Bayesian inference and decisions under partial specification

我提议的研究将侧重于开发方法论和计算工具，以便在科学和其他研究环境中更广泛地使用贝叶斯统计范式。贝叶斯方法使研究人员能够对感兴趣的未知量(例如，治疗或暴露对结果的影响的程度)做出连贯的推断，并在存在随机性和不确定性的情况下做出最佳决策。传统形式的贝叶斯方法受到非常严格的假设的限制，这些假设限制了它的适用性，或者至少做出了相当强的建模假设：这可能被视为一个负面方面。此外，贝叶斯方法通常比经典的统计程序更难实现，而且往往带有更大的计算负担。我的目标是发展理论、方法和计算工具，使贝叶斯推理更容易为研究人员所接受和接受。拟议的研究计划的主要方向是受到最近的工作的启发，这些工作表明，除了通常的贝叶斯更新之外，存在更一般的“信念更新”机制，可以在不损失贝叶斯方法的优势的情况下，允许更简单的规范和计算(具体地说，通过概率论证进行推断的事实)。我提议的研究将涉及对这些新方法的调查，这些方法有可能彻底改变贝叶斯思维。除了与更标准的贝叶斯方法建立理论联系外，我还将研究挑战统计推断设置的具体例子，这些设置将受益于开发一种新的、更简单和更计算高效的方法。这些例子来自我目前对因果推理(旨在确定治疗或暴露的明确影响)和系统发育学(旨在分析物种或分子遗传样本之间的进化关系)的研究兴趣，但也延伸到我研究的一个与机器学习例子相关的新领域。机器学习和人工智能(AI)研究在定量分析的所有领域都越来越重要，尽管它在很大程度上由计算机科学主导，但统计学家在验证所使用的模型、算法和其他程序方面发挥着重要作用。我拟议的工作将通过研究形式贝叶斯过程在机器学习和人工智能领域做出贡献，这两个过程都使用标准贝叶斯公式和新提出的框架。

My proposed research will focus on developing methodology and computational tools to allow the wider use of the Bayesian statistical paradigm in scientific and other research settings. The Bayesian approach allows researchers to make coherent inferences about unknown quantities of interest (eg the magnitude of the effect of a treatment or exposure on an outcome), and also to make optimal decisions in the presence of randomness and uncertainty. Bayesian methodology in its traditional form is bound by quite strict assumptions that limit its applicability, or at least makes quite strong modelling assumptions: this might be viewed as a negative aspect. In addition, Bayesian methods are typically much harder to implement than classical statistical procedures, and often carry a greater computational burden. My goal is to develop the theory, methodology and computational tools to make Bayesian inference more accessible and palatable to researchers. The main direction of the proposed research program is inspired by recent work that has demonstrated that more general 'belief updating' mechanisms exist, beyond the usual Bayesian update, that could allow simpler specifications and computation without losing the advantages of the Bayesian approach (specifically, the fact that inferences are made through probabilistic arguments). My proposed research will involve an investigation of these new methods which have the potential to revolutionize Bayesian thinking. As well as establishing theoretical connections with more standard Bayesian methods, I will study concrete examples of challenging statistical inference settings which would benefit from the development of a new, simpler and more computationally efficient approach. These examples are drawn from my current research interests in causal inference (which aims to identify the unconfounded effect of a treatment or exposure) and phylogenetics (which aims to analyze evolutionary relationships between species or molecular genetic samples), but extend to a new area of my research related to machine learning examples. Machine learning and artificial intelligence (AI) research is of growing importance in all areas of quantitative analysis, and although it is largely dominated by computer science, there is an important role for statisticians to play in validating the models, algorithms and other procedures utilized. My proposed work will contribute in the area of machine learning and AI by studying formal Bayesian procedures, both using the standard Bayesian formulation, and the newly proposed framework.