Bayesian Methods, Computation, Model Selection and Goodness of Fit with Complex Data

复杂数据的贝叶斯方法、计算、模型选择和拟合优度

• 批准号: RGPIN-2018-05008
• 负责人: Muthukumarana, Palavinnage
• 金额: $ 1.31万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=660519
• 关键词: Bayesian; Methods; Computation; Model; Selection

My primary research interests lie broadly in Bayesian methods and computation for complex models which integrate both modelling and computational aspects. In my research program, I develop, study, and implement methods for providing statistical inference for large or complicated data arising from health, environmental, sports and social sciences. In this research proposal, I'm particularly interested in developing novel Bayesian methods for complex data types arising from social networks, environmental, ecological and health systems.******We are in the era of data science where enormous amounts of data arise in every discipline with various complexities. These complexities could be in the form of incompleteness, dimensionality, complex structures or big data. In developing a statistical model for these data, we typically embody a set of statistical assumptions concerning the generation of data, either uncertain future data or already observed data. This involves linking a set of parameters to the data in a structural fashion. This can be achieved using a parametric or nonparametric model. In a parametric model, the parameters are in finite-dimensional spaces while the parameters are in infinite-dimensional spaces in a nonparametric model. Note that the parameters are assumed to be fixed unknowns in both approaches. In Bayesian models, we assume that these parameters arise from their own distributions called prior distributions. A prior distribution is used to quantify our prior knowledge about the parameters. When data are available, we can update our prior knowledge using the conditional distribution of parameters, given the data. ******I will develop generative Bayesian hierarchical models where parameter spaces lie in finite dimensions. I will then consider nonparametric Bayesian models whose parameter space has infinite dimension. To define a nonparametric Bayesian model, we have to define a probability distribution on an infinite dimensional space. These models are useful to model distributions as mixtures of simpler distributions and to identify latent classes that can explain the complex dependencies between variables. This allows using a countably infinite number of mixtures, which bypasses the need to determine the correct number of components in a finite mixture model. When models are based on conjugate prior distributions, sampling from the posterior distribution of the parameters of the component distributions and/or of the associations of mixture components is feasible through Gibbs sampling. When they are not conjugate, I will develop Markov chain Monte Carlo (MCMC) sampling methods to learn about the model parameters. Model selection and goodness-of-fit methods will also be developed. The methods developed here will be useful to predict the online social network structures, newborn safety and child health, environmental behavior in Hudson Bay and Eastern Canadian Arctic. ********

我的主要研究兴趣是贝叶斯方法和复杂模型的计算，它将建模和计算结合在一起。在我的研究项目中，我开发、研究和实施方法，为来自健康、环境、体育和社会科学的大型或复杂数据提供统计推断。在这个研究计划中，我对开发新的贝叶斯方法来处理来自社会网络、环境、生态和卫生系统的复杂数据类型特别感兴趣。******我们正处于数据科学的时代，每个学科都有大量的数据，具有各种复杂性。这些复杂性可能以不完整性、维度、复杂结构或大数据的形式出现。在为这些数据开发统计模型时，我们通常包含一组关于数据生成的统计假设，这些数据可能是不确定的未来数据，也可能是已经观察到的数据。这涉及到以结构方式将一组参数链接到数据。这可以使用参数模型或非参数模型来实现。在参数模型中，参数在有限维空间中，而在非参数模型中，参数在无限维空间中。注意，在这两种方法中，参数都假定为固定的未知数。在贝叶斯模型中，我们假设这些参数来自它们自己的分布，称为先验分布。先验分布用于量化我们对参数的先验知识。当数据可用时，我们可以使用给定数据的参数条件分布来更新先验知识。******我将开发生成贝叶斯层次模型，其中参数空间位于有限维度。然后我将考虑参数空间具有无限维的非参数贝叶斯模型。为了定义一个非参数贝叶斯模型，我们必须定义一个无限维空间上的概率分布。这些模型对于将分布建模为简单分布的混合物以及识别可以解释变量之间复杂依赖关系的潜在类非常有用。这允许使用可数的无限数量的混合物，从而绕过了在有限混合模型中确定正确数量的组分的需要。当模型基于共轭先验分布时，通过吉布斯抽样从成分分布和/或混合成分关联的参数的后验分布中抽样是可行的。当它们不是共轭时，我将开发马尔可夫链蒙特卡罗（MCMC）采样方法来了解模型参数。模型选择和拟合优度方法也将发展。该方法将有助于预测哈德逊湾和加拿大东部北极地区的在线社会网络结构、新生儿安全和儿童健康、环境行为。＊＊＊＊＊＊＊＊