Bayesian Time Series and Dynamic Models

摘要本研究涉及发展新的统计模型、方法和计算算法来分析和预测时间序列。研究将包括时间序列贝叶斯状态空间建模的各个方面，介绍非平稳时间序列模型的新模型，结构化潜在过程分析和时间序列分解的方法，多时间序列分析的新模型和计算方法，包括动态潜在因素模型，动态贝叶斯层次模型，非高斯和非线性模型。部分研究涉及到高维时间序列数据集的处理策略以及时间序列数据的约简和汇总问题的研究。随机模拟和计算机算法是组成部分，它们将为基于仿真的贝叶斯分析在各种动态建模和时间序列分析问题中带来新的计算工具。相关研究领域将包括时间序列模型的不确定性、评估和事先规范、污染结构和数据清理问题，以及涉及统计混合结构的模型。这些项目代表了时间序列建模和分析方面的进展，以及对统计科学其他领域的贡献，将引起各学科的科学家和研究人员以及统计学家的广泛兴趣和实际意义。该项目产生的新的统计方法扩展了当前时间序列分析工具的适用范围，以解决更复杂、非线性和多元的问题。该研究的一个重要组成部分涉及计算密集型方法来拟合和探索应用中的数据模型。这项研究的动机，部分是由于目前在几个领域的应用领域中存在的统计建模和推理问题，具体包括神经科学、全球环境变化问题驱动的地质学、金融建模和预测、生物医学工程和信号处理等项目。

Bayesian Time Series and Dynamic Models Mike West Abstract This research involves development of new statistical models, methods and computational algorithms for analysis and forecasting of time series. The investigations will include various aspects of Bayesian state-space modelling for time series, introducing new models for non-stationary time series models, methodology for structured latent process analysis and time series decompositions, new models and computational methods for multiple time series analysis including dynamic latent factor models, dynamic Bayesian hierarchical models, and non-Gaussian and non-linear models. Part of the research involves investigation of strategies for dealing with high-dimensional time series data sets and issues of time series data reduction and summary. Stochastic simulation and computer algorithms are ingredients, and will lead to new computational tools for simulation-based Bayesian analyses in various problems of dynamic modelling and time series analysis. Related areas of the research will include time series model uncertainty, assessment and prior specifications, problems of contamination structures and data cleaning, and models involving statistical mixture structure. These projects represent advances in time series modelling and analysis, and contributions to other areas of statistical science, that will be of broad interest and practical relevance to scientists and researchers in various disciplines as well as to statisticians. The new statistical methods resulting from this project extend the scope of applicability of current time series analysis tools to more complex, non-linear and multivariate problems. A significant component of the research involves computationally intensive methods to fit and explore models to data in applications. The research is motivated, in part, by existing problems of statistical modelling and inference in current application areas in several fields, specifically inclu ding projects in the neurosciences, in geology driven by issues of global environmental change, in financial modelling and forecasting, and in biomedical engineering and signal processing.