Designed Experiments: Recent Advances in Methods and Applications: DEMA 2011
Tuesday 30th August 2011 to Friday 2nd September 2011
08:30 to 09:20  Registration  
09:20 to 09:25 
Welcome from Sir David Wallace (INI Director) Session: Opening 
INI 1  
09:25 to 09:30 
Introduction from Steven Gilmour, Chair of Organising Committee Session: Opening 
INI 1  
09:30 to 10:30 
J Wu ([Georgia Tech]) PostFisherian Experimentation: from Physical to Virtual Session: Plenary Session Chair: Steven Gilmour
Experimental design has been a scientific discipline since the founding work of Fisher. During the 80year history, its development has been largely dominated by work in physical experiments. With advances in highperformance computing and numerical modeling, virtual experiments on a computer have become viable. This talk will highlight some major developments (physical and virtual) in this long period. Fisher’s principles (replication, randomization, blocking) will be reviewed, together with principles (effect hierarchy, sparsity, heredity) for factorial experiments. A fresh look at interactions and effect aliasing will be provided, with some surprisingly new insights on an ageold problem. Robust parameter design, another significant development which focuses on variation modeling and reduction, will be mentioned. Turning to computer experiments, the key differences with physical experiments will be highlighted. These include the lack of replication errors which ent ails new governing principles other than Fisher’s and the use of spacefilling designs instead of fractional factorials. There are two strategies for modeling and analysis: based on Gaussian processes or on function approximations. These seemingly conflicting approaches can be better linked by bringing a stochastic structure to the numerical errors. Throughout the talk, real experiments/data, ranging from manufacturing to nano technology, will be used for illustration. (Note: this talk will be an adapted version of the COPSS Fisher Lecture the speaker will deliver during the Joint Statistical Meetings in Miami in August).

INI 1  
10:30 to 11:00  Morning coffee  
11:00 to 11:30 
Randomization, Regularization and Covariate Balance in ResponseAdaptive Designs for Clinical Trials Session: Clinical Trials Chair: Barbara Bogacka
Results on the sequential construction of optimum experimental designs yield a very general procedure for generating responseadaptive designs for the sequential allocation of treatments to patients in clinical trials. The designs provide balance across prognostic factors with a controllable amount of randomization and speciable skewing towards better treatments. Results on the loss, bias and power of such rules will be discussed and the importance of regularization will be stressed in the avoidance of extreme allocations. The designs will be considered in the wider context of decisions about treatment allocation to patients within the study and to the population of future patients.

INI 1  
11:30 to 12:00 
N Flournoy ([MissouriColumbia]) Information in adaptive optimal design with emphasis on the two stage case Session: Clinical Trials Chair: Barbara Bogacka
In 1963, Box and Hunter, followed by many others, recommended selecting sequential treatments to maximize the increment of some information measure (e.g., the determinant of the Fisher information matrix). Under nonlinear regression models, because information is a function of unknown parameters, such increments must be estimated; and the information from different stages is not independent. To explore the accrual of information in adaptive designs, we study a basic one parameter nonlinear regression model with additive independent normal errors. The stage 1 treatment is taken to be fixed, the treatment allocation rule for stage 2 is taken to be a unique function of maximum likelihood estimates derived from stage 1 data. Although conditioning on the design is common in data analyses, we show in this scenario, that conditioning on the stage 2 treatment is equivalent to conditioning on the stage 1 data. This raises questions about the role of conditioning in the analysis o f adaptive designs. We also explore the efficiency conducting studies in stages and the effect of allocating different proportions of subjects to stage 1 versus stage 2.

INI 1  
12:00 to 12:30 
A particle filter for Bayesian sequential design Session: Clinical Trials Chair: Barbara Bogacka
A particle filter approach is presented for sequential design with a focus on Bayesian adaptive dose finding studies for the estimation of the maximum tolerable dose. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple reweighting step. Furthermore, the method does not require prior information represented as imagined data as in other dose finding approaches, although such data can be included straightforwardly if available. We also consider a flexible parametric model together with a newly developed hybrid design utility that can produce more robust estimates of the target dose in the presence of substantial model and parameter uncertainty.

INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
14:00 to 14:30 
D Montgomery ([Arizona State]) Constructing and Assessing Exact GOptimal Designs Session: Advances in Industry and Technology Chair: Jeff Wu
Methods for constructing Goptimal designs are reviewed. A new and very efficient algorithm for generating near Goptimal designs is introduced, and employed to construct designs for secondorder models over cuboidal regions. The algorithm involves the use of Brent’s minimization algorithm with coordinate exchange to create designs for 2 to 5 factors. Designs created using this new method either match or exceed the Gefficiency of previously reported designs. A new graphical tool, the variance ratio fraction of design space (VRFDS) plot, is used for comparison of the prediction variance for competing designs over a given region of interest. Using the VRFDS plot to compare Goptimal designs to Ioptimal designs shows that the Goptimal designs have higher prediction variance over the vast majority of the design region. This suggests that, for many response surface studies, Ioptimal designs may be superior to Goptimal designs.

INI 1  
14:30 to 15:00 
Causal Inference from 2level factorial designs Session: Advances in Industry and Technology Chair: Jeff Wu
A framework for causal inference from twolevel factorial and fractional factorial designs with particular sensitivity to applications to social, behavioral and biomedical sciences is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of parameters other than "average factorial effects" and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model. It also ensures validity of statistical inference when the investigation becomes an observational study in lieu of a randomized factorial experiment due to randomization restrictions.

INI 1  
15:00 to 15:30 
EngineeringDriven Statistical Adjustment and Calibration Session: Advances in Industry and Technology Chair: Jeff Wu
There can be discrepancy between physicsbased models and reality, which can be reduced by statistically adjusting and calibrating the models using real data. Gaussian process models are commonly used for capturing the bias between the physicsbased model and the truth. Although this is a powerful approach, the resulting adjustment can be quite complex and physically noninterpretable. A different approach is proposed here which is to postulate adjustment models based on the engineering judgment of the observed discrepancy. This often leads to models that are very simple and easy to interpret. The approach will be illustrated using many real case studies.

INI 1  
15:30 to 16:00  Afternoon tea  
16:00 to 16:30 
An overview of functional data analysis with an application facial motion modelling Session: HighDimensional Responses Chair: Rosemary Bailey
Data in the form of curves, trajectories and shape changes present unique challenges. We present an overview of functional data analysis. We show how these methods can be used to model facial motion with application to cleft lip surgery.

INI 1  
16:30 to 17:00 
Robust microarray experiments by design: a multiphase framework Session: HighDimensional Responses Chair: Rosemary Bailey Speed and Yang with Smyth (2008) outlined six main phases in genomics, proteomics and metabolomics microarray experiments. They suggested that statisticians could assist in the design of experiments in each phase of such an experiment. That being the case, the experiments potentially involve multiple randomizations (Brien and Bailey, 2006) and are multiphase. Consequently, a multiphase framework for their design will be explored, the first step of which is to list out the phases in the experiment. One set of six phases for the physical conduct of microarray experiments will be described and the sources of variability that affect these phases discussed. The multiphase design of an example microarray experiment will be investigated, beginning with the simplest option of completely randomizing in every phase and then examining the consequences of batching in one or more phases and of not randomizing in all phases. To examine the properties of a design, a mixed model and ANOVA that include terms and sources for all the identified phases will be derived. For this, the factorallocation description of Brien, Harch, Correll and Bailey (2011) will be used. It is argued that the multiphase framework used is flexible, promotes the consideration of randomization in all phases and facilitates the identification of all sources of variability at play in a microarray experiment. 
INI 1  
17:00 to 17:30 
Designed Biofluid Mixtures Allow FeatureWise Evaluation Of Metabolic Profiling Analytical Platforms Session: HighDimensional Responses Chair: Rosemary Bailey
The development of spectral analysis platforms for targeted metabolic profiling may help streamline quantification and will undoubtedly facilitate biological interpretation of metabolomics/metabonomics datasets. A general method for evaluating the performance, coverage and applicability of analytical methods in metabolic profiling is much needed to aid biomarker assessment.
The substantial variation in spectral and compositional background that exist in samples generated by real biofluid studies are often not capture by traditional evaluations of analytical performance that use compounds addition (spikes). Such approaches may therefore underestimate the contribution of matrix effects to the measurement of major metabolites and confound analysis.
We illustrate how a strategy of mixing intact biofluids in a predetermined experimental design can be used to evaluate, compare and optimise the performance of quantitative spectral analysis tools in conditions that better approximate a real metabolic profiling experiment.
Results of preliminary experiments on two commonlyused profiling platforms (highresolution 1D 1H nuclear magnetic resonance (NMR) spectroscopy and ultra high performance liquid chromatographymass spectrometry (UPLCMS)) are discussed. Use of multivariate regression allowed featurewise statistics to be generated as a summary of the overall performance of each platform.
The use of designed biofluid mixtures as a basis of evaluating the featurewise variation in instrument response provides a rational basis for exploiting information from several samples simultaneously, in contrast to spectral deconvolution, which is typically applied to one spectrum at a time.

INI 1  
17:30 to 18:30  Welcome drink reception  
18:45 to 19:30  Dinner at Wolfson Court (residents only) 
09:00 to 09:45 
P Goos ([Antwerpen]) Optimal design of blocked and splitplot experiments for fixedeffects and variancecomponents estimation Session: Hierarchical Models Chair: Heiko Grossmann
Many industrial experiments, such as block experiments and splitplot experiments, involve one or more restrictions on the randomization. In these experiments the observations are obtained in groups. A key difference between blocked and splitplot experiments is that there are two sorts of factors in splitplot experiments. Some factors are held constant for all the observations within a group or whole plot, whereas others are reset independently for each individual observation. The former factors are called wholeplot factors, whereas the latter are referred to as subplot factors. Often, the levels of the wholeplot factors are, in some sense, hard to change, while the levels of the subplot factors are easy to change. Doptimal designs, which guarantee efficient estimation of the fixed effects of the statistical model that is appropriate given the random block or splitplot structure, have been constructed in the literature by various authors. However, in general, model estimation for block and splitplot designs requires the use of generalized least squares and the estimation of two variance components. We propose a new Bayesian optimal design criterion which does not just focus on fixedeffects estimation but also on variancecomponent estimation. A novel feature of the criterion is that it incorporates prior information about the variance components through lognormal or beta prior distributions. Finally, we also present an algorithm for generating efficient designs based on the new criterion. We implement several lesserknown quadrature approaches for the numerical approximation of the new optimal design criterion. We demonstrate the practical usefulness of our work by generating optimal designs for several reallife experimental scenarios.

INI 1  
09:45 to 10:20 
SplitPlot Experiments with FactorDependent Whole Pot Sizes Session: Hierarchical Models Chair: Heiko Grossmann
In industrial splitplot experiments, the number of runs within each whole plot is usually determined independently from the factor settings. As a matter of fact, it is often equal to the number of runs that can be done within a given period of time or to the number of samples that can be processed in one oven run or with one batch. In such cases, the size of every whole plot in the experiment is fixed no matter what factor levels are actually used in the experiment. In this talk, we discuss the design of a reallife experiment on the production of coffee cream where the number of runs within a whole plot is not fixed, but depends on the level of one of the wholeplot factors. We provide a detailed discussion of various ways to set up the experiment and discuss how existing algorithms to construct optimal splitplot designs can be modified for that purpose. We conclude with a few general recommendations.

INI 1  
10:30 to 11:00  Morning coffee  
11:00 to 12:00 
Panel Discussion: Future Directions for DOE Chair: Steven Gilmour
Five prominent researchers, each from a different background, will briefly describe some of the directions future research in design of experiments could take. Among the challenges addressed will be increasingly large and complex data sets, increased computing power and its impact on design and analysis and challenges arising from unexplored areas of application. The audience will be invited to contribute their own opinions.
Featuring Anthony Atkinson, Robert Wilkinson, John Stufken, David M. Steinberg and R. A. Bailey. 
INI 1  
12:00 to 12:20 
Poster Storm Chair: Ken Russell 
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12:30 to 13:30  Lunch at Wolfson Court  
14:00 to 14:30 
H Dette (RuhrUniversität Bochum) Optimal designs, matrix polynomials and random matrices Session: Nonlinear Models Chair: Ben Torsney
In this talk we relate classical optimal design problems for weighted polynomial regression to random matrix theory. Exploring this relation we are able to derive old and new results in this important field of mathematical physics. In particular, we study the asymptotic eigenvalue distribution of random band matrices generalizing.

INI 1  
14:30 to 15:00 
NatureInspired Metaheuristic Algorithms for Generating Optimal Experimental Designs Session: Nonlinear Models Chair: Ben Torsney
We explore a particle swarm optimization (PSO) method for finding optimal experimental designs. This method is relatively new, simple yet powerful and widely used in many fields to tackle real problems. The method does not assume the objective function to be optimized is convex or differentiable. We demonstrate using examples that once a given regression model is specified, the PSO method can generate many types of optimal designs quickly, including optimal minimax designs where effective algorithms to generate such designs remain elusive.

INI 1  
15:00 to 15:30 
Doptimal designs for TwoVariable Binary Logistic Models with Interaction Session: Nonlinear Models Chair: Ben Torsney
It is not uncommon for medical researchers to administer two drugs simultaneously to a patient and to monitor the response as binary, that is either positive or negative. Interest lies in the interaction of the drugs and specifically in whether that interaction is synergistic, antagonistic or simply additive. A number of statistical models for this setting have been proposed in the literature, some complex, but arguably the most widely used is the twovariable binary logistic model which can be formulated succinctly as ln (p/(1p)) = beta0 + beta1 x1 + beta2 x2 + + beta12 x1 x2 (*) where p is the probability of a positive response, x1 and x2 are the doses or logdoses of the drugs and beta0, beta1, beta2 and beta12 are unknown parameters. There is a broad base of research on the fitting, analysis and interpretation of this model but, somewhat surprisingly, few studies on the construction of the attendant optimal designs. In fact there are two substantive reports on this design problem, both unpublished, namely the Ph.D. thesis of Kupchak (2000) and the technical report of Jia and Myers (2001). In this talk the problem of constructing Doptimal designs for the model (*) is addressed. The approach builds on that of Jia and Myers (2001) with design points represented in logit space and lying on hyperbolae in that space. Algebraic results proved somewhat elusive and just two tentative propositions are given. To counter this, a taxonomy of designs, obtained numerically and dictated by the values of the unknown parameters, is also reported. This work forms part of the Ph.D. thesis of Kabera (2009) and is joint with Gaetan Kabera of the Medical Research Council of South Africa and Prince Ndlovu of the University of South Africa. References Jia Y. and Myers R.H. (2001). “Optimal Experimental Designs for Twovariable Logistic Regression Models.” Technical Report, Department of Statistics, VPI & SU, Backsberg, Virginia. Kabera M.G. (2009). “Doptimal Designs for Drug Synergy.” Ph.D. thesis, University of KwaZuluNatal. Kupchak P.I. (2000). “Optimal Designs for the Detection of Drug Interaction.” Ph.D. thesis, University of Toronto.

INI 1  
15:30 to 16:00  Afternoon tea  
16:00 to 16:30 
Estimating the heterogeneity distribution of willingnesstopay using individualized choice sets Session: Choice Experiments Chair: Brad Jones
Two prominent approaches exist nowadays for estimating the distribution of willingnesstopay (WTP) based on choice experiments. One is to work in the usual preference space in which the random utility model is expressed in terms of partworths. These partworths or utility coefficients are estimated together with their distribution. The WTP and the corresponding heterogeneity distribution of WTP is derived from these results. The other approach reformulates the utility in terms of WTP (called WTPspace) and estimates the WTP and the heterogeneity distribution of WTP directly. Though often used, working in preference space has severe drawbacks as it often leads to WTPdistributions with long flat tails, infinite moments and therefore many extreme values.
By moving to WTPspace, authors have tried to improve the estimation of WTP and its distribution from a modeling perspective. In this paper we will further improve the estimation of individual level WTP and corresponding heterogeneity distribution by designing the choice sets more efficiently. We will generate individual sequential choice designs in WTP space. The use of this sequential approach is motivated by findings of Yu et al. (2011) who show that this approach allows for superior estimation of the utility coefficients and their distribution. The key feature of this approach is that it uses Bayesian methods to generate individually optimized choice sets sequentially based on prior information of each individual which is further updated after each choice made. Based on a simulation study in which we compare the efficiency of this sequential design procedure with several nonsequential choice designs, we can conclude that the sequential approach improves the estimation results substantially. 
INI 1  
16:30 to 17:00 
Assessing the Efficiencies of Optimal Discrete Choice Experiments in the Presence of Respondent Fatigue Session: Choice Experiments Chair: Brad Jones Discrete choice experiments are an increasingly popular form of marketing research due to the accessibility of online respondents. While statistically optimal experimental designs have been developed for use in discrete choice experiments, recent research has suggested that efficient designs often fatigue or burden the respondent to the point that decreased response rates and/or decreased response precision are observed. Our study was motivated by high earlytermination rates for one such optimallydesigned study. In this talk, we examine the design of discrete choice experiments in the presence of respondent fatigue and/or burden. To do so, we propose a model that links the respondent's utility error variance to a function that accommodates respondent fatigue and burden. Based on estimates of fatigue and burden effects from our own work and published studies, we study the impact of these factors on the realized efficiencies of commonlyused Doptimal choice designs. The tradeoffs between the number of surveys, the number of choice sets per survey, and the number of profiles per choice set are delineated. 
INI 1  
17:00 to 17:30 
M Crabbe ([KU, Leuven]) Improving the efficiency of individualized designs for the mixed logit model by including covariates Session: Choice Experiments Chair: Brad Jones
Conjoint choice experiments have become an established tool to get a deeper insight in the choice behavior of consumers. Recently, the discrete choice literature focused attention on the use of covariates like demographics, socioeconomic variables or other individualspecific characteristics in design and estimation of discrete choice models, more specifically on whether the incorporation of such choice related respondent information aids in increasing estimation and prediction accuracy. The discrete choice model considered in this paper is the panel mixed logit model. This randomeffects choice model accommodates preference heterogeneity and moreover, accounts for the correlation between individuals’ successive choices. Efficient choice data for the panel mixed logit model is obtained by individually adapted sequential Bayesian designs, which are customized to the specific preferences of a respondent, and reliable estimates for the model parameters are acquired by means of a hierarchical Bayes estimation approach. This research extends both experimental design and model estimation for the panel mixed logit model to include covariate information. Simulation studies of various experimental settings illustrate how the inclusion of influential covariates yields more accurate estimates for the individual parameters in the panel mixed logit model. Moreover, we show that the efficiency loss in design and estimation resulting from including choice unrelated respondent characteristics is negligible.

INI 1  
18:45 to 19:30  Dinner at Wolfson Court (residents only) 
09:00 to 09:30 
Optimal designs for 2^k experiments with binary response Session: Discrete Responses Chair: Dave Woods
We consider optimal designs for an experiment with k qualitative factors at 2 levels each with binary response. For local Doptimality we derive theoretical results, propose algorithms to search for optimal designs and study properties of the algorithms. The robustness of optimal designs to specification of assumed parameter values is studied. We also briefly examine Bayesian optimal designs.

INI 1  
09:30 to 10:00 
Doptimal designs for multinomial experiments Session: Discrete Responses Chair: Dave Woods
Consider a multinomial experiment where the value of a response variable falls in
one of k classes. The k classes are not assumed to have a hierarchical structure.
Let ij represent the probability that the ith experimental unit gives a response
that falls in the jth class. By modelling ln(ij=i1) as a linear function of the
values of m predictor variables, we may analyse the results of the experiment
using a Generalized Linear Model.
We describe the construction of Doptimal experimental designs for use in such
an experiment. Difficulties in obtaining these designs will be described, together
with attempts to overcome these obstacles.

INI 1  
10:00 to 10:30 
B Torsney (University of Glasgow) Fitting Latent Variable Models for Paired Comparisons and Ranking Studies  An Application of Optimal Design Theory Session: Discrete Responses Chair: Dave Woods In a paired comparisons experiment a subject has to indicate which of two 'treatments' Ti, Tj is preferred. We observe Oij, the frequency with which Ti is preferred to Tj.in nij comparisons. Under a class of models for such data, which include the Bradley Terry and Thurstone models, P(Ti is preferred to Tj) = F( i  j), where F(.) is a symmetric distribution function and ( i) is a treatment index. For identifiability purposes constraints must be imposed on parameters. One is to assume that ipi = 1, where pi = ln( i); an alternative is ipi = 1. Thus theorems identifying optimal design weights and algorithms for determining them carry over to the maximum likelihood estimation of these parameters. Of course these tools can also be used to determine locally optimal designs for such models. We will explore this fusion of topics, taking the opportunity to expand on the class of models, both for simple paired comparisons data and also for data consisting of orderings or rankings. In particular we will exploit multiplicative algorithms for maximum likelihood estimation. 
INI 1  
10:30 to 11:00  Morning coffee  
11:00 to 11:30 
Bayesian Adaptive Design for Statespace Models with Covariates Session: Design for Observational Systems Chair: Stefanie Biedermann
Modelling data that change over space and time is important in many areas, such as environmental monitoring of air and noise pollution using a sensor network over a long period of time. Often such data are collected dynamically together with the values of a variety of related variables. Due to resource limitations, an optimal choice (or design) for the locations of the sensors is important for achieving accurate predictions. This choice depends on the adopted model, that is, the spatial and temporal processes, and the dependence of the responses on relevant covariates. We investigate adaptive designs for statespace models where the selection of locations at time point $t_{n+1}$ draws on information gained from observations made at the locations sampled at preceding time points $t_1, \ldots, t_n$. A Bayesian design selection criterion is developed and its performance is evaluated using several examples.

INI 1  
11:30 to 12:00 
Design of Networked Experiments Session: Design for Observational Systems Chair: Stefanie Biedermann
We consider experiments on a number of subjects, and examine how the links between subjects in an experiment, affect the optimal design. For example, in a marketing experiment, it is reasonable to believe that a product may be preferred more by a subject whose 'friend' also prefers that product, and we may wish to use this 'friendship' information to improve our design.
We present optimal designs to measure both the direct effect and the network effect. We discuss how the structure of the network has a large influence on the optimal design, but show that even if we know many properties of the network, as represented by the eigenvalues of a graph, we cannot determine an absolute design.
We present examples based on marketing experiments, and show how the results can be applied to experiments in social sciences and elsewhere.

INI 1  
12:00 to 12:20 
Poster Storm Chair: Ken Russell 
INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
14:30 to 16:00 
Trip to Rothamsted  Tour of longterm field experiments Chair: Sue Welham 

16:00 to 16:20  Trip to Rothamsted  Tea  
16:20 to 16:50 
Trip to Rothamsted  The Development of Statistical Design Concepts at Rothamsted
Modern applied statistics began in 1919, when R.A. Fisher was appointed as the first statistician at Rothamsted. Experiments were already taking place of course, notably the Broadbalk longterm fertiliser trial of wheat at Rothamsted which had been running since 1843. However, concepts like replication, randomization, blocking and factorial structure were unknown – and it took some strong persuasion by Fisher before they became accepted.
Only very limited analysis options were available too, and again some of the concepts like degrees of freedom, or methodology like maximum likelihood, proved to be very controversial. Nevertheless, by the time that Fisher left Rothamsted in 1935, the foundations had been laid for very many of the design principles and statistical methods that we now take for granted.
In this talk I shall describe how some of the key ideas developed under the challenges from the biological research at Rothamsted, sketch out a few of the events and controversies, and indicate how some of the research threads have been continued by his successors.


19:30 to 22:00  Conference dinner at Christ's College 
09:00 to 09:30 
On MinimalPoint Designs Session: Factorial Designs and Blocking Chair: Peter Goos
A minimalpoint design has its number of experimental runs equals to the number of parameters. This is the minimal effort possible to obtain an unbiased estimate for all parameters. Some recent advances for minimalpoint design under various models will be discussed. Specifically, a new class of minimalpoint design robust to interactions for firstorder model is proposed; a new class of minimalpoint design, making use of Conference Matrices, for definitive screening will be explored, and if time permits, new minimalpoint designs for full secondorder response surface models will be discussed.
A related issue on the construction of conference matrix and its applications in design of experiment will be introduced.

INI 1  
09:30 to 10:00 
J Godolphin ([Surrey]) The Specification of Robust Binary Block Designs Against the Loss of Whole Blocks Session: Factorial Designs and Blocking Chair: Peter Goos
A new criterion is suggested for measuring the robustness of a binary block design D against the loss of whole blocks, which is based on the concept of rectangle concurrencies.
This criterion is superior to the notion of minimal concurrence that has been employed previously and it enables improved conditions for classifying the robustness status of D to be derived. It is shown that several classes of binary block designs, with the positive feature of possessing either partial balance or near balance, are maximally robust; thus expanding a classic result in the literature, known as Ghosh's theorem, that confines this status to balanced designs. 
INI 1  
10:00 to 10:30 
New Classes of SecondOrder EquivalentEstimation SplitPlot Designs Session: Factorial Designs and Blocking Chair: Peter Goos
In many industrial experiments, complete randomization of the runs is impossible as, often, they involve factors whose levels are hard or costly to change. In such cases, the splitplot design is a costefficient alternative that reduces the number of independent settings of the hardtochange factors. In general, the use of generalized least squares is required for model estimation based on data from splitplot designs. However, the ordinary least squares estimator is equivalent to the generalized least squares estimator for some splitplot designs, including some secondorder splitplot response surface designs. These designs are called equivalentestimation designs. An important consequence of the equivalence is that basic experimental design software can be used to analyze the data. We introduce two new families of equivalentestimation splitplot designs, one based on subset designs and another based on a class of rotatable response surface designs constructed using supp lementary difference sets. The resulting designs complement existing catalogs of equivalentestimation designs and allow for a more flexible choice of the number of hardtochange factors, the number of easytochange factors, the number and size of whole plots and the total sample size.

INI 1  
10:30 to 11:00  Morning coffee  
11:00 to 11:30 
The algebraic method in statistics: Betti numbers and Alexander duality Session: Advances in Computational Design and Computer Experiments Chair: Hugo MaruriAguilar
After a brief review of the algebraic method in statistics, using Gbases, some newer results are described. The first relates the average degree concept to the Betti numbers of the monomial ideal of models. "Flatter" models in the sense of having lower degree are associated with more complex ideals having larger Betti numbers. The Alexander duality relates models and their complements within a factorial framework and leads to large classes of design for which it is straightforward to read off the model structure.

INI 1  
11:30 to 12:00 
An Evolutionary Approach to Experimental Design for Combinatorial Optimization Session: Advances in Computational Design and Computer Experiments Chair: Hugo MaruriAguilar
In this presentation we investigate an approach which combines statistical methods and optimization algorithms in order to explore a large search space when the great number of variables and the economical constraints limit the ability of classical techniques to reach the optimum of a function. The method we propose  the Model Based Ant Colony Design (MACD)  couples real experimentation with simulated experiments and boosts an “Ant Colony” algorithm (Dorigo et al., 2004) by means of a simulator (strictly speaking an emulator), i.e. a predictive statistical model. Candidate solutions are generated by computer simulation using Ant Colony Optimization, a probabilistic technique for solving computational problem which consists in finding good paths through graphs and is based on the foraging behaviour of real ants. The evaluation of the candidate solutions is achieved by physical experiments and is fed back into the simulative phase in a recursive way.
The properties of the proposed approach are studied by means of numerical simulations, testing the algorithm on some mathematical benchmark functions. Generation after generation, the evolving design requires a small number of experimental points to test, and consequently a small investment in terms of resources. Furthermore, since the research was inspired by a real problem in Enzyme Engineering and Design, namely finding a new enzyme with a specific biological function, we have tested MACD on the real application. The results shows that the algorithm has explored a region of the sequence space not sampled by natural evolution, identifying artificial sequences that fold into a tertiary structure closely related to the target one.

INI 1  
12:00 to 12:30 
A Boukouvalas ([Aston]) Optimal Design under Heteroscedasticity for Gaussian Process Emulators with replicated observations Session: Advances in Computational Design and Computer Experiments Chair: Hugo MaruriAguilar
Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty.
For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. We examine the effect of such optimal designs on both model parameter uncertainty and predictive variance through a series of simulation experiments on both synthetic and real world simulators.

INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 14:00 
Optimal design of experiments with very low average replication
Trials of new crop varieties usually have very low average replication. Thus one possiblity is to have a single plot for each new variety and several plots for a control variety, with the latter well spread out over the field. A more recent proposal is to ignore the control, and instead have two plots for each of a small proportion of the new varieties.
Variation in the field may be accounted for by a polynomial trend, by spatial correlation, or by blocking. However, if the experiment has a second phase, such as making bread from flour milled from the grain produced in the first phase, then that second phase usually has blocks. The optimality criterion used is usually the A criterion: the average variance of the pairwise differences between the new varieties. I shall compare designs under the A criterion when the average replication is much less than two.

INI 1  
14:00 to 14:30 
A Dean ([Ohio State]) Screening strategies in the presence of interactions Session: Screening and Model Uncertainty Chair: Sue Lewis
Screening is the process of using designed experiments and statistical analyses to search through a large number of potentially influential factors in order to discover the few factors that have a substantial effect on a measured response (i.e. that are "active"). In this setting, conventional fractional factorial experiments typically require too many observations to be economically viable. To overcome this problem in practice, interactions are often dropped from consideration and assumed to be negligible, sometimes without substantive justification. Such loss of information can be a serious problem in industrial experimentation because exploitation of interactions is a key tool for product improvement. This talk describes an assessment and comparison of two screening strategies for interactions, namely supersaturated designs and group screening, together with a variety of data analysis methods, based on shrinkage regression and Bayesian methods. Recommendation s on the use of the screening strategies are provided through simulation studies.

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14:30 to 15:00 
B Jones (JMP) A Class of ThreeLevel Designs for Definitive Screening in the Presence of SecondOrder Effects Session: Screening and Model Uncertainty Chair: Sue Lewis
Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Experimenters often prefer quantitative factors with three levels over twolevel factors because having three levels allows for some assessment of curvature in the factorresponse relationship. Yet, the most familiar screening designs limit each factor to only two levels. We propose a new class of designs that have three levels, provide estimates of main effects that are unbiased by any secondorder effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of secondorder effects. Moreover, for designs having six factors or more, our designs allow for the estimation of the full quadratic model in any three factors. In this respect, our designs may render followup experiments unnecessary in many situations, thereby increasing the efficiency of the entire experimentation process.

INI 1  
15:00 to 15:30 
A comparison of three Bayesian approaches for constructing model robust designs Session: Screening and Model Uncertainty Chair: Sue Lewis
While optimal designs are commonly used in the design of experiments, the optimality of those designs frequently depends on the form of an assumed model. Several useful criteria have been proposed to reduce such dependence, and efficient designs have been then constructed based on the criteria, often algorithmically. In the model robust design paradigm, a space of possible models is specified and designs are sought that are efficient for all models in the space. The Bayesian criterion given by DuMouchel and Jones (1994), posits a single model that contains both primary and potential terms. In this article we propose a new Bayesian model robustness criterion that combines aspects of both of these approaches. We then evaluate the efficacy of these three alternatives empirically. We conclude that the model robust criteria generally lead to improved robustness; however, the increased robustness can come at a significant cost in terms of computing requirements.

INI 1  
15:30 to 16:00  Afternoon tea  
16:00 to 16:30 
B Rosenberger ([George Mason]) Sequential Monitoring of Randomization Tests Session: Developments in Medical and Pharmaceutical Design Chair: Anthony Atkinson
The U. S. Food and Drug Administration often requires a randomizationbased analysis of the primary outcome in a clinical trial, which they sometimes refer to as "rerandomization tests" (we prefer "randomization tests"). Conditional inference is inherently difficult when using a Monte Carlo approach to "rerandomize", and is impossible using standard techniques for some randomization procedures. We describe a new approach by deriving the exact conditional distribution of the randomization procedure and then using Monte Carlo to generate sequences directly from the conditional reference set. We then extend this technique to sequential monitoring, by computing the exact joint distribution of sequentiallycomputed conditional randomization tests. This allows for a spendingfunction approach using randomization tests instead of populationbased tests. Defining information under a randomization model is tricky, and we describe various ways to & quot;estimate" information using the exact conditional variance of the randomization test statistics.

INI 1  
16:30 to 17:00 
Optimising the allocation of participants in a twostage randomised experiment to estimate selection, preference and treatment effects Session: Developments in Medical and Pharmaceutical Design Chair: Anthony Atkinson
Experimental outcomes may be affected by the choice of treatment that participants might make (if they were indeed allowed to choose), a socalled selection effect, and by whether they actually receive their preferred treatment, a socalled preference effect. Selection and preference effects can be important (possibly even larger than the usual treatment effect), but they cannot be estimated in conventional randomised experimental designs.
An alternative approach is the twostage randomised design, in which participants are first randomly divided into two subgroups. In one subgroup, participants are randomly assigned to treatments, while in the other, participants are allowed to choose their own treatment. This approach can yield estimates of the direct treatment effect, and of the preference and selection effects. The latter two provide insight that goes considerably beyond what is possible in standard randomised experiments, notably the usual parallel group design.
In this presentation, we will consider the optimal proportion of participants who should be allocated to the choice subgroup and allowed to determine their own treatment. The precision of the estimated selection, preference and treatment effects are functions of: the total sample size; the proportion of participants allocated to choose their treatment; the variances of the response (or outcome); the proportions of participants who select each treatment in the choice group; and the selection, preference and treatment effects themselves. We develop general expressions for the optimum proportion of participants in the choice group, depending on the inverses of these variances, and on which effects are of primary interest. We illustrate the results with trial data comparing alternative clinical management strategies for women with abnormal results on cervical screening.

INI 1  
18:45 to 19:30  Dinner at Wolfson Court (residents only) 