Bayesian Models and Methods for Dynamic and Spatio-Dynamic Systems

本研究涉及结构化动态和空间动态多变量过程的新统计理论、模型和方法。该范围包括多和矩阵变量时间序列中动态协方差结构的新一类随机过程模型的理论发展，包括多变量波动率建模的新一类平稳马尔可夫过程。理论和应用的发展包括新的方法稀疏建模越来越高维，时变参数随机系统，适用于动态回归，时变向量自回归，动态因子模型和协方差波动模型。额外的研究重点是新的空间网格和空间变化的随机场模型，再加上时间序列过程，以定义灵活的时空模型模型，通过时间观察到越来越高的分辨率格数据。该研究员开发基于贝叶斯模拟的统计计算-包括基于GPU的并行算法-用于模型实现，以及金融时间序列以及大气和生物医学科学研究的跨学科应用。面对时间和空间系统研究中产生的越来越高维的数据集，统计科学研究旨在大幅提高表示能力，分析和使用增加维度，现实主义和复杂性的数学模型。研究人员开发数学和统计建模理论以及相关的基于模拟的计算方法，部分原因是金融，大气科学和神经科学领域的跨学科合作应用。统计研究的创新包括：（i）新的和改进的模型，用于描述和预测几个或多个时间序列之间的复杂关系模式的时间变化-例如金融指标，或基于纳米技术的大脑成像神经信号记录;（ii）新的理论和方法，用于诱导稀疏性-即，控制应用随机模型的复杂性，以便能够按比例处理日益高维的问题，例如大气研究中的高分辨率卫星成像以及大规模金融时间序列中出现的问题; ㈢统计计算模拟技术的创新，包括并行桌面计算，以提高拟合能力，探索和使用规模和复杂性不断增加的模型，以及越来越大的数据集。通过跨学科的合作者和学生，该研究推进了核心数学和统计建模理论和技术，并在几个特定的应用环境中为建模和数据分析提供了新的，精炼的和相关的方法，以及生成更广泛使用的方法。

The research concerns novel statistical theory, models and methods for structured dynamic and spatio-dynamic multivariate processes. The scope includes theoretical developments of new classes of stochastic process models for dynamic covariancestructures in multi- and matrix-variate time series, including novel classes of stationary Markov processes for multivariate volatility modeling. Theoretical and applied developments include new approaches to sparsity modeling for increasingly high-dimensional, time-varying parameter stochastic systems, applying to dynamic regression, time-varying vector auto-regression, dynamic factor models and covariance volatility models. Additional research focuses on new classes of spatial lattice and spatially-varying random field models, coupled with time series processes to define flexible models of spatio-temporal models for increasingly high-resolution lattice data observed through time. The investigator develops Bayesian simulation-based statistical computation-- including GPU-based parallelized algorithms-- for model implementations, and cross-disciplinary applications in financial time series as well as studies in atmospheric and biomedical sciences.Faced with increasingly high-dimensional data sets generated in studies of temporal and spatial systems, statistical science research aims to substantially advance the ability to represent, analyze and use mathematical models of increasing dimension, realism and complexity. The investigator develops mathematical and statistical modelling theory and associated simulation-based computational methods for a range of contexts, motivated in part by collaborative cross-disciplinary applications in areas of finance, atmospheric science and the neurosciences. Innovations in statistical research include: (i) new and improved models for describing and predicting change in time of the complex patterns of relationships among several or many time series-- such as financial indicators, or nano-technology based recordings of neural signals in brain imaging; (ii) new theory and methods for inducing sparsity-- i.e., controlling complexity-- of applied stochastic models, to enable scaling to increasingly high-dimensional problems, such as arise in high-resolution satellite imaging in atmospheric studies as well as large-scale financial time series;(iii) innovations in simulation techniques for statistical computing, including parallel desktop computing, to advance the ability to fit, explore and use models of increasing scale and complexity and with increasingly large data sets. With cross-disciplinary collaborators and students, the research advances core mathematical and statistical modeling theory and technology, and contributes new, refined and relevant approaches to modeling and dataanalysis in several specific applied contexts as well as generating methods for broader use.