Efficient Statistical and Computational Methods for Genetics and Dynamical Models

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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.