Statistics and Probability Commons^™

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Challenges In Developing Applications For Aging Populations, Drew Marie Williams, Md O. Gani, Ivor D. Addo, Akm Jahangir Alam Majumder, Chandana Tamma, Mong-Te Wang, Chih-Hung Chang, Sheikh Iqbal Ahamed, Cheng-Chung Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Elderly individuals can greatly benefit from the use of computer applications, which can assist in monitoring health conditions, staying in contact with friends and family, and even learning new things. However, developing accessible applications for an elderly user can be a daunting task for developers. Since the advent of the personal computer, the benefits and challenges of developing applications for older adults have been a hot topic of discussion. In this chapter, the authors discuss the various challenges developers who wish to create applications for the elderly computer user face, including age-related impairments, generational differences in computer use, and the …

An Online Statistics Course From Faculty And Students' Perspectives: A Case Study, Ruth Best

Walden Dissertations and Doctoral Studies

Faculty at a private college in the northeastern United States found students lacked prerequisite mathematical skills and were unable to transfer quantitative reasoning skills to upper level business courses. Guided by Mezirow's transformative learning theory and Knowles' approach to self-directed learning, this study examined how undergraduate students learn statistics online. The purpose of this qualitative embedded case study was to examine faculty and students' perspectives about the online statistics course design and delivery while exploring possible barriers to students' learning. Data collection occurred by review of course documents and the learning management system. Archival data generated questions for semistructured interviews …

Improved Parameter Estimation Of The Log-Logistic Distribution With Applications, Joseph Reath

Dissertations, Master's Theses and Master's Reports

In this report, we work with parameter estimation of the log-logistic distribution. We first consider one of the most common methods encountered in the literature, the maximum likelihood (ML) method. However, it is widely known that the maximum likelihood estimators (MLEs) are usually biased with a finite sample size. This motivates a study of obtaining unbiased or nearly unbiased estimators for this distribution. Specifically, we consider a certain `corrective' approach and Efron's bootstrap resampling method, which both can reduce the biases of the MLEs to the second order of magnitude. As a comparison, we also consider the generalized moments (GM) …

Bayesian Parameter Estimation For The Birnbaum-Saunders Distribution And Its Extension, Tun Lee Ng

Open Access Theses & Dissertations

We utilize the Bayesian approach to estimate the parameters of the Birnbaum-Saunders (BS) distribution devised by Birnbaum and Saunders (1969a), as well as the Generalized Birnbaum-Saunders (GBS) distribution obtained by Owen (2006), in the presence of random right censored data. We also derive the classical MLE expressions for the observed Information matrix of the GBS distribution, in order to illustrate the fact that no closed form expressions are available for the MLE, and numerical approximations are required to obtain the point estimates and asymptotic confidence intervals. Where Bayesian approach is concerned, new sets of priors are considered based on the …

Unequal Edge Inclusion Probabilities In Link-Tracing Network Sampling With Implications For Respondent-Driven Sampling, Miles Q. Ott, Krista J. Gile

Statistical and Data Sciences: Faculty Publications

Respondent-Driven Sampling (RDS) is a widely adopted linktracing sampling design used to draw valid statistical inference from samples of populations for which there is no available sampling frame. RDS estimators rely upon the assumption that each edge (representing a relationship between two individuals) in the underlying network has an equal probability of being sampled. We show that this assumption is violated in even the simplest cases, and that RDS estimators are sensitive to the violation of this assumption.

A Multistep Approach To Single Nucleotide Polymorphism-Set Analysis: An Evaluation Of Power And Type I Error Of Gene-Based Tests Of Association After Pathway-Based Association Tests, Alessandra Valcarcel, Kelsey Grinde, Kaitlyn Cook, Alden Green, Nathan Tintle

Statistical and Data Sciences: Faculty Publications

The aggregation of functionally associated variants given a priori biological information can aid in the discovery of rare variants associated with complex diseases. Many methods exist that aggregate rare variants into a set and compute a single p value summarizing association between the set of rare variants and a phenotype of interest. These methods are often called gene-based, rare variant tests of association because the variants in the set are often all contained within the same gene. A reasonable extension of these approaches involves aggregating variants across an even larger set of variants (eg, all variants contained in genes within …

A General Method For Combining Different Family-Based Rare-Variant Tests Of Association To Improve Power And Robustness Of A Wide Range Of Genetic Architectures, Alden Green, Kaitlyn Cook, Kelsey Grinde, Alessandra Valcarcel, Nathan Tintle

Statistical and Data Sciences: Faculty Publications

Current rare-variant, gene-based tests of association often suffer from a lack of statistical power to detect genotype-phenotype associations as a result of a lack of prior knowledge of genetic disease models combined with limited observations of extremely rare causal variants in population-based samples. The use of pedigree data, in which rare variants are often more highly concentrated than in population-based data, has been proposed as 1 possible method for enhancing power. Methods for combining multiple gene-based tests of association into a single summary p value are a robust approach to different genetic architectures when little a priori knowledge is available …

Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler

Pomona Senior Theses

This thesis provides an overview of stochastic optimization (SP) problems and looks at how the Sample Average Approximation (SAA) method is used to solve them. We review several applications of this problem-solving technique that have been published in papers over the last few years. The number and variety of the examples should give an indication of the usefulness of this technique. The examples also provide opportunities to discuss important aspects of SPs and the SAA method including model assumptions, optimality gaps, the use of deterministic methods for finite sample sizes, and the accelerated Benders decomposition algorithm. We also give a …

Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset. Similarly For Neutrosophic Over-/Under-/Off- Logic, Probability, And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities.

He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}.

This is no surprise with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has …

Pcr5 And Neutrosophic Probability In Target Identification, Florentin Smarandache, Nassim Abbas, Youcef Chibani, Bilal Hadjadji, Zayen Azzouz Omar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we use PCR5 in order to fusion the information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur.

Comparison Of Option Price From Black-Scholes Model To Actual Values, Matthew J. Krznaric

Williams Honors College, Honors Research Projects

The Black-Scholes model is a widely used method for pricing European-style options in a straightforward way, through the use of calculations and ideal market assumptions. Due to certain unrealistic ideal conditions exercised by the model, The Black-Scholes technique of pricing options may not be entirely accurate in implementation. This paper addresses these problems due to the model limitations, determining how The Black-Scholes method compares to the results when using the actual data. Using a mix of historical S&P500 data and generated normal distributions, we first calculated and graphed option prices through the Black-Scholes formulas. With the help of R, we …

Collective Estimation Of Multiple Bivariate Density Functions With Application To Angular-Sampling-Based Protein Loop Modeling, Mehdi Maadooliat, Lan Zhou, Seyed Morteza Najibi, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed …

Almost Perfect Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We call a restriction semigroup almost perfect if it is proper and the least congruence that identifies all its projections is perfect. We show that any such semigroup is isomorphic to a ‘W -product’ W(T,Y)W(T,Y), where T is a monoid, Y is a semilattice and there is a homomorphism from T into the inverse semigroup TI_YTIY of isomorphisms between ideals of Y. Conversely, all such W-products are almost perfect. Since we also show that every restriction semigroup has an easily computed cover of this type, the combination yields a ‘McAlister-type’ theorem for all restriction semigroups. …

Two Combinatorial Proofs Of Identities Involving Sums Of Powers Of Binomial Coefficients, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang

Mathematics, Statistics and Computer Science Faculty Research and Publications

The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar …

An Ensemble Model Of Qsar Tools For Regulatory Risk Assessment, Prachi Pradeep, Richard J. Povinelli, Shannon White, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting …

Pain Level Detection From Facial Image Captured By Smartphone, Md Kamrul Hasan, Golam Mushih Tanimul Ahsan, Sheikh Iqbal Ahamed, Rechard Love, Reza Salim

Mathematics, Statistics and Computer Science Faculty Research and Publications

Accurate symptom of cancer patient in regular basis is highly concern to the medical service provider for clinical decision making such as adjustment of medication. Since patients have limitations to provide self-reported symptoms, we have investigated how mobile phone application can play the vital role to help the patients in this case. We have used facial images captured by smart phone to detect pain level accurately. In this pain detection process, existing algorithms and infrastructure are used for cancer patients to make cost low and user-friendly. The pain management solution is the first mobile-based study as far as we found …

Solving Set Cover With Pairs Problem Using Quantum Annealing, Yudong Cao, Shuxian Jiang, Debbie Perouli, Sabre Kais

Mathematics, Statistics and Computer Science Faculty Research and Publications

Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph …

A Generalized Gamma-Weibull Distribution: Model, Properties And Applications, R. S. Meshkat, H. Torabi, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prepare a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized gamma-Weibull (GGW) distribution is studied as a special case of this family. Certain mathematical properties of moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distribution of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution, as well as its effectiveness in comparison with other distributions, are shown via an application of a real data set.