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Title: Gibbs optimal design of experiments Authors:  Antony Overstall - University of Southampton (United Kingdom) [presenting]
Abstract: Gibbs (or generalised Bayesian) inference is a generalisation of Bayesian inference made by replacing the log-likelihood in Bayes' theorem by a (negative) loss function. The loss function identifies desirable parameter values for given responses. The advantage of Gibbs inference over traditional Bayesian inference is that it does not require the specification of a probabilistic data-generating process and, therefore, should be less sensitive to this process. Gibbs optimal design of experiments are proposed for this inferential framework, extended decision-theoretic Bayesian optimal design. The challenge is that the decision-theoretic approach relies on a probabilistic data-generating process that is notably absent from Gibbs inference. This is circumvented by assuming a designer model: a probabilistic data-generating process which is only used to find a design rather than in the ensuing inference. Because of this, the designer model can encapsulate very general data-generating processes with the aim of introducing robustness into the design procedure. The proposed Gibbs optimal design framework is demonstrated in several illustrative examples.