A storage model with random release rate for modeling exposure to food contaminants

Patrice Bertail (1, 2) , Stéphan Clémençon (1, 3, 4) , Jessica Tressou (4, 5)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CREST - Centre de Recherche en Économie et Statistique
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 MET@RISK - Méthodologies d'Analyse de Risque Alimentaire
5 HKUST-ISMT - Hong Kong University of Science and Technology - Information Systems, Business Statistics & Operations Management

This paper is devoted to present and study a specific continuous-time piecewise-deterministic Markov process for describing the temporal evolution of exposure to a given food contaminant. The quantity X of food contaminant present in the body evolves through its accumulation after repeated dietary intakes on the one hand and the pharmacokinetics behavior of the chemical on the other hand. In the dynamic modeling considered here, the accumulation phenomenon is modeled by a simple marked point process with positive i.i.d. marks and elimination in between intakes occurs at a random linear rate X, randomness of the coefficient accounting for the variability of the elimination process due to metabolic factors. Via embedded chain analysis, ergodic properties of this extension of the standard compound Poisson dam with (deterministic) linear release rate are investigated, the latter being of crucial importance for describing the long-term behavior of the exposure process (Xt)t0 and assessing values of quantities such as the proportion of time the body burden in contaminant is over a certain threshold. The exposure process being not directly observable, simulation-based statistical methods for estimating steady-state or time-dependent quantities are also investigated by coupling analysis. Finally, applications to methylmercury contamination data are considered.

Mots clés: piecewise deterministic Markov process; dietary contamination; ergodicity; stability; simulation estimators; storage models; methylmercury

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Patrice Bertail, Stéphan Clémençon, Jessica Tressou. A storage model with random release rate for modeling exposure to food contaminants. 2007. ⟨hal-00138279v3⟩