Statistics and Probability Commons^™

On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to a finite dimensional one via center manifold reduction, we derive a non-dimensional transition number that determines the types of dynamical transition. We show by careful numerical evaluation of the transition number that both continuous transitions (supercritical Hopf bifurcation) and catastrophic transitions (subcritical Hopf bifurcation) can happen at the critical Reynolds number, depending on the aspect ratio and stratification. The regions separating the continuous and catastrophic transitions are delineated on the parameter plane.

Mittag–Leffler Stability Of Systems Of Fractional Nabla Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

Ranking And Clustering Of Drosophila Olfactory Receptors Using Mathematical Morphology, Jayanta Kumar Das, Pabitra Pal Choudhury, Neelambuj Chaturvedi, Mohd Tayyab, Sk Sarif Hassan

Journal Articles

This article introduces an alignment-free clustering method in order to cluster all the 66 DORs sequentially diverse protein sequences. Two different methods are discussed: one is utilizing twenty standard amino acids (without grouping) and another one is using chemical grouping of amino acids (with grouping). Two grayscale images (representing two protein sequences by order pair frequency matrices) are compared to find the similarity index using morphology technique. We could achieve the correlation coefficients of 0.9734 and 0.9403 for without and with grouping methods respectively with the ClustalW result in the ND5 dataset, which are much better than some of the …

The Odd Nadarajah-Haghighi Family Of Distributions: Properties And Applications, Abraão D.C. Nascimento, Kássio F. Silva, Gauss M. Cordeiro, Morad Alizadeh, Haitham M. Yousof, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of …

On Continuous Images Of Ultra-Arcs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.

Statin Prescription For Patients With Atherosclerotic Cardiovascular Disease From National Survey Data, Kristina Vatcheva, Vicente Aparicio, Ayesha Araya, Eduardo Gonzalez, Susan T. Laing

School of Mathematical & Statistical Sciences Faculty Publications

Despite strong evidence for the use of statins for patients with atherosclerotic cardiovascular disease (ASCVD), statin prescription is still suboptimal. We aimed to determine the rates and factors that influence statin prescription using national survey data. This is a cross-sectional retrospective study on 8,468 patients with clinical ASCVD who were drawn from the National Ambulatory Medical Care Survey and the National Hospital Ambulatory Medical Care Survey from years 2011 to 2015. Survey-weighted analysis was conducted to estimate weighted prevalence and odds ratios for statin prescription. There was a significant increase in statin prescription from the years 2011 to 2015. Nevertheless, …

A First Look At Sublimation Rates In Toss Island Region, Antarctica, Rebecca Baiman, Scott Landolt

STAR Program Research Presentations

70% of Earth’s fresh water is held in Antarctica ice sheet. If the sheet melts, it has the potential to raise global sea levels by 190 feet (Klekociuk and Wiennecke, 2016). As the climate changes, it is imperative that to understand precipitation systems of Antarctica in order to measure and predict weather around the world. One aspect of precipitation events that we do not understand fully in Antarctica is sublimation. Data was collected from four Ott Pluvio Precipitation Gauges with Belfort Double Alter Shields placed in and around the Ross Ice Shelf from November of 2017 to present. An R …

A Descriptive Study Of Variable Discretization And Cost-Sensitive Logistic Regression On Imbalanced Credit Data, Lili Zhang, Jennifer Priestley, Herman Ray, Soon Tan

Published and Grey Literature from PhD Candidates

Training classification models on imbalanced data tends to result in bias towards the majority class. In this paper, we demonstrate how variable discretization and cost-sensitive logistic regression help mitigate this bias on an imbalanced credit scoring dataset, and further show the application of the variable discretization technique on the data from other domains, demonstrating its potential as a generic technique for classifying imbalanced data beyond credit scoring. The performance measurements include ROC curves, Area under ROC Curve (AUC), Type I Error, Type II Error, accuracy, and F1 score. The results show that proper variable discretization and cost-sensitive logistic regression with …

Statistical Analysis Of Interval-Censored Data Subject To Additional Complications, Qiang Zheng

Theses and Dissertations

Survival analysis is an important branch of statistics that studies time to event data (or survival data), in which the response variable is time to a certain event of interest. The most prominent feature of survival data is that the response is not exactly observed due to limits of the study design or nature of the event of interest. Interval-censored data are a common type of survival data and occur frequently in real life studies where subjects are examined at periodical follow ups. The response time is usually not observed, but the status of the event of interest is known …

Extension Of Risk-Based Measure Of Time-Varying Prognostic Discrimination For Survival Models, Shujie Chen

Theses and Dissertations

The Cox proportional hazards (PH) model and time dependent PH model are the most popular survival models in survival analysis. The hazard discrimination summary HDS(t) proposed by Liang and Heagerty [2017] is used to evaluate the mean hazard difference between cases and controls at time t. Liang and Heagerty [2017] evaluated the discrimination performance under the PH model and time dependent PH model with right censoring.

In this thesis, first, we further investigate their method via comprehensive simulations including 1) We extend the simulation in Liang and Heagerty [2017] under the PH model by adding more scenarios such as different …

Estimation Problems For Pooled Data, Xichen Mou

Theses and Dissertations

In epidemiological applications, individual specimens (e.g., blood, urine, etc.) are often pooled together to detect the presence of disease or to measure the concentration level of a specific biomarker. Due to the advantage of cost efficiency, pooled data are also seen in diverse areas such as genetics, animal ecology, and environmental science. With pooled data, individual observations are masked and new statistical methods are needed to estimate characteristics such as disease prevalence, the underlying density function of a biomarker, etc. We focus on three estimation problems for pooled data. Chapters 2 and 3 propose nonparametric estimators for the density function …

Investigations On Multiple Interval Estimators, Taeho Kim

Theses and Dissertations

Multiple interval estimation for a set of parameters is investigated. To begin, a strategy of optimization for a multiple interval estimator (MIE) is introduced. This approach allocates distinct optimized levels to individual interval estimators so that the global expected content can be minimized while the global coverage probability is still maintained at a global level. This optimal allocation is achieved by a decision theoretic procedure which consists of two global risk functions. The major part of this manuscript is devoted to two multiple interval estimation procedures. Both procedures adopt prior information added to the classical setting, but these procedures do …

Multivariate Probit Models For Interval-Censored Failure Time Data, Yifan Zhang

Theses and Dissertations

Survival analysis is an important branch of statistics that analyzes the time to event data. The events of interest can be death, disease occurrence, the failure of a machine part, etc.. One important feature of this type of data is censoring: information on time to event is not observed exactly due to loss to follow-up or non-occurrence of interested event before the trial ends. Censored data are commonly observed in clinical trials and epidemiological studies, since monitoring a person’s health over time after treatment is often required in medical or health studies. In this dissertation we focus on studying multivariate …

Copula-Based Zero-Inflated Count Time Series Models, Mohammed Sulaiman Alqawba

Mathematics & Statistics Theses & Dissertations

Count time series data are observed in several applied disciplines such as in environmental science, biostatistics, economics, public health, and finance. In some cases, a specific count, say zero, may occur more often than usual. Additionally, serial dependence might be found among these counts if they are recorded over time. Overlooking the frequent occurrence of zeros and the serial dependence could lead to false inference. In this dissertation, we propose two classes of copula-based time series models for zero-inflated counts with the presence of covariates. Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals of the …

Interpreting Patient Reported Outcomes In Orthopaedic Surgery: A Systematic Review, Shgufta Docter, Zina Fathalla, Michael Lukacs, Michaela Khan, Morgan Jennings, Shu-Hsuan Liu, Dong Zi, Dianne Bryant

Western Research Forum

Background: Reporting methods of patient reported outcome measures (PROMs) vary in orthopaedic surgery literature. While most studies report statistical significance, the interpretation of results would be improved if authors reported confidence intervals (CIs), the minimally clinically important difference (MCID), and number needed to treat (NNT).

Objective: To assess the quality and interpretability of reporting the results of PROMs. To evaluate reporting, we will assess the proportion of studies that reported (1) 95% CIs, (2) MCID, and (3) NNT. To evaluate interpretation, we will assess the proportion of studies that discussed results using the MCID or the effect sizes and how …

Generalized Interventional Approach For Causal Mediation Analysis With Causally Ordered Multiple Mediators, Sheng-Hsuan Lin

Harvard University Biostatistics Working Paper Series

Causal mediation analysis has demonstrated the advantage of mechanism investigation. In conditions with causally ordered mediators, path-specific effects (PSEs) are introduced for specifying the effect subject to a certain combination of mediators. However, most PSEs are unidentifiable. To address this, an alternative approach termed interventional analogue of PSE (iPSE), is widely applied to effect decomposition. Previous studies that have considered multiple mediators have mainly focused on two-mediator cases due to the complexity of the mediation formula. This study proposes a generalized interventional approach for the settings, with the arbitrary number of ordered multiple mediators to study the causal parameter identification …

Where On Ice? Algorithmically Deconstructing Nhl Shot Locations As A Method For Player Classification, Devan Becker, Douglas G. Woolford, Charmaine B. Dean

Western Research Forum

Where do hockey players shoot from? How does this vary from player to player? We present the results of a study that uses data-driven statistical methods to investigate these questions. The locations of shots by National Hockey League (NHL) players from 2011 to 2017 are analyzed using a combination of an image recognition algorithm and spatial statistical methodology. An unsupervised classifier is applied to output from a spatial point process model in order to determine which shot locations best characterize a given player. We define the number of regions a priori, but the image recognition algorithm chooses the shape …

Incidence And Cost Of Acute Kidney Injury In Hospitalized Patients With Infective Endocarditis, Victor M. Ortiz-Soriano, Katherine Donaldson, Gaixin Du, Ye Li, Joshua Lambert, Dan Cleland, Alice C. Thornton, Laura C. Fanucchi, Moises A. Huaman, Javier A. Neyra

Internal Medicine Faculty Publications

Acute kidney injury (AKI) is a frequent complication of hospitalized patients with infective endocarditis (IE). Further, AKI in the setting of IE is associated with high morbidity and mortality. We aimed to examine the incidence, clinical parameters, and hospital costs associated with AKI in hospitalized patients with IE in an endemic area with an increasing prevalence of opioid use. This retrospective cohort study included 269 patients admitted to a major referral center in Kentucky with a primary diagnosis of IE from January 2013 to December 2015. Of these, 178 (66.2%) patients had AKI by Kidney Disease Improving Global Outcomes (KDIGO) …

Automated Monitoring Of Behaviour In Zebrafish After Invasive Procedures, Anthony G. Deakin, Jonathan Buckley, Hamzah S. Alzu'bi, Andrew R. Cossins, Joseph W. Spencer, Waleed Al'nuaimy, Iain S. Young, Jack S. Thomson, Lynne U. Sneddon

Validation of Animal Experimentation Collection

Fish are used in a variety of experimental contexts often in high numbers. To maintain their welfare and ensure valid results during invasive procedures it is vital that we can detect subtle changes in behaviour that may allow us to intervene to provide pain-relief. Therefore, an automated method, the Fish Behaviour Index (FBI), was devised and used for testing the impact of laboratory procedures and efficacy of analgesic drugs in the model species, the zebrafish. Cameras with tracking software were used to visually track and quantify female zebrafish behaviour in real time after a number of laboratory procedures including fin …

Dietary Inflammatory Index, Dietary Non-Enzymatic Antioxidant Capacity, And Colorectal And Breast Cancer Risk(Mcc-Spain Study), Mireia Obón-Santacana, Dora Romaguera, Esther Gracia-Lavedan, Amaia Molinuevo, Esther Molina-Montes, Nitin Shivappa, James R. Hébert, Adonia Tardón, Gemma Castaño-Vinyals, Ferran Moratalla, Elisabet Guinó, Rafael Marcos-Gragera, Mikel Azpiri Leire Gil, Rocío Olmedo-Requena, Macarena Lozano-Lorca, Juan Alguacil, Tania Fernández-Villa, Vicente Martín, Antonio J. Molina, María Ederra, Beatriz Perez, Nuria Aragonés, Adela Castello, José Mª Huerta, Trinidad Dierssen-Sotos, Ana Molina-Barceló, Marina Pollán, Manolis Kogevinas, Victor Moreno, Pilar Amiano

Faculty Publications

Inflammation and antioxidant capacity have been associated with colorectal and breast cancer. We computed the dietary inflammatory index (DII®), and the total dietary non-enzymatic antioxidant capacity (NEAC) and associated them with colorectal and breast cancer risk in the population-based multi case-control study in Spain (MCC-Spain). We included 1852 colorectal cancer and 1567 breast cancer cases, and 3447 and 1486 population controls, respectively. DII score and NEAC were derived using data from a semi-quantitative validated food frequency questionnaire. Unconditional logistic regression models were used to estimate odds ratios (OR) and 95% confidence intervals (95%CI) for energy-adjusted DII (E-DII), and a score …

Dietary Inflammatory Index, Dietary Non-Enzymatic Antioxidant Capacity, And Colorectal And Breast Cancer Risk (Mcc-Spain Study), Mireia Obon-Santacana, Dora Romaguera, Esther Gracia-Lavedan, Amaia Molinuevo, Esther Molina-Montes, Nitin Shivappa, James R. Hébert, Adonina Tardon, Gemma Castano-Vinyals, Ferran Moratalla, Elisabet Guino, Rafael Marcos-Gragera, Mikel Azpiri, Leire Gil, Rocio Olmedo-Requena, Macarena Lozano-Lorca, Juan Alguacil, Tania Fernandez-Villa, Vicente Martin, Antonio J. Molina, Maria Ederra, Conchi Moreno-Iribas, Beatriz Perez, Nuria Aragones

Faculty Publications

Inflammation and antioxidant capacity have been associated with colorectal and breast cancer. We computed the dietary inflammatory index (DII^®), and the total dietary non-enzymatic antioxidant capacity (NEAC) and associated them with colorectal and breast cancer risk in the population-based multi case-control study in Spain (MCC-Spain). We included 1852 colorectal cancer and 1567 breast cancer cases, and 3447 and 1486 population controls, respectively. DII score and NEAC were derived using data from a semi-quantitative validated food frequency questionnaire. Unconditional logistic regression models were used to estimate odds ratios (OR) and 95% confidence intervals (95%CI) for energy-adjusted DII (E-DII), and …

Modelling Weighted Signed Networks, Alberto Caimo, Isabella Gollini

Conference papers

In this paper we introduce a new modelling approach to analyse weighted signed networks by assuming that their generative process consists of two models: the interaction model which describes the overall connectivity structure of the relations in the network without taking into account neither the weight nor the sign of the dyadic relations; and the conditional weighted signed network model describes how the edge signed weights form given the interaction structure. We then show how this modelling approach can facilitate the interpretation of the overall network process. Finally, we adopt a Bayesian inferential approach to illustrate the new methodology by …

Cancerous Male And Female Gene Expression, Clarissa Farmer, E. Shannon Tass

Journal of Undergraduate Research

Genetic diagnosing is becoming more popular, as well as more and more accurate. However, many genetic diseases have complex genetic effects and are still not fully understood. Transthyretin Amyloidosis (ATTR; also known as familial or hereditary amyloidosis) is a terminal genetic disease. It is caused by unstable transthyretin proteins that fold improperly, and then deteriorate. The fragmented proteins are deposited outside of the cell and build up in the tissues over time, forming insoluble oligomers. The oligomers continue to grow into Amyloid fibrils, which adversely affect many organs in the body, eventually causing their failure. In order to accurately diagnose, …

Cluster Analysis Via Random Partition Distributions, Brandon Carter, Dr. David B. Dahl

Journal of Undergraduate Research

Cluster analysis is an important exploratory data analysis technique used in a wide variety of fields. Cluster analysis seeks to discover a natural grouping of the data, where items in the same cluster or group are more similar than items from different clusters. Through our research, we developed a novel method for cluster analysis which takes pairwise distance information as input. Our new method improves upon traditional cluster analysis methods which also take pairwise distance information as input, such as hierarchical clustering. Our method, cluster analysis via random partition distributions (CaviarPD) is based on probability distributions and therefore allows the …

Data Mining And Machine Learning To Improve Northern Florida’S Foster Care System, Daniel Oldham, Nathan Foster, Mihhail Berezovski

Beyond: Undergraduate Research Journal

The purpose of this research project is to use statistical analysis, data mining, and machine learning techniques to determine identifiable factors in child welfare service records that could lead to a child entering the foster care system multiple times. This would allow us the capability of accurately predicting a case’s outcome based on these factors. We were provided with eight years of data in the form of multiple spreadsheets from Partnership for Strong Families (PSF), a child welfare services organization based in Gainesville, Florida, who is contracted by the Florida Department for Children and Families (DCF). This data contained a …

Probabilistic Modeling Of Personalized Drug Combinations From Integrated Chemical Screen And Molecular Data In Sarcoma, Noah E. Berlow, Rishi Rikhi, Mathew Geltzeiler, Jinu Abraham, Matthew N. Svalina, Lara E. Davis, Erin Wise, Maria Mancini, Jonathan Noujaim, Atiya Mansoor, Michael J. Quist, Kevin L. Matlock, Martin W. Goros, Brian S. Hernandez, Yee C. Doung, Khin Thway, Tomohide Tsukahara, Jun Nishio, Elaine T. Huang, Susan Airhart, Carol J. Bult, Regina Gandour-Edwards, Robert G. Maki, Robin L. Jones, Joel E. Michalek, Milan Milovancev, Souparno Ghosh, Ranadip Pal, Charles Keller

Department of Statistics: Faculty Publications

Background: Cancer patients with advanced disease routinely exhaust available clinical regimens and lack actionable genomic medicine results, leaving a large patient population without effective treatments options when their disease inevitably progresses. To address the unmet clinical need for evidence-based therapy assignment when standard clinical approaches have failed, we have developed a probabilistic computational modeling approach which integrates molecular sequencing data with functional assay data to develop patient-specific combination cancer treatments. Methods: Tissue taken from a murine model of alveolar rhabdomyosarcoma was used to perform single agent drug screening and DNA/RNA sequencing experiments; results integrated via our computational modeling approach identified …

Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm, Jonathan S. Turner

Theses and Dissertations

This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density" presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time" presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm" expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well …

Dietary Inflammatory Index And Sleep Quality In Southern Italian Adults, Justyna Godos, Raffaele Ferri, Filippo Caraci, Filomena I. I. Cosentino, Sabrina Castellano, Nitin Shivappa, James R. Hébert, Fabio Galvano, Giuseppe Grosso

Faculty Publications

Background: Current evidence supports the central role of a subclinical, low-grade inflammation in a number of chronic illnesses and mental disorders; however, studies on sleep quality are scarce. The aim of this study was to test the association between the inflammatory potential of the diet and sleep quality in a cohort of Italian adults. Methods: A cross-sectional analysis of baseline data of the Mediterranean healthy Eating, Aging, and Lifestyle (MEAL) study was conducted on 1936 individuals recruited in the urban area of Catania during 2014-2015 through random sampling. A food frequency questionnaire and other validated instruments were used to calculate …

Measure Of Departure From Marginal Average Point-Symmetry For Two-Way Contingency Tables, Kiyotaka Iki, Sadao Tomizawa

Journal of Modern Applied Statistical Methods

For the analysis of two-way contingency tables with ordered categories, Yamamoto, Tahata, Suzuki, and Tomizawa (2011) considered a measure to represent the degree of departure from marginal point-symmetry. The maximum value of the measure cannot distinguish two kinds of marginal complete asymmetry with respect to the midpoint. A measure is proposed which can distinguish two kinds of marginal asymmetry with respect to the midpoint. It also gives large-sample confidence interval for the proposed measure.

The Impact Of Equating On Detection Of Treatment Effects, Youn-Jeng Choi, Seohyun Kim, Allan S. Cohen, Zhenqiu Lu

Journal of Modern Applied Statistical Methods

Equating makes it possible to compare performances on different forms of a test. Three different equating methods (baseline selection, subgroup, and subscore equating) using common-item item response theory equating were examined for their impact on detection of treatment effects in multilevel models.