Robustness of Design

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I intend to continue my investigations into problems related to the design of experimental studies, with an eye to obtaining inferential procedures that are robust against various model inadequacies. In Statistics, 'robustness' refers to the ability of a procedure to retain its validity when the assumptions underlying its derivation are violated. This notion is particularly important in experimental studies, where the experimenter may have only a vague knowledge of the structure of the response generating the data. In recent years it has also been recognized within the Machine Learning community that what they know as 'active learning' is largely synonymous with experimental design, with an accompanying need for a robustification of the ways in which the field is approached. My work in this area has evolved from investigations of quite general problems, for instance designing to fit a response function when the true response is in fact an unknown member of a neighbourhood of this fitted response, through investigations of other forms of misspecification (heteroscedasticity, dependence, etc.) and on to particular fields of application. These fields of application have led to problems in spatial design – for instance, the placement of environmental monitoring stations in the face of uncertainty about the correlation structure between neighbouring stations, in discrimination – for instance the problem of designing so as to allow one to choose between two particular and convenient methods of modelling pharmacological reactions, while admitting that neither is necessarily very accurate, and in dose-response – for instance designing so as to predict a minimum effective dose of a drug or level of a medical treatment, something typically calling for a logistic or probit analysis, while recognizing that both of these analyses might be biased. Extensions and further forays into all of these approaches to design are anticipated. Some particular problems (among many others) that I would like to address:(i) There is a gap in the literature as regards the combination of robust methods of designs and robust methods of estimation and prediction. Some years ago I initiated an investigation into robustness of design when M-estimation was to be the intended method of estimation. Currently, quantile regression estimation is coming into vogue, but so far without correspondingly robust design strategies to make it 'fully robust'. This will be a further focus of my research in the next few years.(ii) Designs for Clinical Trials – this is an area of particular importance in design, given that medical practitioners tend to be wedded to longstanding 'classical' models relating response to various covariates. The designers are primarily concerned with 'balance' across treatment and covariate groups, with little thought being given to efficiency. As well, typical methods of assigning incoming patients to treatment groups often fail to take possible heteroscedasticity into account, or employ variance functions whose validity may be seriously in doubt. There is then a clear need for more robust approaches; both static and sequential design strategies may be considered.(iii) In Machine Learning, several researchers have in recent years borrowed some of the techniques introduced by me and adapted them as applications of 'active learning'. They have in particular applied these techniques via a simulated annealing algorithm proposed by me. Such algorithms are quite appropriate for small scale problems, but less so for the massive data sets being modelled and sampled in some applications. I intend to study more efficient algorithms for dealing with such problems.(iv) I intend to extend my work to the field of Computer Experimentation.