Bayesian Hierarchical/Multilevel Models for Inference and Prediction Using Cross-System Lake Data

  • Craig A. Stow
  • E. Conrad Lamon
  • Song S. Qian
  • Patricia A. Soranno
  • Kenneth H. Reckhow


Cross-system data have been extensively used to estimate models for predicting lake responses to management actions. Using data from many lakes for model estimation is based on an implicit assumption that all lakes in the data set behave similarly. A common strategy to help meet this assumption is to group the data by common lake features, such as geography, landscape setting or morphometry, and estimate separate models for each lake group. Multilevel/hierarchical models offer a rigorous approach to combine data from many lakes and/or groups of lakes for inference at multiple levels of aggregation. We use data from 382 Michigan lakes and reservoirs to develop and evaluate several alternative multilevel models for predicting chlorophyll a concentration from total phosphorus concentration. Working in a Bayesian framework provides measures of uncertainty that can be used to evaluate probability that management objectives can be achieved under differing strategies.


Posterior Distribution Markov Chain Monte Carlo Prior Distribution Secchi Depth Total Phosphorus Concentration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Akaike’s Information Criterion


Analysis of Variance


Bayesian classification and regression tree


Bayesian Information Criterion


Classification and Regression Tree


Deviance Information Criterion


Log Integrated likelihood


Markov Chain Monte Carlo


Maximum Likelihood Estimator


Schwarz's Bayesian criterion


Total phosphorus


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Craig A. Stow
    • 1
  • E. Conrad Lamon
    • 2
  • Song S. Qian
    • 3
  • Patricia A. Soranno
    • 4
  • Kenneth H. Reckhow
    • 5
  1. 1.NOAA Great Lakes Environmental Research LaboratoryAnn ArborUSA
  2. 2.Levine Science Research CenterDuke University, Nicholas School of the Environment and Earth SciencesDurhamUSA
  3. 3.Duke University, Nicholas School of the Environment and Earth SciencesDurhamUSA
  4. 4.Department of Fisheries and wildlifeMichigan state UniversityEast LansingUSA
  5. 5.A317 Levine Science Research CenterDuke University, Nicholas School of the Environment and Earth SciencesDurhamUSA

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