Bayesian Analysis

Hierarchical model building, fitting, and checking: a behind-the-scenes look at a Bayesian analysis of arsenic exposure pathways

Catherine A. Calder, Peter F. Craigmile, Noel Cressie, Hongfei Li, and Rajib Paul

Full-text: Open access

Abstract

In this article, we present a behind-the-scenes look at a Bayesian hierarchical analysis of pathways of exposure to arsenic (a toxic heavy metal) using the Phase I National Human Exposure Assessment Survey carried out in Arizona. Our analysis combines individual-level personal exposure measurements (biomarker and environmental media) with water, soil, and air observations from the ambient environment. We include details of our model-building exercise that involved a combination of exploratory data analysis and substantive knowledge in exposure science. Then we present our strategies for model fitting, which involved piecing together components of the hierarchical model in a systematic fashion to assess issues including parameter identifiability, Bayesian learning, model fit, and convergence diagnostics. We also discuss practical issues of data management and algorithm debugging, especially in the light of missing and censored data. We believe that our presentation of these behind-the-scenes details will be of use to other researchers who build complex Bayesian hierarchical models.

Article information

Source
Bayesian Anal., Volume 4, Number 1 (2009), 1-35.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370385

Digital Object Identifier
doi:10.1214/09-BA401

Mathematical Reviews number (MathSciNet)
MR2486234

Zentralblatt MATH identifier
1330.62384

Keywords
Arizona Bayesian learning data management environmental health Markov chain Monte Carlo (MCMC) algorithm model validation National Human Exposure Assessment Survey (NHEXAS)

Citation

Craigmile, Peter F.; Calder, Catherine A.; Li, Hongfei; Paul, Rajib; Cressie, Noel. Hierarchical model building, fitting, and checking: a behind-the-scenes look at a Bayesian analysis of arsenic exposure pathways. Bayesian Anal. 4 (2009), no. 1, 1--35. doi:10.1214/09-BA401. https://projecteuclid.org/euclid.ba/1340370385


Export citation

References

  • Banerjee, S., Carlin, B., and Gelfand, A. (2004). Hierarchical Modeling and Analysis for Spatial Data. Boca Raton, FL: Chapman & Hall/CRC.
  • Berliner, L. M. (2003). “Physical-statistical modeling in geophysics.” Journal of Geophysical Research (Atmospheres), 108 (D24): 8776, doi: 10.1029/2002JD002865.
  • Calder, C. A., Craigmile, P. F., and Zhang, J. (2008). “Regional Spatial Modeling of Topsoil Geochemistry.” Biometrics. doi: 10.1111/j.1541-0420.2008.01038.x.
  • Clayton, C. A., Pellizzari, E. D., and Quackenboss, J. J. (2002). “National Human Exposure Assessment Survey: Analysis of exposure pathways and routes for arsenic and lead in EPA Region 5.” Journal of Exposure Analysis and Environmental Epidemiology, 12: 29–43.
  • Committee on Advances in Assessing Human Exposure to Airborne Pollutants, N. R. C. (1991). Human Exposure Assessment for Airborne Pollutants: Advances and Opportunities. The National Academies Press.
  • Cressie, N., Buxton, B. E., Calder, C. A., Craigmile, P. F., Dong, C., McMillan, N. J., Morara, M., Santner, T. J., Wang, K., Young, G., and Zhang, J. (2007). “From Sources to Biomarkers: A Hierarchical Bayesian Approach for Human Exposure Modeling.” Journal of Statistical Planning and Inference, 137: 3361–3379.
  • Cressie, N., Richardson, S., and Jaussent, I. (2004). “Ecological Bias: Use of Maximum- entropy Approximations.” Australian and New Zealand Journal of Statistics, 46: 233–255.
  • Gelfand, A. E. and Smith, A. F. M. (1990). “Sampling-based Approaches to Calculating Marginal Densities.” Journal of the American Statistical Association, 85: 398–409.
  • Gelman, A. (2006). “Comment on “A Comparison of Bayesian and Likehood-based Methods for Fitting Mutilevel Models” by W. J. Browne and D. Draper.” Bayesian Analysis, 1: 515–534.
  • Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004). Bayesian Data Analysis, 2nd edn. Boca Raton, FL: Chapman & Hall/CRC.
  • Geweke, J. (1991). “Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints.” In Keramidas, E. M. (ed.), Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface, 571–568. Fairfax, VA: Interface Foundation of North America.
  • Lauritzen, S. L. (1996). Graphical Models. Oxford, UK: Oxford University Press.
  • Lindley, D. V. and Smith, A. F. M. (1972). “Bayes Estimates for the Linear Model (with Discussion).” Journal of the Royal Statistical Society, Series B, 34: 1–41.
  • McMillan, N. J., Morara, M., and Young, G. S. (2006). “Hierarchical Bayesian Modeling of Human Exposure Pathways and Routes.” 2492–2503. Alexandria, VA: American Statistical Association.
  • NERL and National Center for Environmental Assessment (2000). Strategic Plan For The Analysis Of The National Human Exposure Assessment Survey (NHEXAS) Pilot Study Data. ORD, U.S. EPA. URL http://www.epa.gov/nerl/research/nhexas/strategy.pdf
  • O’Rourke, M. K., Van de Water, P. K., Jin, S., Rogan, S. P., Weiss, A. D., Gordon, S., Moschandreas, D., and Lebowitz, M. (1999). “Evaluations of Primary Metals from NHEXAS Arizona: Distributions and Preliminary Exposures.” Journal of Exposure Analysis and Environmental Epidemiology, 9: 435–445.
  • Pellizzari, E., Lioy, P., Quackenboss, J., Whitmore, R., Clayton, A., Freeman, N., Waldman, J., Thomas, K., Rodes, C., and Wilcosky, T. (1995). “Population-Based Exposure Measurements in EPA Region 5: A Phase I Field Study in Support of the National Human Exposure Assessment Survey.” Journal of Exposure Analysis and Environmental Epidemiology, 5: 327–358.
  • R Development Core Team (2007). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. URL http://www.R-project.org
  • Robertson, G., Lebowitz, M., O’Rourke, M., Gordon, S., and Moschandreas, D. (1999). “The National Human Exposure Assessment Survey (NHEXAS) Study in Arizona – Introduction and Preliminary Results.” Journal of Exposure Analysis and Environmental Epidemiology, 9: 427–434.
  • Samet, J. and Jaakkola, J. (1999). “The Epidemiologic Approach to Investigating Outdoor Air Pollution.” In Holgate, S., Samet, J., Koren, H., and Maynard, R. (eds.), Air Pollution and Health. London, UK: Academic Press.
  • Santner, T. J., Craigmile, P. F., Calder, C. A., and Paul, R. (2008). “Effect and Pathways Modifiers in a Bayesian Pathways Analysis of the National Human Exposure Assessment Survey for Arsenic in EPA Region 5.” Environmental Science and Technology, 42(15): 5607–5614.
  • Seaber, P., Kapinos, F., and Knapp, G. (1987). Hydrologic Unit Maps. U.S. Geological Survey, Denver, CO.
  • Tapio, S. and Grosche, B. (2006). “Arsenic in the aetiology of cancer.” Mutation Research, 612: 215–246.
  • Tierney, L. (1994). “Markov Chains for Exploring Posterior Distributions.” Annals of Statistics, 22: 1701–1728.
  • WHO (1981). Arsenic. Geneva: World Health Organization. Environmental Health Criteria 18.

See also

  • Related item: Christopher David Barr, Francesca Dominici. Comment on article by Craigmile et al. Bayesian Anal., Vol. 4, Iss. 1 (2009), 37-39.
  • Related item: David B. Dunson. Comment on article by Craigmile et al. Bayesian Anal., Vol. 4, Iss. 1 (2009), 41-43.
  • Related item: Alexandra M. Schmidt. Comment on article by Craigmile et al. Bayesian Anal., Vol. 4, Iss. 1 (2009), 45-53.
  • Related item: Catherine A. Calder, Peter F. Craigmile, Noel Cressie, Hongfei Li, Rajib Paul. Rejoinder. Bayesian Anal., Vol. 4, Iss. 1 (2009), 55-62.