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

2 The work reported here was developed under the STAR Research Assistance Agreement CR 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 Achieve Results (STAR) Program Cooperative Agreement #CR

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 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

8 Spatial Correlation in Bayes Networks  Brief background  MAIA data—macro-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 ( ).  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 10’s 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