area estimation2. Develop methods to estimate the cumulative distribution
function3. Methods to infer causality from non-experimental
spatially referenced data
26
STARMAP PROJECT 2: STARMAP PROJECT 2: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 2: STARMAP PROJECT 2: Some Recent Accomplishments Some Recent Accomplishments
Goal 1: Small area estimation Combining probability survey data with non-probability
data to make spatially-explicit predictions Bayesian models to construct a set of ensemble estimates
to predict some response Data not observed everywhere, but methods will provide
predictions over entire region along with estimates of uncertainty
Current emphasis: characteristics of water quality for Mid-Atlantic Highlands region
27
STARMAP PROJECT 2: STARMAP PROJECT 2: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 2: STARMAP PROJECT 2: Some Recent Accomplishments Some Recent Accomplishments
• Goal 1: Developing and comparing different methods for small area estimation Developing new semi-parametric methods Compared to parametric and non-parametric methods,
can optimize over the benefits of both• Goal 2: Nonparametric regression estimators for
two-stage samples Incorporates auxiliary information available at the level
of the primary sampling unit Current emphasis: EMAP Northeast Lakes
• Presented results at recent EMAP conference
28
STARMAP PROJECT 3: STARMAP PROJECT 3: Development and Evaluation of Aquatic IndicatorsDevelopment and Evaluation of Aquatic Indicators
STARMAP PROJECT 3: STARMAP PROJECT 3: Development and Evaluation of Aquatic IndicatorsDevelopment and Evaluation of Aquatic Indicators
Project leader: Dave Theobald, CSU Natural Resources Ecology
Lab
Two of the project goals:1. Develop and determine landscape indicators for analyses
of EMAP data2. Develop better GIS tools for relevant agencies
29
STARMAP PROJECT 3: STARMAP PROJECT 3: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 3: STARMAP PROJECT 3: Some Recent Accomplishments Some Recent Accomplishments
Goal 1: Develop and determine landscape indicators for analyses of EMAP data
• Developing predictors for stream size and flow status to overcome limitations of the National Hydrological Database Classification of perennial versus non-perennial streams
• Estimation of regional indicators of taxa richness Quantifying taxa richness in terms of rarity assessed by a fixed
count Sampling macroinvertebrates: compositing and structure of
variance• Compiling indicators and additional GIS data coverage for
MAHA and Western Pilot Study
30
STARMAP PROJECT 3: STARMAP PROJECT 3: Some Recent Accomplishments Some Recent Accomplishments
STARMAP PROJECT 3: STARMAP PROJECT 3: Some Recent Accomplishments Some Recent Accomplishments
Goals 2: Develop better GIS tools
• Software for Generalized Random Tessellation Stratified (GRTS) sampling
• GRTS: Robust spatially balanced random sampling• Software implements the GRTS algorithm in
ARCVIEW• Software is in final testing stages
31
Laramie Foothills Study Area and Sample PointsLaramie Foothills Study Area and Sample PointsLaramie Foothills Study Area and Sample PointsLaramie Foothills Study Area and Sample Points
32
Photo interpretation points displayed with predicted current condition map
Photo interpretation points displayed with predicted current condition map