Statistics and Probability Commons^™

Trivial Meet And Join Within The Lattice Of Monotone Triangles, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

The lattice of monotone triangles (�_n, ≼) ordered by entry-wise comparisons is studied. Let τ_min denote the unique minimal element in this lattice, and τ_max the unique maximum. The number of r-tuples of monotone triangles (τ₁...,τ_r) with minimul infimum τ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 as n→ ∞. Thus, with high probability this even implies that one of the τ_i is τ_min (τ_max, resp.). Higher-order error terms are also discussed.

Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma multiforme (GBM) is the most common malignant brain tumor. GBM samples are classified into subtypes based on their transcriptomic and epigenetic profiles. Despite numerous studies to better characterize GBM biology, a comprehensive study to identify GBM subtype-specific master regulators, gene regulatory networks, and pathways is missing. Here, we used FastMEDUSA to compute master regulators and gene regulatory networks for each GBM subtype. We also ran Gene Set Enrichment Analysis and Ingenuity Pathway Analysis on GBM expression dataset from The Cancer Genome Atlas Project to compute GBM- and GBM subtype-specific pathways. Our analysis was able to recover some of the …

Hp-Daemon: HIgh PErformance DIstributed ADaptive ENergy-Efficient MAtrix-MultiplicatiOn, Li Tan, Longxiang Chen, Zizhong Chen, Ziliang Zong, Rong Ge, Dong Li

Mathematics, Statistics and Computer Science Faculty Research and Publications

The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than …

Recurrence Relations For Moments Of Dual Generalized Order Statistics From Weibull Gamma Distribution And Its Characterizations, M. A. W. Mahmoud, Y. Abdel-Aty, N. M. Mohamed, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazard function.

Indemics: An Interactive High-Performance Computing Framework For Data Intensive Epidemic Modeling, Keith R. Bisset, Jiangzhuo Chen, Suruchi Deodhar, Xizhou Feng, Yifei Ma, Madhav V. Marathe

Mathematics, Statistics and Computer Science Faculty Research and Publications

We describe the design and prototype implementation of Indemics (_Interactive; Epi_demic; _Simulation;)—a modeling environment utilizing high-performance computing technologies for supporting complex epidemic simulations. Indemics can support policy analysts and epidemiologists interested in planning and control of pandemics. Indemics goes beyond traditional epidemic simulations by providing a simple and powerful way to represent and analyze policy-based as well as individual-based adaptive interventions. Users can also stop the simulation at any point, assess the state of the simulated system, and add additional interventions. Indemics is available to end-users via a web-based interface.

Detailed performance analysis shows that Indemics greatly enhances the …

Efficient Detection Of Counterfeit Products In Large-Scale Rfid Systems Using Batch Authentication Protocols, Farzana Rahman, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID technology facilitates processing of product information, making it a promising technology for anti-counterfeiting. However, in large-scale RFID applications, such as supply chain, retail industry, pharmaceutical industry, total tag estimation and tag authentication are two major research issues. Though there are per-tag authentication protocols and probabilistic approaches for total tag estimation in RFID systems, the RFID authentication protocols are mainly per-tag-based where the reader authenticates one tag at each time. For a batch of tags, current RFID systems have to identify them and then authenticate each tag sequentially, one at a time. This increases the protocol execution time due to …

Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations …

The Transmuted Marshall-Olkin Fréchet Distribution: Properties And Applications, Ahmed Z. Afify, Gholamhossein Hamedani, Indranil Ghosh, M. E. Mead

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.

Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moment of certain function of the 1st order statistic.

Varieties Of P-Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular …

A New Bivariate Distribution With Applications, Sathya Amarasekara

Open Access Theses & Dissertations

We construct a bivariate distribution of (X, Y ) by assuming that the conditional distribution of Y given X is a two-parameter Gamma (s, ν(x)), where the scale parameter depends on X. If X is assumed to be any distribution, then clearly the joint distribution is well defined in all cases. We will study this new distribution by developing all possible properties, moments, shapes and estimation of parameters with a view towards applications of the distribution to data from many random number generation methods.

A Long- And Short-Run Analysis Of Electricity Demand In Ciudad Juarez, Ericka Cecilia Mendez

Open Access Theses & Dissertations

Economic growth and appliance saturation are increasing electricity consumption in Mexico. Annual frequency data from 1990 to 2012 are utilized to develop an error correction framework that sheds light on short- and long-run electricity consumption behavior in Ciudad Juarez, a large Mexican metropolitan economy at the border with the United States. The results for this study reveal that electricity is an inelastic normal good in this market. Moreover, natural gas is found to be a weak complement to electricity. With regards to the customer base in this urban economy, population, employment, and income exercise positive and statistically significant impacts on …

Variable Selection For Cox Proportional Hazards Models Via Subtle Uprooting, Chalani S. Wijayasinghe

Open Access Theses & Dissertations

Cox proportional hazards model (Cox PH model) is heavily used in survival analysis to assess the importance of various covariates on the survival times of individuals or objects through the hazard function. This study suggests a new variables selection method for Cox PH models, under the title 'Subtle uprooting', that does variable selection and model estimation for Cox proportional hazards (PH) models simultaneously.

There are subset selection methods and shrinkage selection methods suggested in the context of Cox PH model. However the subset selection methods become infeasible in higher dimensions and the available shrinkage methods need tuning of parameters making …

The Impact Of Nested Testing On Experiment-Wise Type I Error Rate, Jack Sawilowsky

Wayne State University Dissertations

When conducting a statistical test the initial risk that must be considered is a Type I error, also known as a false positive. The Type I error rate is set by nominal alpha, assuming all underlying conditions of the statistic are met. Experiment-wise Type I error inflation occurs when multiple tests are conducted overall for a single experiment. There is a growing trend in the social and behavioral sciences utilizing nested designs. A Monte Carlo study was conducted using a two layer design. Five theoretical distributions and four real datasets taken from Micceri (1989) were used, each with five different …

Causality Is Logically Definable-Toward An Equilibrium-Based Computing Paradigm Of Quantum Agents And Quantum Intelligence (Qaqi), Wen-Ran Zhang, Karl E. Peace

Biostatistics: Faculty Publications

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle’s causality principle and its historical extensions by David Hume, Bertrand Russell, Lotfi Zadeh, Donald Rubin, Judea Pearl, Niels Bohr, Albert Einstein, David Bohm, and the causal set initiative are reviewed; bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning; bipolar quantum linear algebra (BQLA) is introduced as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with …

Robust Regression Methods For Massively Decayed Intelligence Data, Akiva Joachim Lorenz

Wayne State University Dissertations

Homeland Security, sponsored by governmental initiatives, has become a vibrant academic research field. However, most efforts were placed with the recognition of threats (e.g. theory) and response options. Less effort was placed in the analysis of the collected data through statistical modeling. In a field that collects more than 20 terabyte of information per minute though diverse overt and covert means and indexes it for future research, understanding how different statistical models behave when it comes to massively decayed data is of vital importance.

Using Monte Carlo methods, three regression techniques (ordinary least squares, least-trimmed, and maximum likelihood) were tested …

La Formazione Degli Insegnanti: Una Necessità Non Più Rinviabile, Anna E. Bargagliotti

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Modular Network Construction Using Eqtl Data: An Analysis Of Computational Costs And Benefits, Yen Yi Ho, Leslie M. Cope, Giovanni Parmigiani

Faculty Publications

Background: In this paper, we consider analytic methods for the integrated analysis of genomic DNA variation and mRNA expression (also named as eQTL data), to discover genetic networks that are associated with a complex trait of interest. Our focus is the systematic evaluation of the trade-off between network size and network search efficiency in the construction of these networks. Results: We developed a modular approach to network construction, building from smaller networks to larger ones, thereby reducing the search space while including more variables in the analysis. The goal is achieving a lower computational cost while maintaining high confidence in …

Native Insect Herbivory Limits Population Growth Rate Of A Non-Native Thistle, James O. Eckberg, Brigitte Tenhumberg, Svata M. Louda

Brigitte Tenhumberg Papers

The influence of native fauna on non-native plant population growth, size, and distribution is not well documented. Previous studies have shown that native insects associated with tall thistle (Cirsium altissimum) also feed on the leaves, stems, and flower heads of the Eurasian congener Cirsium vulgare, thus limiting individual plant performance. In this study, we tested the effects of insect herbivores on the population growth rate of C. vulgare. We experimentally initiated invasions by adding seeds at four unoccupied grassland sites in eastern Nebraska, USA, and recorded plant establishment, survival, and reproduction. Cumulative foliage and floral herbivory …

Fusarium Head Blight Resistance And Agronomic Performance In Soft Red Winter Wheat Populations, Daniela Sarti Dvorjak

Theses and Dissertations--Plant and Soil Sciences

Fusarium head blight (FHB), caused by Fusarium graminearum Schwabe [telomorph: Gibberella zeae Schwein.(Petch)], is recognized as one of the most destructive diseases of wheat (Triticum aestivum L. and T. durum L.) and barley (Hordeum vulgare L.) worldwide. Breeding for FHB resistance must be accompanied by selection for desirable agronomic traits. Donor parents with two FHB resistance quantitative trait loci (QTL) Fhb1 (chromosome 3BS) and QFhs.nau-2DL (chromosome 2DL) were crossed to four adapted SRW wheat lines to generate backcross and forward cross progeny. F₂ individuals were genotyped and assigned to 4 different groups according to presence/ absence of …

Scalable Collaborative Filtering Recommendation Algorithms On Apache Spark, Walker Evan Casey

CMC Senior Theses

Collaborative filtering based recommender systems use information about a user's preferences to make personalized predictions about content, such as topics, people, or products, that they might find relevant. As the volume of accessible information and active users on the Internet continues to grow, it becomes increasingly difficult to compute recommendations quickly and accurately over a large dataset. In this study, we will introduce an algorithmic framework built on top of Apache Spark for parallel computation of the neighborhood-based collaborative filtering problem, which allows the algorithm to scale linearly with a growing number of users. We also investigate several different variants …

An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun

College of Graduate Studies: Theses & Dissertations

Change point is a statistic phenomenon, which has many direct applications in climatology, bioinformatics, finance, oceanography and medical imaging. In this thesis, we investigate the sensitivity of the F-test for detecting change points in linear regression, using a two-phase linear regression model. it offers an effective method to detect "undocumented" change points using a form of an F-test. Using simulated data, we explore its sensitivity and accuracy with respect t different parameters in the model.

The Bivariate Erlang And Its Application In Modeling Recurrence Times Of Kidney Dialysis Data, Norou Diawara, S.H. Sathish Indika, Melva Grant, Edgard M. Maboudou-Tchao

Mathematics & Statistics Faculty Publications

Recent advances in computer modeling allows us to find closer fits to data. Our emphasis is on the interdependence between occurrence at kidney dialysis. The interdependence between kidney dialysis occurrences is modelled by a bivariate exponential that we propose in this article. The application is shown on the McGilchrist and Aisbett kidney data set with the use of the exponential distribution. The proposed bivariate exponential model has exponential marginal densities, correlated via a latent random variables and with finite probability of simultaneous occurrence. Extension of the model to a bivariate Erlang type distribution with same shape parameter is presented.

How Many Are Out There? A Novel Approach For Open And Closed Systems, Zia Rehman

Electronic Theses and Dissertations

We propose a ratio estimator to determine population estimates using capture-recapture sampling. It's different than traditional approaches in the following ways: (1) Ordering of recaptures: Currently data sets do not take into account the "ordering" of the recaptures, although this crucial information is available to them at no cost. (2) Dependence of trials and cluster sampling: Our model explicitly considers trials to be dependent and improves existing literature which assumes independence. (3) Rate of convergence: The percentage sampled has an inverse relationship with population size, for a chosen degree of accuracy. (4) Asymptotic Attainment of Minimum Variance (Open Systems: (=population …

Measuring Circuit Splits: A Cautionary Note, Aaron-Andrew P. Bruhl

Faculty Publications

A number of researchers have recently published new measures of the Supreme Court’s behavior in resolving conflicts in the lower courts. These new measures represent an improvement over prior, cruder approaches, but it turns out that measuring the Court’s resolutions of conflicts is surprisingly difficult. The aim of this methodological comment is to describe those difficulties and to establish several conclusions that follow from them. First, the new measures of the Court’s behavior are certainly imprecise and may reflect biased samples. Second, using the Supreme Court Database, which some studies rely on to assemble a dataset of cases resolving conflicts, …

Methods For Integrative Analysis Of Genomic Data, Paul Manser

Theses and Dissertations

In recent years, the development of new genomic technologies has allowed for the investigation of many regulatory epigenetic marks besides expression levels, on a genome-wide scale. As the price for these technologies continues to decrease, study sizes will not only increase, but several different assays are beginning to be used for the same samples. It is therefore desirable to develop statistical methods to integrate multiple data types that can handle the increased computational burden of incorporating large data sets. Furthermore, it is important to develop sound quality control and normalization methods as technical errors can compound when integrating multiple genomic …

Applications Of Bayesian Nonparametrics To Reliability And Survival Data, Li Li

Theses and Dissertations

Reliability and survival data are widely encountered across many common settings. Subjects under investigation often include machines, bioassays, patients, etc.; their reliability or survival distribution, and its association with covariate processes, are commonly of interest. Within this dissertation, the first two chapters focus on reliability data where repairable systems fail and get interventions, e.g. repairs in the event process. It begins with a nonparametric test for the commonly assumed ''good as old'' assumption for minimal repair models and then a semi-parametric regression model is introduced for reliability data using Kijima's effective age. The third chapter focuses on survival data observed …

Methods For Clustering Mixed Data, Jeanmarie L. Hendrickson

Theses and Dissertations

We give a brief introduction to cluster analysis and then propose and discuss a few methods for clustering mixed data. In particular, a model-based clustering method for mixed data based on Everitt's (1988) work is described, and we use a simulated annealing method to estimate the parameters for Everitt's model. A penalized log likelihood with the simulated annealing method is proposed as a remedy for the parameter estimates being drawn to extremes. Everitt's approach and the proposed method are compared based on their performance in clustering simulated data. We then use the penalized log likelihood method on a heart disease …

Bayesian Analysis Of Continuous Curve Functions, Wen Cheng

Theses and Dissertations

We consider Bayesian analysis of continuous curve functions in 1D, 2D and 3D spaces. A fundamental feature of the analysis is that it is invariant under a simultaneous warping/re-parameterization of all target curves, as well as translation, rotation and scale of each individual if necessary. We introduce Bayesian models based on a special curve representation named Square Root Velocity Function (SRVF) introduced by Srivastava et al. (2011, IEEE PAMI). A Gaussian process model for the SRVFs of curves is proposed, and suitable prior models such as the Dirichlet distribution are employed for modeling the warping function as a cumulative distribution …

A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop

Senior Independent Study Theses

Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …