Fully Bayesian optimal design using the approximate coordinate exchange algorithm and normal-based approximations to posterior quantities
Overstall, Antony M., McGree, James, & Drovandi, Christopher C. (2016) Fully Bayesian optimal design using the approximate coordinate exchange algorithm and normal-based approximations to posterior quantities. [Working Paper] (Unpublished)
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A new general approach for finding Bayesian optimal designs is proposed, which combines computationally efficient normal-based approximations to posterior quantities to aid in approximating the expected loss, and the approximate coordinate exchange algorithm. This new methodology is demonstrated on non-trivial examples of practical importance including hierarchical models for blocked experiments and experimental aims of parameter estimation and model selection. Where possible the results of the proposed methodology are compared, both in terms of performance and computing time, to results from using computationally more expensive, but potentially more accurate, Monte Carlo approximations. Moreover the methodology is also applied to problems where the use of Monte Carlo approximations is computationally infeasible.
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|Item Type:||Working Paper|
|Keywords:||Loss function, Model selection, Bayesian optimal design, Parameter estimation, Quadratic loss, Self-information loss, 0-1 loss|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Statistical Theory (010405)
|Divisions:||Current > QUT Faculties and Divisions > Science & Engineering Faculty|
|Copyright Owner:||Copyright 2016 The Author(s)|
|Deposited On:||29 Aug 2016 02:00|
|Last Modified:||29 Aug 2016 22:56|
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