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

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。

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.