Optimal experimental designs and response-adaptive designs

最佳实验设计和响应自适应设计

• 批准号: RGPIN-2018-06452
• 负责人: Mandal, Saumendranath
• 金额: $ 1.68万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=658622
• 关键词: Optimal; experimental; designs; response; adaptive

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.

优化作为一个基本工具，在大多数领域的理论和应用科学。本提案强调需要有客观的方法来解决最佳设计和具有潜在应用的响应自适应设计中的最佳化问题。当数据不包含足够的信息时，统计模型会受到与有效估计参数相关的问题的影响。这个问题出现在潜变量模型中。我们需要确定最佳设计，以最大限度地利用小样本量的信息。我首先计划研究配对比较潜变量模型参数的最大似然估计。然后，我将工作扩展到适用于其他研究领域（如体育和机器学习）的此类模型的一般类。在优化设计中，我们通常假设模型在设计阶段是已知的。然而，在许多情况下，情况并非如此。我们需要实现一个设计，是有效的两个或更多的模型，区分，并选择最好的模型。我计划工作的模型歧视的约束优化方法，然后研究自适应序贯设计，同时实现选择正确的模型和有效地估计参数的目标方面。我还计划研究几种分布的优化问题，并将这些方法应用于图像处理等领域。一个常见的问题是具有关于图片或图形的像素的真实状态的不完整信息。我计划开发最佳设计方法，提供减少模糊性和增加初始随机标记一致性的方法。响应自适应设计现在变得越来越流行。已经开发了几种响应自适应设计，但是，将这些应用于圆形数据的努力有限。出于这一动机，我建议开发一个通用类的循环响应的分配设计，并在比较前瞻性随机干预试验的实际数据集上工作。大多数此类数据涉及可能影响响应的各种协变量。很自然地，下一步是在模型中引入这些协变量，以便实现更有效的设计。拟议的研究将为培训各级高素质人员提供机会。他们将学习潜变量模型（在体育和机器学习中的应用）和模型判别（在工业和化学工程中的应用，用于进行模型测试）领域的统计理论。循环数据的响应自适应设计将为生物医学研究，气象学和天文学的应用研究人员提供实用的工具，因为循环数据在这些科学研究中自然出现。