PhD, University of Cincinnati, 2020, Arts and Sciences: Mathematical Sciences

Multiple testing on large-scale dependent count data faces challenges in two basic modeling elements, that is, modeling of the dependence structure across observations and the distribution specification on the null and non-null states. We propose three Poisson hidden Markov models (PHMM) under the Bayesian hierarchical model framework to handle these challenges. The dependence structure across hypotheses is modeled through the hidden Markov process. To address the challenge of the distribution specification under the non-null state, several model selection methods are employed and compared to determine the number of mixture components in the non-null distribution. Furthermore, we examine two different ways to include covariate effects, PHMM with homogeneous covariate effects (PHMM-HO) and PHMM with heterogeneous covariate effects (PHMM-HE). Modeling covariate effects helps take consideration of multiple factors which are directly or indirectly related to the hypotheses under investigation. We carry out extensive simulation studies to demonstrate the performance of the proposed hidden Markov models. The stable and robust results show the significant advantages of our proposed models in handling complex data structure in dependent counts. Multiple hypotheses testing with PHMM is valid and optimal compared with a group of commonly used testing procedures. Both PHMM-HO and PHMM-HE improve the multiple testing performance and are able to detect the dynamic data pattern along with the covariate effects.

Committee: Xia Wang Ph.D. (Committee Chair); Hang Joon Kim Ph.D. (Committee Member); Siva Sivaganesan Ph.D. (Committee Member); Seongho Song Ph.D. (Committee Member); Bin Zhang Ph.D. (Committee Member) Subjects: Statistics

Master of Science (MS), Bowling Green State University, 2024, Applied Statistics (ASOR)

The New Testament contains thirteen epistles written in the name of the Apostle Paul, and from the earliest records of church history, Christian theologians received all thirteen as authentically Pauline. Since the 19th century, however, many scholars have doubted Paul's authorship of some epistles based on, among other factors, their vocabulary and writing style, which differ from undisputed Pauline epistles. In particular, three epistles called the Pastoral Epistles (1 Timothy, 2 Timothy, and Titus) have been subject to the most doubt. This thesis will use a Hidden Markov Model that analyzes the transitions between different parts of speech in the whole Pauline corpus and classifies sentences as belonging to a “Pauline” or “non-Pauline” style. Then, informed by New Testament scholarship, we will interpret these results and judge the possibility of Pauline authorship for the Pastoral Epistles.

Committee: Shuchismita Sarkar (Committee Chair); Riddhi Ghosh (Committee Member); Christopher Rump (Committee Member) Subjects: Statistics

Master of Science (MS), Bowling Green State University, 2023, Applied Statistics (ASOR)

This thesis delves into the intricate analysis of multidimensional enrollment records spanning two and half decades, covering various regions within U.S. academic institutions. Leveraging Hidden Markov Models (HMMs) with hypothesis testing, we seek to unearth underlying patterns and trends in higher education enrollment. The study commences with data preparation, involving the extraction and aggregation of data across institutions, majors, and genders over two and half decades, resulting in a rich, 4-dimensional dataset. To streamline the analysis, the dataset is divided into nine geographic divisions. The results offer a granular view of enrollment trends, enabling institutions and policymakers to make informed decisions regarding diversity and education equality. This research bridges the gap in modelling matrix-variate data within the HMM framework, addressing the unique challenges posed by multidimensional datasets. By adopting this innovative approach, we contribute valuable insights to the field of higher education enrollment analysis, facilitating more inclusive and data-driven educational policies. This thesis comprises four chapters. The first chapter talks about the motivation and objective of this paper, and the second chapter introduces the HMM tailored for matrix-variate time series data. The third chapter demonstrates the application of this model with hypothesis testing using undergraduate enrollment data from US institutions, and the fourth chapter concludes with the key findings and the significance of this method.

Committee: Shuchismita Sarkar Ph.D. (Committee Chair); Umar Islambekov Ph.D. (Committee Member); Yuhang Xu Ph.D. (Committee Member) Subjects: Education; Education Policy; Statistics

Master of Science, Miami University, 2021, Computational Science and Engineering

This project seeks to investigate and apply anomaly detection algorithms for a wideband receiver, that will flag anomalous radar behaviors sent by some transmitter external to the receiver's system. Flagging these anomalies will indicate to the receiver system that the radar's behavior has been reprogrammed, knowledge which is important for determining optimal countermeasures. The programs developed have investigated several approaches to accomplish this. Firstly, clustering methods like DBSCAN can group the observed pulses into distinct classes, reducing the problem to finding disruptions in patterns of numerical labels. Semi-supervised techniques like Hidden Markov Models and Long Short-Term Memories can be applied to learn these patterns for normal behavior and flag anomalies where the patterns are broken. Lastly, an unsupervised technique based on cross-correlations takes an alternative approach of flagging all the different behaviors in a sequence, without any initial training. Simulation results on test data demonstrate the functionality of these techniques, which are offered as potential suggestions for implementation in a real system.

Committee: Chi-Hao Cheng Ph.D. (Advisor); Dmitriy Garmatyuk Ph.D. (Committee Member); Mark Scott Ph.D. (Committee Member) Subjects: Computer Engineering; Computer Science; Electrical Engineering; Remote Sensing

Master of Science, Miami University, 2020, Computational Science and Engineering

Power electronics are critical components in society's modern infrastructure. In electrified vehicles and aircraft, losing power jeopardizes personal safety and incur financial penalties. Because of these concerns, many researchers explore condition monitoring (CM) methods that provide real-time information about a system';s health. This thesis develops a CM method that determines the health of a DC-link capacitor in a three-phase inverter. The approach uses measurements from a current transducer in two Machine Learning (ML) algorithms, a Support Vector Machine (SVM), and an Artificial Neural Network (ANN), that classify the data into groups corresponding to the capacitor's health. This research evaluates six sets of data: time-domain, frequency-domain, and frequency-domain data subjected to four smoothing filters: the moving average with a rectangular window (MARF) and a Hanning window, the locally weighted linear regression, and the Savitzky-Golay filter. The results show that both ML algorithms estimate the DC-link capacitor health with the highest accuracy being 91.8% for the SVM and 90.7% for the ANN. The MARF-smoothed data is an optimal input data type for the ML classifiers due to its low computational cost and high accuracy. Additionally, a Hidden Markov Model increases the classification accuracy up to 98% when utilized with the ANN.

Committee: Mark Scott Dr. (Advisor); Chi-Hao Cheng Dr. (Committee Member); Peter Jamieson Dr. (Committee Member) Subjects: Computer Engineering; Electrical Engineering

MS, University of Cincinnati, 2015, Engineering and Applied Science: Mechanical Engineering

In the field of prognostics and health management, process monitoring is an essential technique to equip the system with the intelligence of being “aware” of any faults. Owing to tool fatigue, upstream material variation and electronic component drift, machine characteristics will often shift from initial states. As a result, sensor signals collected from the same equipment will possess varying correlation structures and offset in distributions, even if the health condition does not change. In order to build an effective data-driven process monitoring model, the constructed model has to be able to robustly differentiate the drifting healthy states from faulty conditions. In this thesis, a sequential process monitoring approach using hidden Markov model is proposed for process monitoring to overcome influences of such drifts. During training stage, a discrete hidden Markov model is constructed using only healthy condition data. A health threshold is determined based on the deviation of normal condition health index, which is the normalized slope of negative log-likelihood. During monitoring stage, the health index of the new process from the same machine is calculated. Faults will be detected when the metric goes beyond the threshold. The developed approach has been validated using a case study for semiconductor etching process. And result of the proposed approach is benchmarked with both global and regime-specific local models using principal component analysis and self-organizing maps.

Committee: Jay Lee Ph.D. (Committee Chair); J. Kim Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member) Subjects: Mechanics

Doctor of Philosophy, Case Western Reserve University, 2015, EECS - System and Control Engineering

This thesis consists of various studies in information theory, including its connection with control theory and the computational aspects of information measures. The first part of the research investigates the connection between control theory and information theory. This part extends previous results that mainly focused on this connection in the context of state estimation and feedback control. For linear systems, mutual information, along with the concepts of controllability and observability, is used to derive a tight connection between control theory and information theory. For nonlinear systems, a weaker statement of this connection is established. Some explicit calculations for linear systems and interesting observations about these calculations are presented. The second part investigates the computation of mutual information. An innovative method to compute the mutual information between two collections of time series data based on a Hidden Markov Model (HMM) is proposed. For continuous-valued data, a HMM with Gaussian emission is used to estimate the underlying dynamics of the original data. Mutual information is computed based on the approximate dynamics provided by the HMM. This work improves the estimation of the upper and lower bounds of entropy for Gaussian mixtures, which is one of the key components in this proposed method. This improvement of these bounds are shown to be robust compared to existing methods in all of the synthetic data experiments conducted. In addition, this research includes the study of the computation of Shannon mutual information in which the strong assumptions of independence and identical distribution (i.i.d.) are imposed. This research shows that even if this assumption is violated, the results process a meaningful interpretation. The study of the computation of Shannon mutual information for continuous-valued random variables is included in this research. Three coupled chaotic systems are used as exemplars to show that the c (open full item for complete abstract)

Committee: Kenneth Loparo (Advisor); Vira Chankong (Committee Member); Marc Buchner (Committee Member); Richard Kolacinski (Committee Member) Subjects: Engineering; Mathematics

Master of Mathematical Sciences, The Ohio State University, 2014, Mathematics

Online education in mathematics has become an important research topic. With more assessment going online, we have to ask ourselves, “How do we measure student performance through a computer?” A second question we ask is, “How do we evaluate the individualized instruction platform itself?” We first provide a summary of personalized education in mathematics. We discuss case studies on certain individualized instruction platforms with commentary on how students are learning mathematics. Analysis of these case studies inform us on possible challenges in their design and use. We next present a hidden Markov model as a way to analyze student learning in an individualized instruction system. The Baum-Welch algorithm provides a means to determine the parameters of a hidden Markov model. It's these parameters that give insight into exercises and how students are performing with each exercise. We then consider the Viterbi algorithm, which is an algorithm used to uncover the hidden states in a hidden Markov model. A student's sequence of observations is recorded by the system, which is the input to the Viterbi algorithm. The hidden performance states of the student (unknowing, emerging, and knowing) are generated as a time-series sequence representing student understanding on a particular exercise over time. We finally provide recommendations for implementing the hidden Markov model in individualized instruction systems and further research questions are posed.

Committee: Rodica Costin (Advisor); Dennis Pearl (Committee Member); Bart Snapp (Committee Member) Subjects: Education; Mathematics; Statistics

Master of Science, The Ohio State University, 2011, Computer Science and Engineering

The United States has the highest annual incidence rates of breast cancer in the world; 128.6 per 100,000 in whites and 112.6 per 100,000 among African Americans. It is the second-most common cancer (after skin cancer) and the second-most common cause of cancer death (after lung cancer). Recent studies have demonstrated that hyper-methylation of CpG islands may be implicated in tumor genesis, acting as a mechanism to inactivate specific gene expression of a diverse array of genes (Baylin et al., 2001). Genes have been reported to be regulated by CpG hyper-methylation, include tumor suppressor genes, cell cycle related genes, DNA mismatch repair genes, hormone receptors and tissue or cell adhesion molecules (Yan et al., 2001). Usually, breast cancer cells may or may not have three important receptors: estrogen receptor (ER), progesterone receptor (PR), and HER2. So we will consider the ER, PR and HER2 while dealing with the data. In this thesis, we first use Hidden Markov Model (HMM) to train the methylation data from both breast cancer cells and other cancer cells. Also we did hierarchy clustering to the gene expression data for the breast cancer cells and based on the clustering results, we get the methylation distribution in each cluster. Finally, we correlate the HMM training results with the methylation distribution and get the biology meanings for the states in the HMM results.

Committee: Victor Jin X (Advisor); Raghu Machiraju (Committee Member) Subjects: Bioinformatics; Computer Science

Doctor of Philosophy, The Ohio State University, 2003, Electrical Engineering

The omnipresent multimedia data calls for efficient and flexible methodologies to annotate, organize, store, and access video resources. Video annotation data, or video meta-data, plays an important role in the future annotation-driven video systems. Although the importance of the video annotation data is widely recognized and a considerable amount of research has been conducted on its various aspects, there is no consistent framework on which to structure video annotation data. In this dissertation, we propose a hierarchical structure for video semantic annotation. Not only do users think in terms of semantic concepts, they also think and operate video systems in a hierarchical fashion. Moreover, hierarchical structures are being used to store and transmit video production data. Consequently, a hierarchical structure for video annotation data is needed. The hierarchical structure is so important that it is likely to affect almost every aspect of multimedia computing. We anticipate that numerous research activities in various aspects of video will be tailored toward this hierarchical structure. Second, various techniques are investigated in terms of how to hierarchically extract video annotations, from low- to mid- to high-levels. The lower the level of the video annotation in the hierarchy, the more applicable automatic approaches are likely to be. Different semantic levels call for different techniques to extract video annotations. For example, high-level video annotations tend to describe high-level video events that are present in the video data. High-level video events are highly structural and the traditional statistical pattern analysis is insufficient. As a result, structural pattern analysis methods such as the syntactic approach are needed to extract high-level video annotations. In this dissertation, we have studied the techniques to hierarchically extract video annotations, from low-, to mid-, and to high-level. In particular, one of the key contribution (open full item for complete abstract)

Committee: Stanley Ahalt (Advisor) Subjects:

Doctor of Philosophy, The Ohio State University, 2003, Computer and Information Science

Two causes of speech degradation exist in practically all listening situations: noise interference and room reverberation. This dissertation investigates three particular aspects of speech processing in noisy and reverberant environments: multipitch tracking for noisy speech, measurement of reverberation time based on pitch strength, and reverberant speech enhancement using one microphone (or monaurally). An effective multipitch tracking algorithm for noisy speech is critical for speech analysis and processing. However, the performance of existing algorithms is not satisfactory. We present a robust algorithm for multipitch tracking of noisy speech. Our approach integrates an improved channel and peak selection method, a new method for extracting periodicity information across different channels, and a hidden Markov model (HMM) for forming continuous pitch tracks. The resulting algorithm can reliably track single and double pitch tracks in a noisy environment. We suggest a pitch error measure for the multipitch situation. The proposed algorithm is evaluated on a database of speech utterances mixed with various types of interference. Quantitative comparisons show that our algorithm significantly outperforms existing ones. Reverberation corrupts harmonic structure in voiced speech. We observe that the pitch strength of voiced speech segments is indicative of the degree of reverberation. Consequently, we present a pitch-based measure for reverberation time (T60) utilizing our new pitch determination algorithm. The pitch strength is measured by deriving the statistics of relative time lags, defined as the distances from the detected pitch periods to the closest peaks in correlograms. The monotonic relationship between the measured pitch strength and reverberation time is learned from a corpus of reverberant speech with known reverberation times. Under noise-free conditions, the quality of reverberant speech is dependent on two distinct perceptual components: coloration a (open full item for complete abstract)

Committee: DeLiang Wang (Advisor) Subjects: Artificial Intelligence