New Developments in Nonparametric Bayesian Inference; Univariate and Multivariate time series with infinite varaince.

非参数贝叶斯推理的新进展；

• 批准号: 203276-2013
• 负责人: Zarepour, Mahmoud
• 金额: $ 0.8万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635784
• 关键词: New; Developments; Nonparametric; Bayesian; Inference

The applicant's research program is concentrated on two major subjects in statistical inference. The first subject is mainly related to Bayesian inference. In the Bayesian paradigm, the statisticians considers having a probabilistic prior knowledge on some unknown parameters. Later, the collected data is used to update their prior knowledge under the chosen model. A nonparametric Bayesian model considers the prior knowledge in a much more general framework with minimal restrictions. The applicant's research area in this field is mostly related to the construction of new processes used in nonparametric Bayesian models and the derivation of fast yet more precise approximation tools for these processes to use them in statistical inference. The applicant also derives efficient simulation techniques for such processes in order to enable practitioners to run their computer programs with faster speed. The applicant's second project investigates the large sample theory for processes which evolve in time. In Statistics, these processes are called time series. Sometimes these time series exhibit unusual and higher spikes or extremes. These spikes and the frequent observation of extremes in time series are modelled with certain random variables with infinite variance. There is extensive research for the univariate infinite variance time series but little is known for multivariate infinite variance time series. In the multivariate case, the size of the spikes in each coordinate may not be of the same type and size. The applicant's research investigates the large sample theory for the infinite variance multivariate time series. The result can be used to model time series in Finance, Telecommunications and many other fields.

申请者的研究计划集中在统计推断的两个主要科目上。第一个主题主要涉及贝叶斯推理。在贝叶斯范式中，统计学家考虑对一些未知参数具有概率先验知识。随后，收集的数据被用来更新他们在所选模型下的先验知识。非参数贝叶斯模型在一个更一般的框架中考虑先验知识，具有最小的限制。申请人在这一领域的研究领域主要涉及非参数贝叶斯模型中使用的新过程的构建，以及为这些过程推导快速但更精确的近似工具，以便将它们用于统计推断。申请人还为这些过程推导出有效的模拟技术，以便使实践者能够以更快的速度运行他们的计算机程序。申请人的第二个项目是研究随时间演化的过程的大样本理论。在统计学中，这些过程被称为时间序列。有时，这些时间序列表现出不寻常的、更高的尖峰或极端。这些尖峰和时间序列中经常观察到的极值是用某些具有无穷方差的随机变量来建模的。人们对单变量无限方差时间序列进行了广泛的研究，但对多变量无限方差时间序列的研究却很少。在多变量情况下，每个坐标中的尖峰的大小可能不是相同的类型和大小。申请人的研究是对无限方差多变量时间序列的大样本理论的研究。所得结果可用于金融、电信等诸多领域的时间序列建模。