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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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One Piece of the Puzzle

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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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Model Specification

( ,1)i cC Mult p

( ,1)i aA Mult p

logit( ) ( , )B MVN

continued…

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Model Specification

if these sites are within 30km

0 1 2i i iC A

2ii

2

0

ij

i j

i j

i j

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Prior Specification

Regression coefficients are given diffuse Normal priors

21/ IG

Unif

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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.

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Acknowledgements

Tom Deitterich Steve Jensen Scott Urquhart