贝叶斯柔性密度方法及其在高维金融数据中的应用

Bayesian Flexible modeling of high dimensional density is the state-of-the-art topic in Bayesian methodology. Financial data have the unique feature such as time-dependent, high-dimensional, non-Gaussian and heavy correlated among variables. Tremendous research has been done on continuous financial data in low-dimensions. Recent research also has found the importance of textual data interfering financial events. Unfortunately there is still lack of research on modeling high-dimensional data combining with textual data and continuous data. This is partially because that constructing high-dimensional density that can be modeled with continuous and discrete margins is not yet efficient. Usual statistical inference tools are less likely to be successful in that setting because of the curse of dimensionality, especially when there are more than a couple of margins...In this project, we propose a general approach for modeling data features in high-dimensional density with flexible continuous and discrete marginal densities. Our approach begins with a two-dimensional copula density where the rank correlation and tail-dependence coefficients are connected with covariates via smooth functions, in which the two marginal densities are from finite mixture of student-t densities and Poisson densities, respectively. We propose a highly efficient MCMC algorithm that updates all the marginal and joint density features jointly. And we also propose an efficient stochastic searching margins permutation algorithm that effectively constructs a high-dimensional flexible copula density with flexible bivariate copulas. Unlike the usual reversible jump MCMC used in the literature which is heavily dependent by the choice of prior and can only update one margin per time. Our algorithm jointly update the joint multivariate density with an efficient propose of margin combinations by Bayesian model comparison techniques based on out of sample predictive performance that eliminates the effect from the prior...Our proposed Bayesian approach is applied to high dimensional stock market data with additional text information provided by Bloomberg.

贝叶斯高维密度柔性建模是贝叶斯方法论的热点和难点课题。然而目前多元密度建模方法的研究成果往往限定在对单一的或者连续或者离散型变量下密度特征的静态研究中，而且实际可操作性停留在响应变量维度小于十的低维情况，尚不能实现有效全面地描述复杂高维数据中关联性尤其是尾部关联性。基于申请者前期研究成果，本课题拟首先从混合有连续边际和离散边际的二维Copula密度的贝叶斯柔性建模出发，以密度估计理论为支撑，利用并改进MCMC抽样技术、结合贝叶斯变量选择理论、深入研究混合离散和连续边际的Copula协变量相依的动态相依性和尾部相依性。其次利用贝叶斯条件独立性、以及基于预测的贝叶斯模型比较理论，将二维Copula柔性密度理论扩展到混合连续边际和离散边际的高维贝叶斯柔性密度的高效构建和估计中。本课题理论成果将为混合有文本信息的高维金融数据建模等复杂数据应用领域提供有效的解决工具。

本课题通过对基于高维金融数据的贝叶斯柔性密度建模,对贝叶斯方法在高维柔性密度估计的模型假设、模型估计、模型验证、模型预测等理论和计算进行研究。从二维离散和连续边际的 Copula的柔性密度模型出发,研究高维 Copula 模型柔性边际相关性以及尾部相依性,并将该成果拓展到混合离散和连续边际的高维 Copula 柔性密度估计,将该方法应用到互联网金融环境下文本信息对股票和金融市场的实时影响分析中。根据同行评审论文反馈,该课题成果内容达到本领域国际领先水平。通过计算机模拟数据表明我们的协变量相依的联合 Copula 建模方式在可以很好地捕获真实的尾部相依特征,我们同时发现传统的 Copula 模型仅能捕获真正尾部相依的平均值,无法涵盖波动性甚至 95%的 HPD。为了进一步说明我们的方法,我们将该方法论应用在标准普尔每日股票收益的金融数据中。..本项目的理论进展实现了复杂 Copula 模型的高效 MCMC 估计。我们联合更新 copula 组件和边缘组件。我们使用Gibbs 采样器与 Metropolis-Hastings 算法结合，即使用 Gibbs 采样器用于更新联合参数组件,每个条件参数块采用经过特殊调整 Metropolis-Hastings 算法。申请者将统计计算与大数据实践结合, 将复杂统计模型部署到大数据分布式计算平台。出版专著《大数据分布式计算》。该书成为全国应用统计专业学位研究生教育指导委员会推荐用书。..申请者形成的理论体系直接吸引波士顿大学医学院主动邀请其加入糖尿病风险预测的全球合作团队 (该国际团队唯一的亚洲研究员) 并将贝叶斯风险预测理论应用到疾病风险预测研究中, 其初期合作成果研究全球糖尿病发展趋势, 并构建目前全球最大的糖尿病研究数据库, 发表在统计与医学交叉顶级期刊 BMJ Open。目前该项合作在进一步深化, 包扩研究基于人口统计学的差异研究全因死亡率以及影响因素, 本项目通过其唯一的资源数据研究二型糖尿病发病率差异以及发展趋势、生物标志物在疾病诊断前后与疾病相关的结果、并发症和早产死亡、以及评估种族/族裔的差异。该项成果具有广泛的科学意义,使得原本应用于金融风险管理的 Copula 模型能够迁移到医学与疾病成因研究中,除现有已发表论文目前该项目还有 2 篇相关论文在投。预计在疾病预防领域会有很好的应用前景。