Statistics and Probability Commons^™

Unequal A Priori Probability Multiple Hypothesis Testing In Space Domain Awareness With The Space Surveillance Telescope, Tyler J. Hardy, Stephen C. Cain, Travis F. Blake

Faculty Publications

This paper investigates the ability to improve Space Domain Awareness (SDA) by increasing the number of detectable Resident Space Objects (RSOs) from space surveillance sensors. With matched filter based techniques, the expected impulse response, or Point Spread Function (PSF), is compared against the received data. In the situation where the images are spatially undersampled, the modeled PSF may not match the received data if the RSO does not fall in the center of the pixel. This aliasing can be accounted for with a Multiple Hypothesis Test (MHT). Previously, proposed MHTs have implemented a test with an equal a priori prior …

Interpretable High-Dimensional Inference Via Score Maximization With An Application In Neuroimaging, Simon N. Vandekar, Philip T. Reiss, Russell T. Shinohara

UPenn Biostatistics Working Papers

In the fields of neuroimaging and genetics a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Oftentimes summary measures of the high-dimensional variable are created to sequentially test and localize the association with the outcome. In some cases, the results for summary measures are significant, but subsequent tests used to localize differences are underpowered and do not identify regions associated with the outcome. We propose a generalization of Rao's score test based on maximizing the score statistic in a linear subspace of the parameter space. If the test rejects the …

Kings And Heirs: A Characterization Of The (2,2)-Domination Graphs Of Tournaments, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom_2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom_2,2(D). But of even more …

Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper

Senior Honors Projects, 2010-2019

The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …

The Relationship Between Time Of Day, Mood, And Electroencephalography (Eeg) Asymmetry, Morgan Tantillo

Honors Projects

Previous researchers have had success in finding a correlation between exercise and an increase in positive mood. Researchers have also found a correlation between time of day and mood. The current study will explore the relationship between time of day, mood, and electroencephalography (EEG) asymmetry. The study utilized a convenient sample of ten undergraduate students at Bowling Green State University. Participants had baseline EEG recordings taken, and then participated in moderate exercise, followed by another EEG recording. Participants’ mood was assessed through a self-reported mood questionnaire before the condition as well as immediately after. Due to multiple statistical tests, the …

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-Differential Equations Using Lyapunov Functionals, Youssef Raffoul, Habib Rai

Mathematics Faculty Publications

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of nite delay Volterra Integro-dierential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-dierential equation

x′(t) = Px(t) + ^t∫ _−∞ C(t, s)g(x(s))ds.

Application Of Esscher Transformed Laplace Distribution In Microarray Gene Expression Data, Shanmugasundaram Devika, Sebastian George, Lakshmanan Jeyaseelan

Journal of Modern Applied Statistical Methods

Microarrays allow the study of the expression profile of hundreds to thousands of genes simultaneously. These expressions could be from treated samples and the healthy controls. The Esscher transformed Laplace distribution is used to fit microarray expression data as compared to Normal and Laplace distributions. The Maximum Likelihood Estimation procedure is used to estimate the parameters of the distribution. R codes are developed to implement the estimation procedure. A simulation study is carried out to test the performance of the algorithm. AIC and BIC criterion are used to compare the distributions. It is shown that the fit of the Esscher …

The Goldilocks Dilemma: Impacts Of Multicollinearity -- A Comparison Of Simple Linear Regression, Multiple Regression, And Ordered Variable Regression Models, Grayson L. Baird, Stephen L. Bieber

Journal of Modern Applied Statistical Methods

A common consideration concerning the application of multiple linear regression is the lack of independence among predictors (multicollinearity). The main purpose of this article is to introduce an alternative method of regression originally outlined by Woolf (1951), which completely eliminates the relatedness between the predictors in a multiple predictor setting.

Solution To The Multicollinearity Problem By Adding Some Constant To The Diagonal, Hanan Duzan, Nurul Sima Binti Mohamaed Shariff

Journal of Modern Applied Statistical Methods

Ridge regression is an alternative to ordinary least-squares (OLS) regression. It is believed to be superior to least-squares regression in the presence of multicollinearity. The robustness of this method is investigated and comparison is made with the least squares method through simulation studies. Our results show that the system stabilizes in a region of k, where k is a positive quantity less than one and whose values depend on the degree of correlation between the independent variables. The results also illustrate that k is a linear function of the correlation between the independent variables.

Symmetric Variants Of Logistic Smooth Transition Autoregressive Models: Monte Carlo Evidences, Olaoluwa S. Yaya, Olanrewaju I. Shittu

Journal of Modern Applied Statistical Methods

The Smooth Transition Autoregressive (STAR) models are becoming popular in modeling economic and financial time series. The asymmetric type of the model is the Logistic STAR (LSTAR) model, which is limited in its applications as a result of its asymmetric property, which makes it suitable for modelling specific macroeconomic time series. This study was designed to develop the Absolute Error LSTAR (AELSTAR) and Quadratic LSTAR (QLSTAR) models for improving symmetry and performance in terms of model fitness. Modified Teräsvirta’s Procedure (TP) and Escribano and Jordá's Procedure (EJP) were used to test for nonlinearity in the series. The performance of the …

Factorial Invariance Testing Under Different Levels Of Partial Loading Invariance Within A Multiple Group Confirmatory Factor Analysis Model, Brian F. French, Holmes Finch

Journal of Modern Applied Statistical Methods

Scalar invariance in factor models is important for comparing latent means. Little work has focused on invariance testing for other model parameters under various conditions. This simulation study assesses how partial factorial invariance influences invariance testing for model parameters. Type I error inflation and parameter bias were observed.

Jmasm36: Nine Pseudo R^2 Indices For Binary Logistic Regression Models (Spss), David A. Walker, Thomas J. Smith

Journal of Modern Applied Statistical Methods

This syntax program is an applied complement to Veall and Zimmermann (1994), Menard (2000), and Smith and McKenna (2013) and produces nine pseudo R² indices, not readily accessible in statistical software such as SPSS, which are used to describe the results from binary logistic regression analyses.

A Spatial Analytical Framework For Examining Road Traffic Crashes, Grace O. Korter

Journal of Modern Applied Statistical Methods

A number of different modeling techniques have been used to examine road traffic crashes for analytic and predictive purposes. Map-based spatial analysis is introduced. Applications are given which show the power in a combination of existing exploratory and statistical methods.

Jmasm38: Confidence Intervals For Kendall's Tau With Small Samples (Spss), David A. Walker

Journal of Modern Applied Statistical Methods

A syntax program, not readily expedient in statistical software such as SPSS, is provided for an application of confidence interval estimates with Kendall’s tau-b for small samples.

An Evaluation Of Pareto, Lognormal And Pps Distributions: The Size Distribution Of Cities In Kerala, India, Christopher A. Vallabados, Subbarayan A. Arumugam

Journal of Modern Applied Statistical Methods

The Pareto-Positive Stable (PPS) distribution is introduced as a new model for describing city size data of a region in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data and the classical Pareto and Zipf distributions are included as a particular case.

Determination Of Optimal Tightened Normal Tightened Plan Using A Genetic Algorithm, Sampath Sundaram, Deepa S. Parthasarathy

Journal of Modern Applied Statistical Methods

Designing a tightened normal tightened sampling plan requires sample sizes and acceptance number with switching criterion. An evolutionary algorithm, the genetic algorithm, is designed to identify optimal sample sizes and acceptance number of a tightened normal tightened sampling plan for a specified consumer’s risk, producer’s risk, and switching criterion. Optimal sample sizes and acceptance number are obtained by implementing the genetic algorithm. Tables are reported for various choices of switching criterion, consumer’s quality level, and producer’s quality level.

Model-Based Outlier Detection System With Statistical Preprocessing, D. Asir Antony Gnana Singh, E. Jebalamar Leavline

Journal of Modern Applied Statistical Methods

Reliability, lack of error, and security are important improvements to quality of service. Outlier detection is a process of detecting the erroneous parts or abnormal objects in defined populations, and can contribute to secured and error-free services. Outlier detection approaches can be categorized into four types: statistic-based, unsupervised, supervised, and semi-supervised. A model-based outlier detection system with statistical preprocessing is proposed, taking advantage of the statistical approach to preprocess training data and using unsupervised learning to construct the model. The robustness of the proposed system is evaluated using the performance evaluation metrics sum of squared error (SSE) and time to …

Analyzing Different Sampling Designs (Sas), Ying Lu

Journal of Modern Applied Statistical Methods

Various sampling designs are reviewed within the framework of probability sampling. SAS® code to estimate means and proportions, and their standard errors, using different sampling designs are illustrated using example data sets.

Bayesian Estimation Of P[Y < X] Based On Record Values From The Lomax Distribution And Mcmc Technique, Mohamed A. W Mahmoud, Rashad M. El-Sagheer, Ahmed A. Soliman, Ahmed H. Abd Ellah

Journal of Modern Applied Statistical Methods

Our interest is in estimating the stress-strength reliability R = P[Y < X], where X and Y follow the Lomax distribution with common scale parameter. We discuss the problem in the situation where the stress measurements and the strength measurements are both in terms of records. Firstly, we obtain the MLE of R in general case (the common scale parameter is unknown). The MLE of the three unknown parameters can be obtained by solving one non-linear equation. We provide a simple fixed point type algorithm to find the MLE. We propose percentile bootstrap confidence intervals of R. A Bayes …

Graphing Effects As Fuzzy Numbers In Meta-Analysis, Christopher G. Thompson

Journal of Modern Applied Statistical Methods

Prior to quantitative analyses, meta-analysts often explore descriptive characteristics of effect sizes. A graphic is proposed that treats effect sizes as fuzzy numbers. This plot can provide meta-analysts with such information such as heterogeneity of effects, precision of estimates, possible clusters, and existence of outliers.