This thesis presents simple efficient algorithms to estimate distribution parameters and to construct prediction intervals for location-scale families. Specifically, we study two scenarios: one is a frequentist method for a general location--scale family and then extend to a 3-parameter distribution, another is a Bayesian method for the Gumbel distribution. At the end of the thesis, a generalized bootstrap resampling scheme is proposed to construct prediction intervals for data with an unknown distribution. Our estimator construction begins with the equivariance principle, and then makes use of unbiasedness principle. These two estimates have closed form and are functions of the sample mean, sample standard deviation, sample size, as well as the mean and variance of a corresponding standard distribution. Next, we extend the previous result to estimate a 3-parameter distribution which we call a mixed method. A central idea of the mixed method is to estimate the location and scale parameters as functions of the shape parameter. The sample mean is a popular estimator for the population mean. The mean squared error (MSE) of the sample mean is often large, however, when the sample size is small or the scale parameter is greater than the location parameter. To reduce the MSE of our location estimator, we introduce an adaptive estimator. We will illustrate this by the example of the power Gumbel distribution. The frequentist approach is often criticized as failing to take into account the uncertainty of an unknown parameter, whereas a Bayesian approach incorporates such uncertainty. The present Bayesian analysis for the Gumbel data is achieved numerically as it is hard to obtain an explicit form. We tackle the problem by providing an approximation to the exponential sum of Gumbel random variables. Next, we provide two efficient methods to construct prediction intervals. The first one is a Monte Carlo method for a general location-scale family, based on our previous parameter estimation. Another is the Gibbs sampler, a special case of Markov Chain Monte Carlo. We derive the predictive distribution by making use of an approximation to the exponential sum of Gumbel random variables . Finally, we present a new generalized bootstrap and show that Efron's bootstrap re-sampling is a special case of the new re-sampling scheme. Our result overcomes the issue of the bootstrap of its ``inability to draw samples outside the range of the original dataset.'' We give an applications for constructing prediction intervals, and simulation shows that generalized bootstrap is better than that of the bootstrap when the sample size is small. The last contribution in this thesis is an improved GRS method used in nuclear engineering for construction of non-parametric tolerance intervals for percentiles of an unknown distribution. Our result shows that the required sample size can be reduced by a factor of almost two when the distribution is symmetric. The confidence level is computed for a number of distributions and then compared with the results of applying the generalized bootstrap. We find that the generalized bootstrap approximates the confidence level very well. / Dissertation / Doctor of Philosophy (PhD)

No / This paper proposes a novel call admission control (CAC) algorithm and develops a two-dimensional markov chain processes (MCP) analytical model to evaluate its performance for heterogeneous wireless network. Within the context of this paper, a hybrid UMTS-WLAN network is investigated. The designed threshold-based CAC algorithm is launched basing on the user’s classification and channel allocation policy. In this approach, channels are assigned dynamically in accordance with user class differentiation. The two-dimensional MCP mathematical analytic method reflects the system performance by appraising the dropping likelihood of handover traffics. The results show that the new CAC algorithm increases the admission probability of handover traffics, while guarantees the system quality of service (QoS) requirement.

yes / Empirical modeling of wireless fading channels using common schemes such as autoregression and thefinitestate Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal-to-noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that afirst-order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed andproven to be less demanding compared to the conventional FSMC approach based on the levelcrossing rate. Simulations confirm the analytical results and promising performance of the new channel modelbased on the Tauchen approach without extracomplexity costs.

Yes / In a laboratory, a model of a mid-channel bar is built to study the turbulent flow structures in its vicinity. The present study on the turbulent flow structure around a mid-channel bar is based on unravelling the fluvial fluxes triggered by the bar’s 3D turbulent burst phenomenon. To this end, the three-dimensional velocity components are measured with the help of acoustic doppler velocimetry (ADV). The results indicate that the transverse component of turbulent kinetic energy cannot be neglected when analyzing turbulent burst processes, since the dominant flow is three-dimensional around the mid-channel bar. Due to the three-dimensionality of flow, the octant events approach is used for analyzing the flow in the vicinity of the mid-channel bar. The aim is to develop functional relationships between the stable movements that are modelled in the present study. To find the best Markov chain order to present experimental datasets, the zero-, first-, and second-order Markov chains are analyzed using the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). The parameter transition ratio has evolved in this research to reflect the linkage of streambed elevation changes with stable transitional movements. For a better understanding of the temporal behaviors of stable transitional movements, the residence time vs. frequency graphs are also plotted for scouring as well as for depositional regions. The study outcome herein underlines the usefulness of the octant events approach for characterizing turbulent bursts around mid-channel bar formation, which is a precursor to the initiation of braiding configuration. / This research and APC was funded by King Saud University, Riyadh, Saudi Arabia through Researchers Supporting Project number (RSP-2021/297).

Generalized hill climbing (GHC) algorithms provide a unifying framework for describing several discrete optimization problem local search heuristics, including simulated annealing and tabu search. A necessary and a sufficient convergence condition for GHC algorithms are presented. The convergence conditions presented in this dissertation are based upon a new iteration classification scheme for GHC algorithms. The convergence theory for particular formulations of GHC algorithms is presented and the implications discussed. Examples are provided to illustrate the relationship between the new convergence conditions and previously existing convergence conditions in the literature. The contributions of the necessary and the sufficient convergence conditions for GHC algorithms are discussed and future research endeavors are suggested. / Ph. D.

The study of stochastic queueing networks is quite important due to the many applications including transportation, telecommunication, and manufacturing industries. Since there is often no explicit solution to these types of control problems, numerical methods are needed. Following the method of Boué-Dupuis, we use a Dynamic Programming approach of optimization on a controlled Markov Chain that simulates the behavior of a fluid limit of the original process. The search for an optimal control in this case involves a Skorokhod problem to describe the dynamics on the boundary of closed, convex domain. Using relaxed stochastic controls we show that the approximating numerical solution converges to the actual solution as the size of the mesh in the discretized state space goes to zero, and illustrate with an example. / Ph. D.

Hearkening to calls from life scientists for aid in interpreting rapidly-growing repositories of data, the fields of bioinformatics and computational systems biology continue to bear increasingly sophisticated methods capable of summarizing and distilling pertinent phenomena captured by high-throughput experiments. Techniques in analysis of genome-wide gene expression (e.g., microarray) data, for example, have moved beyond simply detecting individual genes perturbed in treatment-control experiments to reporting the collective perturbation of biologically-related collections of genes, or "processes". Recent expression analysis methods have focused on improving comprehensibility of results by reporting concise, non-redundant sets of processes by leveraging statistical modeling techniques such as Bayesian networks. Simultaneously, integrating gene expression measurements with gene interaction networks has led to computation of response networks--subgraphs of interaction networks in which genes exhibit strong collective perturbation or co-expression. Methods that integrate process annotations of genes with interaction networks identify high-level connections between biological processes, themselves. To identify context-specific changes in these inter-process connections, however, techniques beyond process-based expression analysis, which reports only perturbed processes and not their relationships, response networks, composed of interactions between genes rather than processes, and existing techniques in process connection detection, which do not incorporate specific biological context, proved necessary. We present two novel methods which take inspiration from the latest techniques in process-based gene expression analysis, computation of response networks, and computation of inter-process connections. We motivate the need for detecting inter-process connections by identifying a collection of processes exhibiting significant differences in collective expression in two liver tissue culture systems widely used in toxicological and pharmaceutical assays. Next, we identify perturbed connections between these processes via a novel method that integrates gene expression, interaction, and annotation data. Finally, we present another novel method that computes non-redundant sets of perturbed inter-process connections, and apply it to several additional liver-related data sets. These applications demonstrate the ability of our methods to capture and report biologically relevant high-level trends. / Ph. D.

Computational systems biology is an inter-disciplinary field that aims to develop computational approaches for a system-level understanding of biological systems. Advances in high-throughput biotechnology offer broad scope and high resolution in multiple disciplines. However, it is still a major challenge to extract biologically meaningful information from the overwhelming amount of data generated from biological systems. Effective computational approaches are of pressing need to reveal the functional components. Thus, in this dissertation work, we aim to develop computational approaches for differential analysis of RNA-seq and methylation data to detect aberrant events associated with cancers. We develop a novel Bayesian approach, BayesIso, to identify differentially expressed isoforms from RNA-seq data. BayesIso features a joint model of the variability of RNA-seq data and the differential state of isoforms. BayesIso can not only account for the variability of RNA-seq data but also combines the differential states of isoforms as hidden variables for differential analysis. The differential states of isoforms are estimated jointly with other model parameters through a sampling process, providing an improved performance in detecting isoforms of less differentially expressed. We propose to develop a novel probabilistic approach, DM-BLD, in a Bayesian framework to identify differentially methylated genes. The DM-BLD approach features a hierarchical model, built upon Markov random field models, to capture both the local dependency of measured loci and the dependency of methylation change. A Gibbs sampling procedure is designed to estimate the posterior distribution of the methylation change of CpG sites. Then, the differential methylation score of a gene is calculated from the estimated methylation changes of the involved CpG sites and the significance of genes is assessed by permutation-based statistical tests. We have demonstrated the advantage of the proposed Bayesian approaches over conventional methods for differential analysis of RNA-seq data and methylation data. The joint estimation of the posterior distributions of the variables and model parameters using sampling procedure has demonstrated the advantage in detecting isoforms or methylated genes of less differential. The applications to breast cancer data shed light on understanding the molecular mechanisms underlying breast cancer recurrence, aiming to identify new molecular targets for breast cancer treatment. / Ph. D.

Liquid chromatography coupled with mass spectrometry (LC-MS) has been widely used in various omic studies for biomarker discovery. Appropriate LC-MS data preprocessing steps are needed to detect true differences between biological groups. Retention time alignment is one of the most important yet challenging preprocessing steps, in order to ensure that ion intensity measurements among multiple LC-MS runs are comparable. In this dissertation, we propose a Bayesian alignment model (BAM) for analysis of LC-MS data. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and provides estimates of the retention time variability along with uncertainty measures, enabling a natural framework to integrate information of various sources. From methodology development to practical application, we investigate the alignment problem through three research topics: 1) development of single-profile Bayesian alignment model, 2) development of multi-profile Bayesian alignment model, and 3) application to biomarker discovery research. Chapter 2 introduces the profile-based Bayesian alignment using a single chromatogram, e.g., base peak chromatogram from each LC-MS run. The single-profile alignment model improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler using a block Metropolis-Hastings algorithm, and 2) an adaptive mechanism for knot specification using stochastic search variable selection (SSVS). Chapter 3 extends the model to integrate complementary information that better captures the variability in chromatographic separation. We use Gaussian process regression on the internal standards to derive a prior distribution for the mapping functions. In addition, a clustering approach is proposed to identify multiple representative chromatograms for each LC-MS run. With the Gaussian process prior, these chromatograms are simultaneously considered in the profile-based alignment, which greatly improves the model estimation and facilitates the subsequent peak matching process. Chapter 4 demonstrates the applicability of the proposed Bayesian alignment model to biomarker discovery research. We integrate the proposed Bayesian alignment model into a rigorous preprocessing pipeline for LC-MS data analysis. Through the developed analysis pipeline, candidate biomarkers for hepatocellular carcinoma (HCC) are identified and confirmed on a complementary platform. / Ph. D.

Reliable and efficient utilization and operation of any engineering asset require carefully designed maintenance planning and maintenance related data in the form of failure times, repair times, Mean Time between Failure (MTBF) and conditioning data etc. play a pivotal role in maintenance decision support. With the advancement in data analytics sciences and industrial artificial intelligence, maintenance related data is being used for maintenance prognostics modeling to predict future maintenance requirements that form the basis of maintenance design and planning in any maintenance-conscious industry like railways. The lack of such available data creates a no. of different types of problems in data driven prognostics modelling. There have been a few methods, the researchers have employed to counter the problems due to lack of available data. The proposed methodology involves data augmentation technique using Markov Chain Monte Carlo (MCMC) Simulation to enhance maintenance data to be used in maintenance prognostics modeling that can serve as basis for better maintenance decision support and planning.