Standard factorial designs may sometimes be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments which uses a criterion that allows for uncertainty in the link function, the linear predictor or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated.

The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional design spaces. We provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm. This methodology uses a Gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps. It has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables, numbers of runs and randomization restrictions. In contrast to existing approaches to Bayesian design, the method can find multi-variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility. The methodology is demonstrated on a variety of challenging examples of practical importance, including design for pharmacokinetic models and design for mixed models with discrete data. For many of these models, Bayesian designs are not currently available. Comparisons are made to results from the literature, and to designs obtained from asymptotic approximations.

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Halite particles about 2 micrometers in size were collected by a quartz crystal microbalance cascade impactor from the El Chichón eruption cloud in the lower stratosphere during April and May 1982. These particles are probably derived from the erupted chloride-rich, alkalic magma. Enrichments of hydrogen chloride and increases in optical depolarization in the eruption cloud observed by lidar measurements may reflect the influence of the halite particles. There is evidence that the halite particles reacted with sulfuric acid after about 1 month, releasing gaseous hydrogen chloride, which can influence the catalytic destruction of ozone in the stratosphere.

Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. In this paper, simulated experiments are used to evaluate the use of E(s2)-optimal and Bayesian D-optimal designs, and to compare three analysis strategies representing regression, shrinkage Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. In this paper, simulated experiments are used to evaluate the use of E(s 2 )-optimal and Bayesian D-optimal designs, and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure. Suggestions are made for choosing the values of the tuning constants for each approach. Findings include that (i) the preferred analysis is via shrinkage; (ii) designs with similar numbers of runs and factors can be effective for a considerable number of active effects of only moderate size; and (iii) unbalanced designs can perform well. Some comments are made on the performance of the design and analysis methods when effect sparsity does not hold.