Bayesian experimental design for a toxicokinetic-toxicodynamic model |
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Authors: | C Albert R AshauerHR Künsch P Reichert |
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Institution: | a Eawag, Aquatic Research, 8600 Dübendorf, Switzerland b Seminar für Statistik, ETH Zürich, 8092 Zürich, Switzerland |
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Abstract: | 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 multinomially distributed data such as survival time series data. |
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Keywords: | Bayesian experimental design Toxicokinetic-toxicodynamic models Expected variance estimation Relative entropy Importance sampling |
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