Doctor of Philosophy, University of Akron, 2015, Civil Engineering

The models that are able to appropriately study the temporal and spatial dependence structure of water quality and hydrological time series are the essential tools to evaluate the future state of water availability, pollution loading, and best watershed management options. The mass-balance model is one of the current approaches for modeling water quality. However, it has the following limitations: extensive data for inputs, limited effectiveness for many water quality parameters, and ineffectiveness for long-term forecasts. To address the above limitations, statistical and stochastic models, such as classical ARIMA, ANN, and TFN modeling approaches have also been applied to investigate water quality and hydrological time series. However, they also have the some limitations, i.e., Gaussian process and/or linear dependence. Thereby, this study proposes to investigate the water quality and hydrological time series with the use of the following methodologies: (1) applying the order series transformation method to fulfill the assumptions and to address the limitations of the classic (F)AR(I)MA time series modeling approach; (2) applying the copula theory to investigate the spatial dependence pattern for water quality and hydrological time series at the different locations within the same watershed; (3) investigating the temporal dependence for the observed sequences with the use of copula-based Markov process to address the limitations existed in the classic Markov process. To valid the proposed approaches, three watersheds (i.e., Stillaguamish and Snohomish watersheds in Washington: Forest watershed, Chattahoochee River Watershed in Georgia: Urban Watershed, and Cuyahoga River Watershed in Ohio: watershed with mixed LULC) are selected as case-studies. The findings of this study showed: (1) the order series transformation may successfully transform the heavy-skewed and/or fat-tailed univariate time series to Gaussian process to fulfill the assumptions of (F)AR(I)model (open full item for complete abstract)

Committee: Lan Zhang Dr (Advisor) Subjects: Civil Engineering; Environmental Engineering; Water Resource Management

Doctor of Philosophy (PhD), Ohio University, 2024, Mechanical and Systems Engineering (Engineering and Technology)

In this research, we develop an innovative approach to assessing the reliability of complex engineering systems, which are typically characterized by multiple interdependent performance characteristics (PCs). Recognizing that the degradation of these PCs often follows a positive, increasing trend, we employ the gamma process as the foundational model for degradation due to its properties of independent and non-negative increments. A critical aspect of our model is the incorporation of random-effect bivariate Gamma process degradation models, which utilize a variety of copula functions. These functions are instrumental in accurately modeling the dependency structure between the PCs, a factor that significantly influences the overall system reliability. In conventional degradation modeling, fixed and predetermined failure thresholds are commonly used to determine system failure. However, this method can be inadequate as different systems may fail at varying times due to uncontrollable factors. Our model addresses this limitation by considering random failure thresholds, which enhances the accuracy of predicting when a system might fail. We implement a hierarchical Bayesian framework for the degradation modeling, data analysis, and reliability prediction processes. This approach is validated through the analysis of a practical dataset, demonstrating the model's applicability in real-world scenarios. Furthermore, our study responds to the increasing market demand for manufacturers to provide reliable information about the longevity of their products. Manufacturers are particularly interested in the 100p-th percentile of a product's lifetime distribution. Degradation tests are vital for this, as they offer insights into the product's lifespan under various conditions over time. Utilizing our proposed model, we propose a method for designing degradation tests. This method optimizes the number of systems to be tested, the (open full item for complete abstract)

Committee: Tao Yuan (Advisor); Felipe Aros-Vera (Committee Member); Bhaven Naik (Committee Member); William Young (Committee Member); Ashley Metcalf (Committee Member) Subjects: Industrial Engineering

Doctor of Philosophy, The Ohio State University, 2019, Computer Science and Engineering

Recent advancements in the field of computational sciences and high-performance computing have enabled scientists to design high-resolution computational models to simulate various real-world physical phenomenon. In order to gain key scientific insights about the underlying phenomena it is important to analyze and visualize the output data produced by such simulations. However, large-scale scientific simulations often produce output data whose size can range from a few hundred gigabytes to the scale of terabytes or even petabytes. Analyzing and visualizing such large-scale simulation data is not trivial. Moreover, scientific datasets are often multifaceted (multivariate, multi-run, multi-resolution, etc.), which can introduce additional complexities to the analyses and visualization activities. This dissertation addresses three broad categories of data analysis and visualization challenges: (i) multivariate distribution-based data summarization, (ii) uncertain analysis in ensemble simulation data, and (iii) simulation parameter analysis and exploration. We proposed statistical and machine learning-based approaches to overcome these challenges. A common strategy to deal with large-scale simulation data is to partition the simulation domain and create data summaries in the form of statistical probability distributions. Instead of storing high-resolution raw data, storing the compact statistical data summaries results in reduced storage overhead and alleviated I/O bottleneck issues. However, for multivariate simulation data using standard multivariate distributions for creating data summaries is not feasible. Therefore, we proposed a flexible copula-based multivariate distribution modeling strategy to create multivariate data summaries during simulation execution time (i.e, in-situ data modeling). The resulting data summaries can be subsequently used to perform scalable post-hoc analysis and visualization. In many cases, scientists execute their simulations mu (open full item for complete abstract)

Committee: Han-Wei Shen (Advisor); Rephael Wenger (Committee Member); Yusu Wang (Committee Member) Subjects: Computer Science; Statistics

Master of Science, University of Akron, 2017, Applied Mathematics

This project is to track the differences and the movements between the Actual and theoretical future prices using Copula. Standard & Poor's 500 Index (SPX) and 10-year treasury bond yield rate was downloaded from Yahoo! website and SPX future prices were downloaded from Moore Research Centre website and their observations from January 2, 2001 to May 27, 2016 were used for this analysis. Log-returns of the future prices were taken to model and analyse the direct movements of the future prices. The distributions of the marginals and the best family of copula was selected and simulated. We compared the copula method to the classical method after 2000 simulation. A high level of mis-pricing in the future price which corresponds to the period 2008-2009 was observed. This observed mis-pricing could be as a result of relative over-reaction of the Financial market compared to future market. Inverse relationship between the performance of SPX and the volatility of future prices was observed. Standardised Student's t-distribution was concluded to be the marginal distribution using the maximum likelihood method to estimate their distribution parameters. Student t-Copula was concluded to be the best family of copula to measure the dependence. In further studies, modelling the risk associated with futures stock price and pricing with copula based simulation will be a major red flag to be addressed.

Committee: Nao Mimoto Dr (Advisor); Patrick Wilber Dr (Other); Kevin Kreider Dr (Other) Subjects: Applied Mathematics

Doctor of Philosophy, The Ohio State University, 2014, Statistics

This dissertation proposes nonparametric Bayesian methods to study a large class of non-Gaussian time-correlated data, including non-Gaussian time series and non-Gaussian longitudinal datasets. When a time series is noticeably non-Gaussian, classical methods with Gaussian innovations will yield poor fits and forecasts, but the joint distribution of a non-Gaussian time series is often difficult to specify. To overcome this difficulty, we propose the copula-transformed AR (CTAR) model. This model utilizes the copula method to determine the joint distribution of the observed series by separating the marginal distribution from the serial dependence. In implementation, we model the observed series as a nonlinear, nonparametric transformation from a latent Gaussian series. The marginal distribution of the observed series follows a nonparametric Bayesian prior distribution having large support, and therefore any non-Gaussian distribution can be well approximated. The dependence structure of the observed series is characterized indirectly through the latent Gaussian time series, so that we can borrow some classic Gaussian time series modeling methods to model the serial dependence. We also extend the proposed nonparametric Bayesian copula methods to model stationary time series with changing conditional volatility by developing copula-transformed AR-GARCH (CTAR-GARCH) model, which describes the observed series as a nonlinear, nonparametric transformation from an AR-GARCH latent series. We conduct simulations and show the CTAR and CTAR-GARCH models' advantages in capturing non-Gaussian marginal and predictive distributions. We also fit the CTAR-GARCH models to stock index return series and conclude that they yield better predictions than the classical AR-GARCH models with Gaussian innovation. We further extend our models to the non-Gaussian longitudinal analysis setting. We model an observed within-subject response series as a transformation from a latent Gaussian ser (open full item for complete abstract)

Committee: Steven MacEachern (Advisor); Xinyi Xu (Advisor); Mario Peruggia (Committee Member) Subjects: Statistics

Doctor of Philosophy, The Ohio State University, 2009, Statistics

In data mining and other settings, there is sometimes a need to identify relationships between variables when the relationship may hold only over a subset of the observations available. For example, expression of a particular gene may cause resistance to an anticancer drug, but only over certain types of cancer cell-lines. It may not be known in advance which types of cancer cell-lines (e.g., estrogen-regulated, newly differentiated, central nervous system) employ such a method of resistance. This situation differs from the usual setting in which partial correlations are estimated conditional on a known selection, such as the value of another variable. For any pair of variables of interest, the goal is to test if these are associated in some unspecified subpopulation that is represented by a subsample of the data we have available. Nothing in the literature deals directly with this problem. We have tried several parametric and non-parametric approaches, and for both inferential and computational reasons have chosen to present a procedure based on a sequential development of Kendall's tau measure of monotone association. The sequence is achieved by reordering observations so that the sample tau coefficients for the first k of the n observations form a monotone decreasing path, ending at Kendall's tau coefficient. Boundaries are constructed so that 95% of the paths remain within the boundaries under the null hypothesis of independence. A boundary crossing at any point k is evidence of a stronger than expected association amongst a subpopulation represented by the k observations involved. The method is used to screen for association between gene expression and compound activity amongst types of cancer cell-lines in the NCI-60 database. We prove that a particular method of reordering the observations is optimal against any other ordering for simultaneously identifying the highest Kendall's tau association in subsets of size k (k = 2,...,n). Furthermore, assuming a (open full item for complete abstract)

Committee: Joseph Verducci (Committee Chair); Douglas E. Critchlow (Other); Shili Lin (Other) Subjects: Statistics

Master of Arts, The Ohio State University, 1995, East Asian Languages and Literatures

Committee: Mineharu Nakayama (Advisor) Subjects:

Doctor of Philosophy, Case Western Reserve University, 2007, Epidemiology and Biostatistics

This dissertation focuses on approaches to the genetic analysis of longitudinal measures of developmental disorders (DD) with specific application to a longitudinal pedigree study of children ascertained on the basis of a Speech Sound Disorder (SSD). Analysis of this longitudinal cohort is complicated by non-normal trait distributions and a potentially non-linear cognitive developmental trajectory. Prior to developing a longitudinal model I measured the power of the SSD dataset to correctly detect linkage of a quantitative trait to a genetic marker. Assuming that the function describing the genetic effect across time is correctly specified the power of the SSD data set is .18 at a .01 level of signficance. Additional data collection is planned and by doubling the sample size (from 200 to 400 sibling pairs) and number of measurement points (from 2 to 4) the power increases to .83 for the same significance level. It is therefore reasonable to develop a longitudinal approach for use at a later date. As an alternative to the longitudinal analysis, multivariate dependence functions, called copulas, are used to develop a cross-sectional model to test for polygenic*age interaction. These functions separate a multivariate joint distribution into two parts: one describing the interdependency of the probabilities (correlation), the other describing the distribution of the margins (the phenotypes). Using these functions for analysis simultaneously addresses both the non-normality problem, as the margins can be modeled with a wide variety of parametric probability distributions and the developmental trajectory question, as we incorporate age into the analysis through the use of a correlation function, the parameter estimate of which can be tested for significance using a chi-square test statistic. Four of the 13 SSD test measures showed nominal p-values less than .05. While at the broadest level the 4 tests measure different cognitive skills, short term memory plays an importan (open full item for complete abstract)

Committee: Sudha Iyengar (Advisor) Subjects: Statistics

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

This dissertation is concerned with the notion of copula and its importance in modeling and estimation. We use the theory of copulas to assess dependence properties of stationary Markov chains and convergence to the Brownian motion. In the introductory chapter we overview the theory of copulas and their relationship with dependence coefficients for Markov chains. In Chapter 1, we investigate the rates of convergence to zero of the dependence coefficients of copula-based Markov chains. We first review some theoretical results, then improve them and propose an estimate of the maximal correlation coefficient between consecutive states. We also comment on the relationship between geometric ergodicity and exponential ρ-mixing for reversible Markov chains. We show that convex combinations of (absolutely regular) geometrically ergodic stationary reversible Markov chains are (absolutely regular) geometrically ergodic and exponential ρ-mixing. Moreover, we show that this result holds if only one of the summands is geometrically ergodic. Most of the results are based on our observation that if the absolutely continuous part of the copula has a density bounded away from 0 on a set of measure 1, then it generates absolutely regular stationary Markov chains. Many other striking results are provided on this topic in subsequent sections of Chapter 1. We also use small sets to investigate β-mixing rates for the Frechet and Mardia families of copulas. We provide new copula families with functions as parameters. We derive the copula for the general Metropolis-Hastings algorithm and use it to apply our results to this class of processes. In Chapter 2, we provide a background survey on functional central limit theorem for stationary Markov chains with a general state space. We emphasize the relationship between the dependence coefficients studied in Chapter 1 and convergence of normalized partial sums of the chain to a standard normal random variable. We present results showing that i (open full item for complete abstract)

Committee: Magda Peligrad Ph.D. (Committee Chair); Wlodzimierz Bryc Ph.D. (Committee Member); Jeesen Chen Ph.D. (Committee Member); Joanna Mitro Ph.D. (Committee Member); Dan Ralescu Ph.D. (Committee Member); Siva Sivaganesan Ph.D. (Committee Member) Subjects: Mathematics