Optimal experimental designs and response-adaptive designs

最优化在理论和应用科学的大多数领域中都是一种基本工具。本提案强调需要客观方法解决最优设计和响应适应设计中的优化问题，并具有潜在的应用价值。 当数据不包含足够的信息时，统计模型受到与参数的有效估计相关的问题的影响。这个问题出现在潜变量模型中。我们需要确定最优设计，以最大限度地利用小样本量的信息。首先，我计划对用于配对比较的潜变量模型的参数进行最大似然估计。然后，我将工作扩展到适用于其他研究领域的一般类别的此类模型，如体育和机器学习。 在优化设计中，我们通常假定模型在设计阶段就已知。然而，在许多情况下，情况并非如此。我们需要实施一种对两个或更多型号有效的设计，以区分并选择最佳型号。我计划研究一种用于模型识别的约束最优化方法，然后研究自适应顺序设计的各个方面，这些方面将同时实现选择正确的模型和有效估计参数的目标。我还计划研究与几个发行版有关的优化问题，并将这些方法应用于图像处理等领域。一个常见的问题是，关于图片或图形的像素的真实状态的信息不完整。我计划开发优化设计方法，提供减少歧义和增加初始随机标签一致性的方法。 响应自适应设计如今正变得越来越流行。已经开发了几种响应自适应设计，然而，将这些设计应用于循环数据的努力有限。受此启发，我建议为一般类型的循环反应开发分配设计，并在比较前瞻性随机干预试验的实用数据集上开展工作。大多数这样的数据涉及可能影响反应的各种协变量。很自然，下一步就是在模型中引入这些协变量，以实现更有效的设计。 拟议的研究将为培训各级高素质人员提供机会。他们将学习在潜在变量模型(在体育和机器学习中的应用)和模型识别(在工业和化学工程中进行模型测试的应用)领域的统计学理论。循环数据的响应自适应设计将为生物医学研究、气象学和天文学中的应用研究人员提供实用工具，因为这些科学研究中自然会产生循环数据。

Optimization serves as a basic tool in most areas of the theoretical and applied sciences. The present proposal highlights the need for objective methodologies for optimization problems in optimal designs and response-adaptive designs with potential applications. A statistical model is affected by problems associated with efficient estimation of parameters when the data do not contain enough information. This problem arises in latent variable models. We need to determine optimal designs to maximize the information with a small sample size. I first plan to work on maximum likelihood estimation of the parameters of latent variable models for paired comparisons. I then extend the work to general class of such models that apply to other fields of research, such as sports and machine learning. In optimal design, we generally assume that the model is known at the design stage. However, in many situations this is not the case. We need to implement a design that is efficient for two or more models, to discriminate, and to select the best model. I plan to work on a constrained optimization approach for model discrimination, and then study aspects of adaptive sequential design that will simultaneously achieve the objectives of selecting the correct model and estimating the parameters efficiently. I also plan to work on optimization problems with respect to several distributions, and apply the methods to areas such as image processing. A common problem is to have incomplete information on true states of the pixels of a picture or a graph. I plan to develop optimal design methods that will provide ways of decreasing ambiguity and increasing consistency of an initial stochastic labeling. Response-adaptive designs are becoming increasingly popular nowadays. Several response-adaptive designs have been developed, however, there has been limited effort in applying these to circular data. Motivated by this, I propose to develop allocation designs for a general class of circular responses, and work on a practical data sets on comparative prospective randomized interventional trials. Most of such data involve various covariates which may influence the responses. Quite naturally, the next step is to induce these covariates in the model, so as to achieve more efficient designs. The proposed research will provide opportunities for training of highly qualified personnel at all levels. They will learn statistical theories in the areas of latent variable models (with applications in sports and machine learning) and model discrimination (with applications in industrial and chemical engineering for carrying out tests for models). The response-adaptive designs for circular data will provide practical tools to applied researchers in biomedical studies, meteorology and astronomy as circular data arise naturally in these scientific studies.