Browsing by Author "Ni, Yang"
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Item Bayesian graphical models for complex biological networks(2015-12-04) Ni, Yang; Vannucci, Marina; Stingo, Francesco CIn this thesis, we propose novel Bayesian methodologies in estimating graphical models from complex genomic/health data, for which traditional methods are often found to be inefficient and unsuitable. Our approaches are motivated by various applications including construction of non-linear gene regulatory networks, data integration, cancer surveillance and precision medicine. This thesis consists of three projects. First, we develop a novel semi/non-parametric directed acyclic graphical model to reconstruct gene regulatory network from cancer gene expression data. The regulatory relationship between genes is assumed to be sparse and is allowed to be nonlinear, which is modeled by penalized splines with a spike-and-slab selection prior. We impose a discrete mixture prior on the smoothing parameter of the splines so that we are able to distinguish between linear and nonlinear relationships. Simulation studies show good performance of our approach in comparison with competing methods. Application to GBM data reveals several interesting findings. Second, we propose a multi-dimensional graphical model based on Cholesky-type decomposition of precision matrices to study the conditional independences of multi-dimensional data that are constituted by measurements along multiple axes. Our proposed approach is a unified framework applicable to both directed and undirected graphs as well as arbitrary combinations of these. We develop efficient sampling algorithm based on partially collapsed Gibbs samplers. Simulation studies show that our method has favorable performance against both benchmark and state-of-the-art approaches. We apply our approach to ovarian cancer protein expression data and U.S. cancer mortality data. Third, we propose a novel class of graphical models, graphical regression, which allow graph structure to vary with additional covariates in a flexible fashion. We impose sparsity in both graph structure and covariates. Our approach produces subject-specific graph and predictive graph for new subject. We provide theoretical property and demonstrate the good performance of our method through simulation studies. Finally, we apply our approach to multiple myeloma gene expression data taking prognostic factors as covariates, which reveals several interesting findings.Item Bayesian graphical models for modern biological applications(Springer Nature, 2022) Ni, Yang; Baladandayuthapani, Veerabhadran; Vannucci, Marina; Stingo, Francesco C.Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.Item Bayesian graphical models for modern biological applications(Springer Nature, 2021) Ni, Yang; Baladandayuthapani, Veerabhadran; Vannucci, Marina; Stingo, Francesco C.Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.