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STARMAP: Project 2Causal Modeling for Aquatic Resources
Alix I GitelmanStephen JensenStatistics Department Oregon State University
August 2003Corvallis, Oregon
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The work reported here 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 the presenter and STARMAP, the Program she represents. EPA does not endorse any products or commercial services mentioned in this presentation.
Project Funding
This research is funded by
U.S.EPA – Science To AchieveResults (STAR) ProgramCooperativeAgreement
#CR-829095
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Context: Section 303(d) CWA
Assessment of water quality. Identify water bodies for which controls
are not stringent enough for the health of indigenous shellfish, fish and wildlife.
TMDL assessments “…a margin of safety which takes into account any lack of knowledge…”
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Specific Points
Meetings and Collaborations
Computational Issues in Bayes Networks
Spatial Correlation in Bayes Networks
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Meetings and Collaborations
Ken Reckhow; Director, Water Resources Research Institute of the University of North Carolina & Professor, Water Resources at Duke University Implemented Bayes Network models for the
Neuse River Watershed Evaluate TMDL standards, Suggest future
monitoring July/August 2003 issue of the Journal of Water
Resources Planning and Management
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Meetings and Collaborations
JoAnn Hanowski, Natural Resources Research Institute, University of Minnesota at Duluth Avian ecology (Great Lakes) Point count data Data at landscape and smaller scales
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Computational Issues
Check out Steve Jensen’s poster on computational issues for Bayesian Belief Networks. Implementation of the Reversible Jump
MCMC algorithm for Bayes networks. Comparison with two-step modeling
approach using “canned” software
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Spatial Correlation in Bayes Networks
Brief background MAIA data—macro-invertebrates A conditional autoregressive (CAR)
component Results
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Bayesian Belief Networks
Graphical models (Lauritzen 1982; Pearl 1985, 1988, 2000).– Joint probability distributions– Nodes are random variables– Edges are “influences”
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Understanding Mechanisms of Ecosystem Health
Mid-Altantic Integrated Assessment (MAIA) Program (1997-1998).
Program to provide information on conditions of surface water resources in the Mid-Atlantic region.
Focus on the condition of macro-invertebrates (BUGIBI).
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Spatial Proximity
The MAIA data were collected (relatively) close together in space.
Some species of macro-invertebrates can travel distances in the 10’s of kilometers.
How can we account for spatial proximity?
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Options for Dealing with Spatial Correlation
Include location in the model Allow additional nodes based on
location (i.e., spatial auto-correlation) Account for spatial dependence in the
residuals (and only in the “response”) Some combination of these
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A Conditional Autoregessive (CAR) Model
( , , , , ) ( | ) ( | , ) ( | , ) ( ) ( )p x w z v y p y z p z x w p v w y p w p x
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A Conditional Autoregessive (CAR) Model
(Besag & Kooperberg, 1995; Qian et al., working paper).
Allow each univariate component to have its own CAR parameterization.
CAR rely on defining neighborhoods, which could have different meaning for the different components (e.g., using the Euclidean metric or a stream network metric).
( , , , , ) ( | ) ( | , ) ( | , ) ( ) ( )p x w z v y p y z p z x w p v w y p w p x
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Some Notation
channel sediment (poor, medium, good)
acid deposit (low, moderate, high)
BUG index of biotic integrity
1 2 3{ , , }iC
1 2 3{ , , }iA
0 100[ , ]iB
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Prior Specification
Two models for the multinomial probabilities,
1. and
2. , where the
are defined according to site proximity
,a cp p
(1,1,1)ap dir (1,1,1)cp dir
1 2 3( , , ), ,z z z zp dir z a c 's
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Results
There are 206 sites. The largest neighborhood set has 5
sites in it. Roughly 2% of the pairwise distances
are less than 30km.
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Final Words
Important additional information can be obtained by incorporating the spatial correlation component.
This approach can be extended to other nodes of the BBN using a different spatial dependence structure, and/or a different distance metric for each node.