Bayesian Analysis

Bayesian nonparametric model with clustering individual co-exposure to pesticides found in the French diet

Amélie Crépet and Jessica Tressou

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This work introduces a specific application of Bayesian nonparametric statistics to the food risk analysis framework. The goal was to determine the cocktails of pesticide residues to which the French population is simultaneously exposed through its current diet in order to study their possible combined effects on health through toxicological experiments. To do this, the joint distribution of exposures to a large number of pesticides, which we called the co-exposure distribution, was assessed from the available consumption data and food contamination analyses. We propose modelling the co-exposure using a Dirichlet process mixture based on a multivariate Gaussian kernel so as to determine groups of individuals with similar co-exposure patterns. Posterior distributions and optimal partition were computed through a Gibbs sampler based on stick-breaking priors. The study of the correlation matrix of the sub-population co-exposures will be used to define the cocktails of pesticides to which they are jointly exposed at high doses. To reduce the computational burden due to the high data dimensionality, a random-block sampling approach was used. In addition, we propose to account for the uncertainty of food contamination through the introduction of an additional level of hierarchy in the model. The results of both specifications are described and compared.

Article information

Bayesian Anal., Volume 6, Number 1 (2011), 127-144.

First available in Project Euclid: 13 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62P12: Applications to environmental and related topics
Secondary: 60G57: Random measures 62F15: Bayesian inference 62G99: None of the above, but in this section 62H25: Factor analysis and principal components; correspondence analysis

Dirichlet process Bayesian nonparametric modeling Multivariate Normal mixtures Clustering Multivariate exposure Food risk analysis


Crépet, Amélie; Tressou, Jessica. Bayesian nonparametric model with clustering individual co-exposure to pesticides found in the French diet. Bayesian Anal. 6 (2011), no. 1, 127--144. doi:10.1214/11-BA604.

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  • AFSSA, French food safety agency (2009). "INCA 2 (2006-2007), Etude Individuelle Nationale des Consommations Alimentaires 2. Report of the Individual and the National Study on Food Consumption. Available on line:". Technical report.
  • Antoniak, C. E. (1974). "Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems." Annals of Statistics, 2: 1152–1174.
  • Blackwell, D. and MacQueen, J. B. (1973). "Ferguson distributions via P�olya urn schemes." Annals of Statistics, 1: 353–355.
  • Cabrera, J., Lau, J. W., and Lo, A. Y. (2009). "Random Block Sampling for high dimensional clustering (from the Bayesian point of view)." Hong Kong University of Science and Technology. Available from the second author upon request.
  • EFSA (European Food Safety Agency) (2010). "Management of left-censored data in dietary exposure assessment of chemical substances." EFSA Journal, 8(3). doi:10.2903/j.efsa.2010.1557 (96pp.). Available online:
  • Escobar, M. D. and West, M. (1995). "Bayesian density estimation and inference using mixtures." Journal of the American Statistical Association, 90: 577–588.
  • Ferguson, T. S. (1973). "A Bayesian analysis of some nonparametric problems." Annals of Statistics, 1: 209–230.
  • Ishwaran, H. and James, L. F. (2001). "Gibbs Sampling Methods for Stick-Breaking Priors." Journal of the American Statistical Association, 96: 161–173.
  • Lau, J. W. and Lo, A. Y. (2007). Model based clustering and weighted Chinese restaurant processes. World Scientific Publishing. Editor: Vijay Nair.
  • Lo, A. Y. (1984). "On a class of Bayesian nonparametric estimates: I. Density Estimates." Annals of Statistics, 12(1): 351–357.
  • Müller, P. and Quintana, F. (2004). "Nonparametric Bayesian data analysis." Statistical Science, 19(1): 95–110.
  • Pitman, J. and Yor, M. (1996). "Some developments of the Blackwell-MacQueen Urn scheme." Institute of Mathematical Statistics, Hayward, California.
  • Quintana, F. and Iglesias, P. (2003). "Bayesian Clustering and Product Partition Models." Journal of the Royal Statistical Society Series B, 65(2): 557–574.
  • Rodríguez, A., Gelfand, A. E., and Dunson, D. B. (2009). "Bayesian nonparametric functional data analysis through density estimation." Biometrika, 96(1): 149–162.
  • Sethuraman, J. (1994). "A constructive definition of Dirichlet prior." Statistica Sinica, 4: 639–650.
  • Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M. (2006). "Hierarchical Dirichlet Processes." Journal of the American Statistical Association, 101(476): 1566–1581.
  • Walker, S. (2007). "Sampling the Dirichlet mixture model with slices." Communications in Statistics, 36: 45–54.
  • Walker, S., Damien, P., Laud, P., and Smith, A. (1999). "Bayesian nonparametric inference for random distributions and related functions." Journal of the Royal Statistical Society : Series B (Statistical Methodology), 61(3): 485–527.