Bayesian inference and computation for confounding adjustment and causation

大多数试图揭示影响因素（例如，接触环境中的有害物质、医疗或经济干预）与应对措施（例如，健康或社会经济结果）之间关系的统计分析程序，如果使用的统计模型指定不当，很容易出现问题。特别是，如果存在影响暴露和反应的因素，则必须仔细得出统计推断。在许多情况下，特别是当潜在影响因素或预测因子的数量很大时，确保正确的模型规范是极其困难的，这代表了相当大的方法和分析挑战。我提出的研究是在因果推理领域，试图量化当潜在的影响因素数量很大时，暴露对反应的真实影响。特别是，我将使用贝叶斯框架，它允许对与分析相关的可变性和不确定性进行更完整的分析。在这一领域存在着重大的数学理论和方法挑战，但一旦建立了必要的理论和方法，拟议的工作就有可能影响统计实践，从而有助于在广泛的科学和其他研究领域对数据进行定量分析。人们普遍认为，正确的统计分析是大多数研究的重要组成部分。拟议研究的目标是增加研究人员可用的统计工具。在未来五年内；我的短期目标是解决具体的方法挑战，这是该领域非常感兴趣的焦点；形成正确的统计推断框架，进行模型选择，减少可变性，增加现有程序的稳定性。由此产生的发展将有助于解决数据统计分析中的实际问题。从长远来看，我将讨论与扩展当前框架有关的一些剩余的方法和理论问题。

Most statistical analysis procedures that attempt to uncover the relationship between influential factors (for example, exposure to hazardous materials in the environment, medical treatment or economic intervention) and response (eg health or socio-economic outcome) are prone to problems if the statistical models used are incorrectly specified. In particular, if there are factors that influence both exposure and response, then statistical inferences must be carefully drawn. In many situations, particularly when the number of potential influential factors or predictors is large, it is extremely difficult to ensure correct model specification, and this represents a considerable methodological and analytic challenge. My proposed research is in the domain of causal inference, that attempts to quantify the true effect of exposure on response when the number of potential influential factors is large. In particular, I will use the Bayesian framework that allows for a more complete analysis of the variability and uncertainty associated with the analysis. There are significant mathematical theory, and methodological, challenges in this area, but once the necessary theory and methods are established, the proposed work has the potential to influence statistical practice, and thereby aid in the quantitative analysis of data in a wide range of scientific and other research domains. It is widely recognized that correct statistical analysis is a vital component of most research pursuits. The goal of the proposed research is to add to the statistical tools available to researchers. In the next five years; my short term goals address specific methodological challenges that are the focus of much interest in this domain; forming a correct framework for statistical inference, performing model selection, and reducing variability and increasing stability of existing procedures. The resulting developments will help to solve real, practical problems in the statistical analysis of data. In the longer term, I will address some remaining methodological and theoretical issues concerned with extending the current framework.