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We estimate the distribution of random parameters in a distributed parametermodel with unbounded input and output for the transdermal transport of ethanolin humans. The model takes the form of a diffusion equation with the inputbeing the blood alcohol concentration and the output being the transdermalalcohol concentration. Our approach is based on the idea of reformulating theunderlying dynamical system in such a way that the random parameters are nowtreated as additional space variables. When the distribution to be estimated isassumed to be defined in terms of a joint density, estimating the distributionis equivalent to estimating the diffusivity in a multi-dimensional diffusionequation and thus well-established finite dimensional approximation schemes,functional analytic based convergence arguments, optimization techniques, andcomputational methods may all be employed. We use our technique to estimate abivariate normal distribution based on data for multiple drinking episodes froma single subject.

Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor