Investigation of Bayes Procedures: Theory, Modeling, and Computation

贝叶斯过程的研究：理论、建模和计算

• 批准号: 1712957
• 负责人: Chao Gao
• 金额: $ 20万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712957&HistoricalAwards=false
• 关键词: Investigation; Bayes; Procedures; Theory; Modeling

Bayesian analysis is a widely used technique in data science for estimation, prediction, and interpretation. The new era of complex and big data imposes unprecedented challenges to Bayesian statistics. This research project addresses these new challenges from three different perspectives. First, the investigator will study the relation between prior knowledge and scientific conclusion by conducting rigorous mathematical analysis in the framework of Bayesian statistics. Second, the investigator aims to find novel ways of modeling data sets that can take into account new features of modern big data. Finally, the investigator intends to push the boundary of Bayesian computation by inventing new algorithms that are both fast and theoretically sound. The results of the research are expected to have a positive impact in areas that apply Bayesian statistics on a routine basis, including population genetics, astronomy, computer vision, political science, social science, and animal science.Bayesian analysis is an important statistical framework for both modeling and computation. However, applying Bayesian procedures correctly when encountering a specific problem is non-trivial. The selections of prior, likelihood, and algorithm all influence the final conclusion drawn from a posterior distribution. Despite many successful applications of Bayesian analysis in various scientific areas, solid theoretical foundations on how to perform Bayesian inference are still lacking. The goal of this project is to develop a coherent theory on optimal Bayesian inference. Specifically, the investigator will study: 1) Bayesian theory: optimal posterior contraction in parametric, nonparametric and high-dimensional models; 2) Bayesian modeling: likelihood functions that are free of nuisance parameters and Bayesian edge-exchangeable network analysis; 3) Bayesian computation: algorithmic and statistical properties of variational inference; and 4) applications to single-cell RNA sequencing analysis.

贝叶斯分析是数据科学中广泛使用的技术，用于估计，预测和解释。复杂和大数据的新时代对贝叶斯统计提出了前所未有的挑战。本研究项目从三个不同的角度解决这些新的挑战。首先，研究者将在贝叶斯统计的框架下进行严格的数学分析，研究先验知识与科学结论之间的关系。其次，研究人员的目标是找到建模数据集的新方法，这些方法可以考虑现代大数据的新特征。最后，研究人员打算通过发明既快速又理论上合理的新算法来推动贝叶斯计算的边界。该研究的结果有望在人口遗传学、天文学、计算机视觉、政治科学、社会科学、动物科学等常规应用贝叶斯统计的领域产生积极影响。贝叶斯分析是建模和计算的重要统计框架。然而，在遇到特定问题时正确应用贝叶斯程序是不平凡的。先验、似然和算法的选择都影响从后验分布得出的最终结论。尽管贝叶斯分析在各个科学领域中有许多成功的应用，但仍然缺乏关于如何执行贝叶斯推理的坚实理论基础。这个项目的目标是发展一个连贯的理论最佳贝叶斯推理。具体而言，研究者将研究：1）贝叶斯理论：参数，非参数和高维模型中的最佳后验收缩; 2）贝叶斯建模：无干扰参数的似然函数和贝叶斯边交换网络分析; 3）贝叶斯计算：变分推理的算法和统计特性;以及4）应用于单细胞RNA测序分析。

项目成果

Robust regression via mutivariate regression depth

• DOI: 10.3150/19-bej1144
• 发表时间: 2017-02
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Chao Gao

Community Detection in Degree-Corrected Block Models

• DOI: 10.1214/17-aos1615
• 发表时间: 2016-07
• 期刊: ArXiv
• 作者: Chao Gao;Zongming Ma;A. Zhang;Harrison H. Zhou

Density estimation with contamination: minimax rates and theory of adaptation

污染密度估计：极小极大率和适应理论

• DOI: 10.1214/19-ejs1617
• 发表时间: 2019
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Liu, Haoyang;Gao, Chao
• 通讯作者: Gao, Chao

A general framework for Bayes structured linear models

• DOI: 10.1214/19-aos1909
• 发表时间: 2015-06
• 期刊: The Annals of Statistics
• 作者: Chao Gao;A. Vaart;Harrison H. Zhou

On estimation of isotonic piecewise constant signals

等张分段常数信号的估计

• DOI: 10.1214/18-aos1792
• 发表时间: 2020
• 期刊: Annals of Statistics
• 影响因子: 4.5
• 作者: Gao, Chao;Han, Fang;Zhang, Cun-Hui
• 通讯作者: Zhang, Cun-Hui