STARMAP: Project 2

1
STARMAP Project 2 Causal Modeling for Aquatic
Resources
Alix I Gitelman Stephen Jensen Statistics
Department Oregon State University August
2003 Corvallis, Oregon
2
Project Funding
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.
3
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

4
Specific Points

• Meetings and Collaborations
• Computational Issues in Bayes Networks
• Spatial Correlation in Bayes Networks

5
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

6
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

7
Computational Issues

• Check out Steve Jensens 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

8
Spatial Correlation in Bayes Networks

• Brief background
• MAIA datamacro-invertebrates
• A conditional autoregressive (CAR) component
• Results

9
Bayesian Belief Networks

• Graphical models (Lauritzen 1982 Pearl 1985,
  1988, 2000).
• Joint probability distributions
• Nodes are random variables
• Edges are influences

10
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).

11
Spatial Proximity

• The MAIA data were collected (relatively) close
  together in space.
• Some species of macro-invertebrates can travel
  distances in the 10s of kilometers.
• How can we account for spatial proximity?

12
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

13
A Conditional Autoregessive (CAR) Model
14
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).

15
One Piece of the Puzzle
16
Some Notation

• channel sediment (poor,
  medium, good)
• acid deposit (low, moderate,
  high)
• BUG index of biotic integrity
  

17
Model Specification

continued
18
Model Specification

• if these sites are within 30km

19
Prior Specification

• Regression coefficients are given diffuse Normal
  priors

20
Prior Specification

• Two models for the multinomial probabilities,
  
• and
• 
  , where the
• are defined according to site
  proximity

21
Results

• There are 206 sites.
• The largest neighborhood set has 5 sites in it.
• Roughly 2 of the pairwise distances are less
  than 30km.

22
Results
23
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.

24
Acknowledgements

• Tom Deitterich
• Steve Jensen
• Scott Urquhart