Master of Science (MS), Ohio University, 2011, Industrial and Systems Engineering (Engineering and Technology)

This thesis develops a Bayesian nonparametric method based on Dirichlet Process Mixture Model (DPMM) and Markov chain Monte Carlo (MCMC) simulation algorithms to analyze non-repairable reliability lifetime data. Kernel distributions of the model will be implemented with Weibull, Lognormal and Exponential. The influence of prior distribution on the model parameters is studied. Both simulated and experimental data are used to test the proposed models. Our data analysis results indicate that the Dirichlet Process Lognormal Mixture (DPLNM) model is more flexible than the Dirichlet Process Exponential Mixture (DPEM) model and the Dirichlet Process Weibull Mixture (DPWM) model in terms of capturing different shapes of the life time distribution functions. Typically, when handling the practical data generated from devices with embedded nano-crystals, only the DPLNM model can produce a good fit towards the data. Although the lognormal distribution does not have closed form reliability function, censored data can still be easily handled using modern sampling techniques, such as Slice Sampling.

Committee: Tao Yuan (Committee Chair) Subjects: Engineering

PhD, University of Cincinnati, 2013, Arts and Sciences: Mathematical Sciences

DNA microarray is a widely used high-throughput technology to measure the expression level of tens of thousands of genes simultaneously. With increasing availability of microarray genomics data, various clustering algorithms have been explored to identify the latent patterns in gene expression data as well as discover disease subtypes. Interesting connections that can be founded correlating differential-expressed genes evidence to other biological information are very important in developing a full picture of the biological pathways as well as in giving insightful suggestions to the new conducted experiments. The abundant biological information we need to identify the disease signature is organized in the functional categories. Thus, relating the microarray experiments to the functional categories could lead to a better understanding of the underlying biological process and help develop targeted treatment to a specific disease. In this dissertation, we investigated several Dirichlet process mixture (DPM) model based clustering methods that explicitly account for interactions across the functional category enrichment scores for improved sample clustering. Our clustering method represents microarray data enrichment score profiles as multivariate Gaussian random variables with structured or unstructured correlation. Also we demonstrate by a simulation study that when correlation exist, our algorithm will outperform the other clustering algorithm assume independence. Furthermore, factor analysis based clustering procedure is developed to search for the correct underlying correlation pattern and we optimize the number of factors using the Metropolised Carlin and Chib method based model selection algorithm. In such a way, we reduce the number of parameters to be estimated in the unstructured covariance matrix model and also incorporate the unknown variance-covariance structure across different functional categories. The main contributions of our ap (open full item for complete abstract)

Committee: Siva Sivaganesan Ph.D. (Committee Chair); Seongho Song Ph.D. (Committee Member); Xia Wang Ph.D. (Committee Member) Subjects: Statistics

Doctor of Philosophy, Case Western Reserve University, 2022, Physics

In the last two decades, advances in experimental techniques have opened up new vistas for understanding bio-molecules and their complex networks of interactions in the cell. In this thesis, we use theoretical modeling and machine learning to explore two surprising aspects that have been revealed by recent experiments: (i) the discovery that many different types of cellular signaling networks, in both prokaryotes and eukaryotes, can transmit at most 1 to 3 bits of information; (ii) the observation that single bio-molecules can exhibit multiple, stable conformational states with extremely heterogeneous functional properties. The first part of the thesis investigates how the energetic costs of signaling in biological networks constrain the amount of information that can be transferred through them. The focus is specifically on the kinase-phosphatase enzymatic network, one of the basic elements of cellular signaling pathways. We find a remarkably simple analytical relationship for the minimum rate of ATP consumption necessary to achieve a certain signal fidelity across a range of frequencies. This defines a fundamental performance limit for such enzymatic systems, and we find evidence that a component of the yeast osmotic shock pathway may be close to this optimality line. By quantifying the evolutionary pressures that operate on these networks, we argue that this is not a coincidence: natural selection is capable of pushing signaling systems toward optimality, particularly in unicellular organisms. Our theoretical framework is directly verifiable using existing experimental techniques, and predicts that many more examples of such optimality should exist in nature. In the second part of the thesis, we develop two machine learning methods to analyze data from single-molecule AFM pulling experiments: a supervised (deep learning) and an unsupervised (non-parametric Bayesian) algorithm. These experiments involve applying an increasing force on a bio-molecul (open full item for complete abstract)

Committee: Michael Hinczewski (Committee Chair); Peter Thomas (Committee Member); Harsh Mathur (Committee Member); Lydia Kisley (Committee Member) Subjects: Biophysics; Physics

PhD, University of Cincinnati, 2012, Arts and Sciences: Mathematical Sciences

In longitudinal studies, we are often interested in simultaneously clustering observations at both subject- and time-levels. Current clustering approaches assume the exchangeability among clustering units, and they are not applicable for our clustering goal. Through the use of a specific base measure, we propose a more suitable method that improves upon the multivariate DP mixture model. A well-known MCMC algorithm, Gibbs sampler, is implemented for the Bayesian posterior distributions and estimates. We compare two kinds of specific base measures from simple to complex. The models are evaluated through simulation studies of multivariate data with different covariance specifications. Performance is assessed by the stationarity, the autocorrelation functions of the Markov chain, the correct classification rates, the 95% credible intervals for parameter estimates, and the CPU time. We illustrate the method with data from a prospective longitudinal study on sleep apnea, tracking the diastolic blood pressure and severity of sleep apnea of 97 children during 24 hours.

Committee: Siva Sivaganesan PhD (Committee Chair); Mekibib Altaye PhD (Committee Member); James Deddens PhD (Committee Member); Paul Horn PhD (Committee Member); Seongho Song PhD (Committee Member); Rhonda VanDyke PhD (Committee Member) Subjects: Statistics