Efficient Statistical and Computational Methods for Genetics and Dynamical Models

我的NSERC研究计划的重点是开发有效的统计和计算方法的问题，遗传学和动力学模型所产生的各种学科，如流行病学和药代动力学。 我的第一个研究主题旨在解决与计算和统计遗传学/基因组学相关领域的挑战性问题。我的目标是开发可扩展的统计推断方法的遗传学，树是用来描述生物序列之间的进化关系。这些方法的发展将允许推断更复杂的统计模型的背景下，相关的遗传学，如重建肿瘤树从单细胞测序数据，系统发育网络模型基因流，以及包括系统发育树和流行病学模型的遗传动力学。我将开发各种复杂的进化模型和有效的贝叶斯模型选择方法。这项研究将使进化生物学家和癌症研究人员在面对大型现代微生物和癌细胞测序数据集时，能够更有效、更准确地进行统计推断。 我还将为成像遗传学开发高效的贝叶斯推理，其中涉及大规模神经成像数据和高维遗传数据。受阿尔茨海默病（AD）神经影像学倡议数据的启发，我将使用各种统计模型和计算方法，如贝叶斯回归，聚类，网络建模，马尔可夫链蒙特卡罗和变分贝叶斯，研究遗传变异对大脑结构和AD状态的影响。我将开发功能主成分分析方法，用于在成像遗传学背景下进行纵向研究的降维和估计状态空间模型。该研究将有助于开发个性化的AD治疗药物。我的第二个研究主题集中在微分方程（DE）的形式表示的动态模型的统计推断。他们将理解神经科学和物理学等领域的复杂动力系统。DE参数通常有科学的解释，但其值往往是未知的。此外，现有的数据往往是嘈杂和部分观察。我的目标是使用DE对真实世界的应用程序进行建模，并开发新的方法来提供准确和可靠的参数估计，同时保持低计算成本。我将集中在高维常微分方程和复杂的随机微分方程的推理。 我的研究将使大规模数据的统计推断更加有效和准确。拟议的研究不仅将支持高素质人员的培训，而且还将产生可供公众使用的软件包。所提出的方法可以转移到许多其他领域的自然科学和工程中使用类似的模型。

My NSERC research program focuses on developing efficient statistical and computational methodologies for problems in genetics and dynamical models arising from various disciplines such as epidemiology and pharmacokinetics. My first research theme aims to tackle challenging problems in fields related to computational and statistical genetics/genomics. I aim to develop scalable statistical inference methodologies for phylogenetics, where trees are used to describe the evolutionary relationship among biological sequences. The development of these methods will allow inference for more complex statistical models in the contexts related to phylogenetics, such as the reconstruction of tumor trees from single-cell sequencing data, phylogenetic networks which model gene flow, and phylodynamics that involves both the phylogenetic tree and epidemiological models. I will develop various complex evolutionary models and efficient Bayesian model selection methods. The proposed research will allow evolutionary biologists and cancer researchers to conduct statistical inference more efficiently and accurately when facing large modern microbial and cancer cell sequencing datasets. I will also develop efficient Bayesian inference for imaging genetics, which involves large-scale neuroimaging data and high-dimensional genetic data. Motivated by data from the Alzheimer's Disease (AD) Neuroimaging Initiative, I will investigate the influence of genetic variation on brain structure and AD status using various statistical models and computational methods such as Bayesian regression, clustering, network modeling, Markov chain Monte Carlo and variational Bayes. I will develop functional principal component analysis methods for dimension reduction and estimating state-space models for longitudinal studies in the context of imaging genetics. This research will help to develop personalized medicine for treating AD. My second research theme focuses on statistical inference for dynamical models expressed in the form of differential equations (DEs). They are to understand complex dynamical systems in areas such as neuroscience and physics. DE parameters usually have scientific interpretations, but their values are often unknown. In addition, the available data are often noisy and partially observed. My goal is to model real-world applications using DEs and to develop novel methodologies to provide accurate and robust parameter estimates while keeping computational costs low. I will focus on the inference of high-dimensional ordinary differential equations and complex stochastic differential equations.  My research will enable more efficient and accurate statistical inference for large-scale data. Not only will the proposed research support the training of highly qualified personnel, but it will also result in publicly available software packages. The proposed methods are transferable to many other fields of natural science and engineering where similar models are used.