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Bayesian Statistical Modeling Of Metagenomics Sequencing Data, Shuang Jiang
Bayesian Statistical Modeling Of Metagenomics Sequencing Data, Shuang Jiang
Statistical Science Theses and Dissertations
Microbiome count data are high-dimensional and usually suffer from uneven sampling depth, over-dispersion, and zero-inflation. In this thesis, we develop specialized analytical models for analyzing such count data. In Chapter 2, I develop a bi-level Bayesian hierarchical framework for microbiome differential abundance analysis. The bottom level is a multivariate count-generating process that links the observed counts to their latent normalized abundances. The top level is a mixture of Gaussian distributions with a feature selection scheme for differential abundance analysis. A simulation study on both simulated and synthetic data is conducted. A colorectal cancer case study demonstrates that a resulting diagnostic …
A Bayesian Hierarchical Mixture Model With Continuous-Time Markov Chains To Capture Bumblebee Foraging Behavior, Max Thrush Hukill
A Bayesian Hierarchical Mixture Model With Continuous-Time Markov Chains To Capture Bumblebee Foraging Behavior, Max Thrush Hukill
Honors Projects
The standard statistical methodology for analyzing complex case-control studies in ethology is often limited by approaches that force researchers to model distinct aspects of biological processes in a piecemeal, disjointed fashion. By developing a hierarchical Bayesian model, this work demonstrates that statistical inference in this context can be done using a single coherent framework. To do this, we construct a continuous-time Markov chain (CTMC) to model bumblebee foraging behavior. To connect the experimental design with the CTMC, we employ a mixture model controlled by a logistic regression on the two-factor design matrix. We then show how to infer these model …