Statistics and Probability Commons^™

Efficient And Long-Time Accurate Second-Order Methods For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wan

Mathematics and Statistics Faculty Research & Creative Works

We propose and study two second order in time implicit-explicit methods for the coupled Stokes-Darcy system that governs flows in karst aquifers and other subsurface flow systems. the first method is a combination of a second-order backward differentiation formula and the second order Gear's extrapolation approach. the second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of decoupled Stokes and Darcy problems at each time-step. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. …

Using Intelligent Prefetching To Reduce The Energy Consumption Of A Large-Scale Storage System, Brian Romoser, Ziliang Zong, Ribel Fares, Joal Wood, Rong Ge

Mathematics, Statistics and Computer Science Faculty Research and Publications

Many high performance large-scale storage systems will experience significant workload increases as their user base and content availability grow over time. The U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) center hosts one such system that has recently undergone a period of rapid growth as its user population grew nearly 400% in just about three years. When administrators of these massive storage systems face the challenge of meeting the demands of an ever increasing number of requests, the easiest solution is to integrate more advanced hardware to existing systems. However, additional investment in hardware may significantly increase the …

The Log-Beta Generalized Half-Normal Regression Model, Rodrigo R. Pescim, Edwin M. M. Ortega, Gauss M. Cordeiro, Clarice G. B. Demtrio, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010). We formulate and develop a log-linear model using a new distribution so-called the log-beta generalized half normal distribution. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments and moment generating function. We characterize the proposed distribution using a simple relationship between two truncated moments. An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We also show that …

Survival Analysis Of Cardiovascular Diseases, Yuanxin Hu

All Theses and Dissertations (ETDs)

No abstract provided.

Road Systems And Betweenness, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A road system is a collection of subsets of a set—the roads—such that every singleton subset is a road in the system and every doubleton subset is contained in a road. The induced ternary (betweenness) relation is defined by saying that a point c lies between points a and b if c is an element of every road that contains both a and b . Traditionally, betweenness relations have arisen from a plethora of other structures on a given set, reflecting intuitions that range from the order-theoretic to the geometric and topological. In this paper we initiate a study …

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation., Ben C. Nolting

Department of Mathematics: Dissertations, Theses, and Student Research

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying the …

Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F₃ in their kernel to the generalized incomplete hypergeometric functions _pΓ_q[z] and _pɣ_q [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.

Assessing Protein Conformational Sampling Methods Based On Bivariate Lag-Distributions Of Backbone Angles, Mehdi Maadooliat, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model …

Progressive Reliability Method And Its Application To Offshore Mooring Systems, Mir Emad Mousavi, Paolo Gardoni, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two …

Parametric Sensitivity Analysis For Biochemical Reaction Networks Based On Pathwise Information Theory, Yannis Pantazis, Markos Katsoulakis, Dionisios G. Vlachos

Markos Katsoulakis

Background: Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. …

Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen Bansal, Gholamhossein Hamedani, Ru Sheng

Naveen Bansal

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …

Creating Composite Age Groups To Smooth Percentile Rank Distributions Of Small Samples, Francesca Lopez, Amy Olson, Naveen Bansal

Naveen Bansal

Individually administered tests are often normed on small samples, a process that may result in irregularities within and across various age or grade distributions. Test users often smooth distributions guided by Thurstone assumptions (normality and linearity) to result in norms that adhere to assumptions made about how the data should look. Test users, however, may come across particular tests or sets of data in which the Thurstone assumptions are untenable. When users expect deviations from normality within age or grade, an alternate method is desirable. The authors present a relatively simple procedure that allows the user to treat observed raw …

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

An Exploratory Study Of Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, Marta Magiera, Leigh A. Van Den Kieboom, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Using algebraic habits of mind as a framework, and focusing on thinking about functions and how they work, we examined the relationship between 18 pre-service middle school teachers’ ability to use the features of the algebraic thinking (AT) habit of mind “Building Rules to Represent Functions” and their ability to recognize and interpret the features of the same AT habit of mind in middle school students. We assessed the pre-service teachers’ own ability to use the AT habit of mind Building Rules to Represent Functions by examining their solutions to algebra-based tasks in a semester-long mathematics content course. We assessed …

The Semigroups B2 And B0 Are Inherently Nonfinitely Based, As Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The five-element Brandt semigroup B₂ and its four-element subsemigroup B₀, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B₂ carries the natural structure of an inverse semigroup. Regarded as such, in the signature {⋅, ^-1}, it is also finitely based. It is perhaps surprising, then, that in the intermediate signature of restriction semigroups — essentially, "forgetting" the inverse operation x ↦ x^-1 and retaining the induced operations x ↦ x^{+ …}

A Bayesian Model For Cluster Detection, Jonathan Wakefield, Albert Y. Kim

Statistical and Data Sciences: Faculty Publications

The detection of areas in which the risk of a particular disease is significantly elevated, leading to an excess of cases, is an important enterprise in spatial epidemiology. Various frequentist approaches have been suggested for the detection of “clusters” within a hypothesis testing framework. Unfortunately, these suffer from a number of drawbacks including the difficulty in specifying a p-value threshold at which to call significance, the inherent multiplicity problem, and the possibility of multiple clusters. In this paper, we suggest a Bayesian approach to detecting “areas of clustering” in which the study region is partitioned into, possibly multiple, “zones” …

Sub-Independence: An Expository Perspective, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent random variables. The concept of sub-independence, which is much weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness.

Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke

Mathematics, Statistics and Computer Science Faculty Research and Publications

A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.

An Investigation Of Teachers' Intentions And Reflections About Using Standards-Based And Traditional Textbooks In The Classroom, Bikai Nie, Tony Freedman, Stephen Hwang, Ning Wang, John Moyer, Jinfa Cai

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study analyzed teachers’ intentions for and reflections on their use of Standards-based [Connected Mathematics Program (CMP)] textbooks and traditional (non-CMP) mathematics textbooks to guide instruction. In this investigation of the interplay between textbooks and instruction, we focused on learning goals, instructional tasks, teachers’ anticipation of students’ difficulties, and their perceptions of students’ achievement of learning goals. All of these are aspects of teachers’ intentions and reflections that have proved fruitful in comparing the roles of the CMP and non-CMP mathematics textbooks in our Longitudinal Investigation of the Effect of Curriculum on Algebra Learning project. Whereas the cognitive level …

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen K. Bansal, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n) without the assumption of continuity and symmetry for each component X_i:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where all αi≥0 are special weights with ∑i=1nαi=1.

Characterizations Of Distributions Of Ratio Of Certain Independent Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distributions of the ratio of two independent gamma and exponential random variables as well as that of two independent Weibull random variables are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics.

On Generalized Gamma Convolution Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions.

A Study Of Non-Central Skew T Distributions And Their Applications In Data Analysis And Change Point Detection, Abeer Hasan

Abeer Hasan

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph K_δ,n-δ is the n-vertex graph with minimum degree δ that has the largest number of independent sets.

In this paper, we begin the project of generalizing this …

Toward An Mhealth Intervention For Smoking Cessation, Golam Mushih Tanimul Ahsan, Ivor D. Addo, Sheikh Iqbal Ahamed, Daniel Petereit, Shalini Kanekar, Linda Burhansstipanov, Linda U. Krebs

Mathematics, Statistics and Computer Science Faculty Research and Publications

The prevalence of tobacco dependence in the United States (US) remains alarming. Invariably, smoke-related health problems are the leading preventable causes of death in the US. Research has shown that a culturally tailored cessation counseling program can help reduce smoking and other tobacco usage. In this paper, we present a mobile health (mHealth) solution that leverages the Short Message Service (SMS) or text messaging feature of mobile devices to motivate behavior change among tobacco users. Our approach implements the Theory of Planned Behavior (TPB) and a phase-based framework. We make contributions to improving previous mHealth intervention approaches by delivering personalized …

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Iterative Statistical Verification Of Probabilistic Plans, Colin M. Potts

Lawrence University Honors Projects

Artificial intelligence seeks to create intelligent agents. An agent can be anything: an autopilot, a self-driving car, a robot, a person, or even an anti-virus system. While the current state-of-the-art may not achieve intelligence (a rather dubious thing to quantify) it certainly achieves a sense of autonomy. A key aspect of an autonomous system is its ability to maintain and guarantee safety—defined as avoiding some set of undesired outcomes. The piece of software responsible for this is called a planner, which is essentially an automated problem solver. An advantage computer planners have over humans is their ability to consider and …

A Study Of Poisson And Related Processes With Applications, Phillip Mingola

Chancellor’s Honors Program Projects

No abstract provided.

Analyzing And Solving Non-Linear Stochastic Dynamic Models On Non-Periodic Discrete Time Domains, Gang Cheng

Masters Theses & Specialist Projects

Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge variety of sequential decision making problems in stochastic cases. Research on stochastic dynamic programming is important and meaningful because stochastic dynamic programming reflects the behavior of the decision maker without risk aversion; i.e., decision making under uncertainty. In the solution process, it is extremely difficult to represent the existing or future state precisely since uncertainty is a state of having limited knowledge. Indeed, compared to the deterministic case, which is decision making under certainty, the stochastic …