Experiment design special event
Wednesday 28th October, 2015 14:00-17:00 Maths 516
Thanks - Antony
2.05pm Steve Gilmour (University of Southampton)
3.15pm Liz Ryan (Kings College, University of London)
4.00pm Tim Waite (University of Manchester)
Steve Gilmour (University of Southampton)
Split-Plot and Multi-Stratum Designs for Statistical Inference
It is increasingly realized that many industrial and engineering experiments use split-plot or other multi-stratum structures. Much recent work has concentrated on finding optimal, or near-optimal, designs for estimating the fixed effects parameters in multi-stratum designs. However often inference, such as hypothesis tests or interval estimation, will also be required and valid inference requires pure error estimates of the variance components. Most optimal designs provide few, if any, pure error degrees of freedom. Gilmour and Trinca (2012) introduced design optimality criteria for inference in the context of completely randomized and block designs. Here these criteria are used stratum-by-stratum in order to obtain multi-stratum designs. It is shown that these designs have better properties for performing inference. Compound criteria, which combine the inference criteria with traditional point estimation criteria are also used and the designs obtained are shown to give good compromise
between point estimation and inference. Designs are obtained for two real split-plot experiments and an illustrative split-split-plot structure.
Liz Ryan (Kings College, University of London)
Simulation-based fully Bayesian experimental design for mixed effects models
In this talk we present fully Bayesian experimental designs for nonlinear mixed effects models, in which we develop simulation-based optimal design methods to search over both continuous and discrete design spaces. Although Bayesian inference has commonly been performed on nonlinear mixed effects models, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. In this paper, the design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and require optimisation using the methods presented in this work.
Tim Waite (University of Manchester)
Random designs for robustness to functional model misspecification
Statistical design of experiments allows empirical studies in science and engineering to be conducted more efficiently through careful choice of the settings of the controllable variables under investigation. Much conventional work in optimal design of experiments begins by assuming a particular structural form for the model generating the data, or perhaps a small set of possible parametric models. However, these parametric models will only ever be an approximation to the true relationship between the response and controllable variables, and the impact of this approximation step on the performance of the design is rarely quantified.
We consider response surface problems where it is explicitly acknowledged that a linear model approximation differs from the true mean response by the addition of a discrepancy function. The most realistic approaches to this problem develop optimal designs that are robust to discrepancy functions from an infinite-dimensional class of possible functions. Typically it is assumed that the class of possible discrepancies is defined by a bound on either (i) the maximum absolute value, or (ii) the squared integral, of all possible discrepancy functions.
Under assumption (ii), minimax prediction error criteria fail to select a finite design. This occurs because all finitely supported deterministic designs have the problem that the maximum, over all possible discrepancy functions, of the integrated mean squared error of prediction (IMSEP) is infinite.
We demonstrate a new approach in which finite designs are drawn at random from a highly structured distribution, called a designer, of possible designs. If we also average over the random choice of design, then the maximum IMSEP is finite. We develop a class of designers for which the maximum IMSEP is analytically and computationally tractable. Algorithms for the selection of minimax efficient designers are considered, and the inherent bias-variance trade-off is illustrated.