Robustness of Design

我打算继续研究与实验研究设计有关的问题，以期获得对各种模型不足具有鲁棒性的推理程序。在统计学中，“鲁棒性”指的是一个过程在其推导的假设被违反时保持其有效性的能力。这一概念在实验研究中尤其重要，因为实验者可能对产生数据的反应结构只有模糊的认识。近年来，机器学习社区也认识到，他们所知道的“主动学习”在很大程度上是实验设计的同义词，同时需要对该领域的方法进行鲁棒化。 我在这一领域的工作已经从调查相当普遍的问题，例如设计，以适应响应函数时，真正的反应实际上是一个未知的成员的一个邻居，这个拟合的反应，通过调查其他形式的误指定（异方差，依赖等）。并应用于特定的应用领域。这些应用领域导致了空间设计方面的问题-例如，在相邻监测站之间的相关性结构不确定的情况下如何安置环境监测站，例如，在设计时允许人们在两种特定和方便的药理反应建模方法之间进行选择的问题，同时承认这两种方法都不一定非常准确，以及剂量-反应-例如，设计以预测药物的最小有效剂量或医疗水平，通常需要逻辑或概率分析，同时认识到这两种分析可能存在偏差。 扩展和进一步进军所有这些方法的设计预期。我想解决的一些特殊问题（以及许多其他问题）： (i)有一个空白，在文献中的稳健设计方法和稳健的估计和预测方法的组合。几年前，当M-估计成为预期的估计方法时，我开始了对设计稳健性的调查。目前，分位数回归估计正在流行，但到目前为止，还没有相应的鲁棒设计策略，使其“完全鲁棒”。这将是我未来几年研究的重点。 (ii)临床试验设计-这是设计中特别重要的一个领域，因为医疗从业者倾向于坚持长期的“经典”模型，这些模型与各种协变量的反应有关。设计者主要关注治疗组和协变量组之间的“平衡”，很少考虑效率。同样，将新入组患者分配到治疗组的典型方法往往没有考虑到可能的异方差性，或者采用有效性可能受到严重怀疑的方差函数。然后，有一个明确的需要更强大的方法，静态和顺序的设计策略可以考虑。 (iii)在机器学习中，近年来有几位研究人员借鉴了我介绍的一些技术，并将其作为“主动学习”的应用。他们通过我提出的模拟退火算法应用了这些技术，这些算法非常适合小规模的问题，但对于在某些应用中建模和采样的大量数据集则不太适合。我打算研究更有效的算法来处理这些问题。 (iv)我打算把我的工作扩展到计算机实验领域。

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.