Bayesian inference and decisions under partial specification

我建议的研究将侧重于开发方法和计算工具，以允许在科学和其他研究环境中更广泛地使用贝叶斯统计范式。 贝叶斯方法允许研究人员对未知的感兴趣的量（例如治疗或暴露对结果的影响的大小）进行连贯的推断，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相当严格的假设的约束，这些假设限制了其适用性，或者至少做出了相当强的建模假设：这可能被视为一个消极的方面。 此外，贝叶斯方法通常比经典的统计过程更难实现，并且通常带来更大的计算负担。 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和可口的研究人员。 拟议的研究计划的主要方向是受到最近的工作的启发，这些工作已经证明，除了通常的贝叶斯更新之外，还存在更一般的“信念更新”机制，可以允许更简单的规范和计算，而不会失去贝叶斯方法的优势（特别是，通过概率参数进行推断的事实）。 我提议的研究将涉及对这些新方法的调查，这些新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，我还将研究具有挑战性的统计推断设置的具体示例，这些示例将受益于开发一种新的，更简单，计算效率更高的方法。 这些例子来自于我目前在因果推理（旨在确定治疗或暴露的无混淆效应）和遗传学（旨在分析物种或分子遗传样本之间的进化关系）方面的研究兴趣，但扩展到了我与机器学习相关的新研究领域。 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，尽管它主要由计算机科学主导，但统计学家在验证模型，算法和其他程序方面发挥着重要作用。 我提出的工作将通过研究正式的贝叶斯过程，在机器学习和人工智能领域做出贡献，无论是使用标准的贝叶斯公式，还是新提出的框架。

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.