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Bayesian experimental design for a toxicokinetic-toxicodynamic model

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Publication details

JournalJournal of Statistical Planning and Inference
DateE-pub ahead of print - 28 Jul 2011
DatePublished (current) - Jan 2012
Issue number1
Number of pages13
Pages (from-to)263-275
Early online date28/07/11
Original languageEnglish


The aim of this study is to apply the Bayesian method of identifying optimal experimental designs to a toxicokinetic-toxicodynamic model that describes the response of aquatic organisms to time dependent concentrations of toxicants. As for experimental designs, we restrict ourselves to pulses and constant concentrations. A design of an experiment is called optimal within this set of designs if it maximizes the expected gain of knowledge about the parameters. Focus is on parameters that are associated with the auxiliary damage variable of the model that can only be inferred indirectly from survival time series data. Gain of knowledge through an experiment is quantified both with the ratio of posterior to prior variances of individual parameters and with the entropy of the posterior distribution relative to the prior on the whole parameter space. The numerical methods developed to calculate expected gain of knowledge are expected to be useful beyond this case study, in particular for multi-nomially distributed data such as survival time series data. 

Bibliographical note

(C) 2011 Elsevier B.V. All rights reserved.

    Research areas

  • Toxicokinetic-toxicodynamic models, Expected variance estimation, Importance sampling, Relative entropy, Bayesian experimental design

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