Bayesian inference and computation for confounding adjustment and causation

大多数统计分析程序试图揭示影响因素(例如，暴露在环境中的有害物质、医疗或经济干预)与反应(例如，健康或社会经济结果)之间的关系，如果所使用的统计模型规定不正确，则容易出现问题。特别是，如果存在影响暴露和反应的因素，则必须仔细进行统计推断。在许多情况下，特别是当潜在影响因素或预测因素的数量很大时，确保正确的模型规范是极其困难的，这是一个相当大的方法论和分析挑战。我建议的研究是在因果推理领域，试图在潜在影响因素较多的情况下量化暴露对反应的真实影响。特别是，我将使用贝叶斯框架，该框架允许对与分析相关的可变性和不确定性进行更全面的分析。在这一领域存在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，从而有助于对广泛的科学和其他研究领域的数据进行量化分析。人们普遍认为，正确的统计分析是大多数研究工作的重要组成部分。拟议研究的目标是增加研究人员可用的统计工具。在接下来的五年里，我的短期目标是解决这一领域引起极大兴趣的具体方法学挑战；形成统计推断的正确框架，进行模型选择，减少现有程序的可变性和增加稳定性。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.