Mathematical Sciences: Bayesian Inference and Computing

数学科学：贝叶斯推理与计算

• 批准号: 9303557
• 负责人: Joseph Kadane
• 金额: $ 104万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1999-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303557&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bayesian; Inference; Computing

Our research is oriented toward implementation of Bayesian inference. There has been increasing interest recently in the Bayesian approach to statistics, in part because advances in computational ability have made it feasible in many settings, and in part because Bayesian analysis of data can make use of information from additional sources. Our work will build on our previous research in Bayesian statistics, part of which has been funded by NSF. Our main concerns are: (1) review and assessment of methods for choosing prior probability distributions by formal rules, and further development of methods for assessing sensitivity to the choices; (2) investigation of approximate and exact computational methods for Bayesian hypotheses testing; (3) modification and enhancement of numerical integration techniques and Monte Carlo simulation of posterior distributions; also, improvement of statistical computing environments including use of animation and three dimensional rendering for visualization of uncertainty in higher dimensions; (4) further work on the foundations of subjective probability; and (5) several other topics related to our previous work on elicitation of priors and asymptotic approximations. When analyzing data, it is important to combine all sources of information effectively. Bayesian statistical methods are tailored to this purpose. Our research focuses on finding practical ways to implement Bayesian methods and on investigating the theoretical basis for these methods. We are concerned with the development of computational and graphical techniques that make Bayesian inference feasible in complicated problems. These include: simulation, animation and the construction of statistical computing environments. We will also investigate theoretical issues that support Bayesian techniques. These issues include the foundations of subjective probability and the development of mathematical approximations.

我们的研究旨在实施贝叶斯推论。最近，贝叶斯统计方法的兴趣越来越多，部分原因是计算能力的进步使其在许多情况下变得可行，部分原因是贝叶斯对数据的分析可以利用来自其他来源的信息。我们的工作将基于我们先前在贝叶斯统计数据的研究，其中一部分是由NSF资助的。我们的主要关注点是：（1）审查和评估通过正式规则选择先前概率分布的方法，以及进一步开发评估对选择敏感性的方法； （2）研究贝叶斯假设测试的近似和精确计算方法； （3）后验分布的数值整合技术和蒙特卡洛模拟的修改和增强；同样，改善统计计算环境，包括使用动画和三维渲染，以可视化较高维度的不确定性； （4）在主观概率的基础上进一步工作； （5）与我们先前有关启发先验和渐近近似的工作有关的其他几个主题。 分析数据时，重要的是有效地组合所有信息源。 贝叶斯统计方法是针对此目的量身定制的。 我们的研究重点是寻找实施贝叶斯方法并研究这些方法的理论基础的实用方法。 我们关注的是计算和图形技术的发展，这些技术使贝叶斯推论在复杂问题中可行。 其中包括：仿真，动画和统计计算环境的构建。 我们还将研究支持贝叶斯技术的理论问题。这些问题包括主观概率的基础和数学近似的发展。