Physical Sciences and Mathematics Commons^™

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

Modeling Joint Survival Probabilities Of Runs Scored And Balls Faced In Limited Overs Cricket Using Copulas, Lochana K. Palayangoda, Hasika W. Senevirathne, Ananda B. Manage

Mathematics & Statistics Faculty Publications

In limited overs cricket, the goal of a batsman is to score a maximum number of runs within a limited number of balls. Therefore, the number of runs scored and the number of balls faced are the two key statistics used to evaluate the performance of a batsman. In cricket, as the batsmen play as pairs, having longer partnerships is also key to building strong innings. Moreover, having a steady opening partnership is extremely important as a team aims to build such a stronger innings. In this study, we have shown a way to evaluate the performance of opening partnerships …

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

A Class Of Copula-Based Bivariate Poisson Time Series Models With Applications, Mohammed Alqawba, Dimuthu Fernando, Norou Diawara

Mathematics & Statistics Faculty Publications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was …

Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula, Hasika K. W. Senevirathne, Ananda B.W. Manage

Mathematics & Statistics Faculty Publications

The Pythagorean Win-Loss formula can be effectively used to estimate winning percentages for sporting events. This formula was initially developed by baseball statistician Bill James and later was extended by other researchers to sports such as football, basketball, and ice hockey. Although one can calculate actual winning percentages based on the outcomes of played games, that approach does not take into account the margin of victory. The key benefit of the Pythagorean formula is its utilization of actual average runs scored and actual average runs allowed. This article presents the application of the Pythagorean Win-Loss formula to two different types …

Novel Statistical Analysis In The Context Of A Comprehensive Needs Assessment For Secondary Stem Recruitment, Norou Diawara, Sarah Ferguson, Melva Grant, Kumer Das

Mathematics & Statistics Faculty Publications

There is a myriad of career opportunities stemming from science, technology, engineering, and mathematics (STEM) disciplines. In addition to careers in corporate settings, teaching is a viable career option for individuals pursuing degrees in STEM disciplines. With national shortages of secondary STEM teachers, efforts to recruit, train, and retain quality STEM teachers is greatly important. Prior to exploring ways to attract potential STEM teacher candidates to pursue teacher training programs, it is important to understand the perceived value that potential recruits place on STEM careers, disciplines, and the teaching profession. The purpose of this study was to explore students’ perceptions …

Comparative Survival Of Asian And White Metastatic Castration-Resistant Prostate Cancer Men Treated With Docetaxel, Susan Halabi, Sandipan Dutta, Catherine M. Tangen, Mark Rosenthal, Daniel P. Petrylak, Ian M. Thompson Jr., Kim N. Chi, Johann S. De Bono, John C. Araujo, Christopher Logothetis, Mario A. Eisenberger, David I. Quinn, Karim Fizazi, Michael J. Morris, Celestia S. Higano, Ian F. Tannock, Eric J. Small, William Kevin Kelly

Mathematics & Statistics Faculty Publications

There are few data regarding disparities in overall survival (OS) between Asian and white men with metastatic castration-resistant prostate cancer (mCRPC). We compared OS of Asian and white mCRPC men treated in phase III clinical trials with docetaxel and prednisone (DP) or a DP-containing regimen. Individual participant data from 8820 men with mCRPC randomly assigned on nine phase III trials to receive DP or a DP-containing regimen were combined. Men enrolled in these trials had a diagnosis of prostate adenocarcinoma. The median overall survival was 18.8 months (95% confidence interval [CI] = 17.4 to 22.1 months) and 21.2 months (95% …

Nonparametric False Discovery Rate Control For Identifying Simultaneous Signals, Sihai Dave Zhao, Yet Tian Nguyen

Mathematics & Statistics Faculty Publications

It is frequently of interest to identify simultaneous signals, defined as features that exhibit statistical significance across each of several independent experiments. For example, genes that are consistently differentially expressed across experiments in different animal species can reveal evolutionarily conserved biological mechanisms. However, in some problems the test statistics corresponding to these features can have complicated or unknown null distributions. This paper proposes a novel nonparametric false discovery rate control procedure that can identify simultaneous signals even without knowing these null distributions. The method is shown, theoretically and in simulations, to asymptotically control the false discovery rate. It was also …

Acute Systemic Inflammatory Response To Lipopolysaccharide Stimulation In Pigs Divergently Selected For Residual Feed Intake, Haibo Liu, Kristina M. Feye, Yet T. Nguyen, Anoosh Rakhshandeh, Crystal L. Loving, Jack C. M. Sekkers, Nicholas K. Gabler, Christopher K. Tuggle

Mathematics & Statistics Faculty Publications

Background: It is unclear whether improving feed efficiency by selection for low residual feed intake (RFI) compromises pigs’ immunocompetence. Here, we aimed at investigating whether pig lines divergently selected for RFI had different inflammatory responses to lipopolysaccharide (LPS) exposure, regarding to clinical presentations and transcriptomic changes in peripheral blood cells.

Results: LPS injection induced acute systemic inflammation in both the low-RFI and high-RFI line (n = 8 per line). At 4 h post injection (hpi), the low-RFI line had a significantly lower (p= 0.0075) mean rectal temperature compared to the high-RFI line. However, no significant differences in complete blood count …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

Density Estimation Of Spatio-Temporal Point Patterns Using Moran’S Statistics, Jennifer L. Lorio, Norou Diawara, Lance A. Waller

Mathematics & Statistics Faculty Publications

Moran’s Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of …

New Approaches To Model Simulated Spatio-Temporal Moran's Index, Nhan Bu, Jennifer Lorio, Norou Diawara, Kumar Das, Lance Waller

Mathematics & Statistics Faculty Publications

The Moran's index is a statistic that measures spatial autocorrelation; it quantifies the degree of dispersion (or clustering) of objects in space. However, when investigating data over a general area, a single global Moran statistic may not give a sufficient summary of the spread, behavior, features or latent surfaces shared by neighboring areas; rather, by partitioning the area and taking the Moran statistic of each divided subareas, we can discover patterns of the local neighbors not otherwise apparent. In this paper, we present a simulation experiment where the local Moran values are computed and a time variable is added to …

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data …

Supervised Classification Using Finite Mixture Copula, Sumen Sen, Norou Diawara

Mathematics & Statistics Faculty Publications

Use of copula for statistical classification is recent and gaining popularity. For example, statistical classification using copula has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rules assume normality. But in this data age time, this assumption is often questionable. In fact features of data could be a mixture of discrete and continues random variables. In this paper, mixture copula densities are used to model class conditional distributions. Such types of densities are useful when the marginal densities of the vector of features are not normally distributed and are of a mixed …

Impairment Of Continuous Insulin Delivery Therapy And Analysis From Graeco-Latin Square Design Model, Norou Diawara, Ayodeji Demuren, Eric Gyuricsko

Mathematics & Statistics Faculty Publications

The desire to deliver measured amount of insulin continuously to patients with type I diabetes, for glycemic control, has attracted a lot of attention. Continuous subcutaneous insulin infusion has seen some success in recent years. However, occlusion of insulin delivery may prevent the patient from receiving the prescribed dosage, with adverse consequence. An in vitro study of insulin delivery is performed, using different insulin pumps, insulin analogs and operating conditions. The aim is to identify incidences of occlusion due to bubble formation in the infusion line. A detailed statistical analysis was performed on the data collected to determine any significant …

Testing Longitudinal Data By Logarithmic Quantiles, Manfred Denker, Lucia Tabacu

Mathematics & Statistics Faculty Publications

The shoulder tip pain study of Lumley [13] is re-investigated. It is shown that the new logarithmic quantile estimation (LQE) technique in [9] applies and behaves well under singular covariance structure and small sample sizes as in the shoulder tip pain study. The findings in [6] can be assured under weaker assumptions using a combination of LQE and an ANOVA type statistic. © 2014, Institute of Mathematical Statistics.

Mate Choice And The Evolutionary Stability Of A Fixed Threshold In A Sequential Search Strategy, Raymond Cheng, Steven M. Seubert, Daniel D. Wiegmann

Mathematics & Statistics Faculty Publications

The sequential search strategy is a prominent model of searcher behavior, derived as a rule by which females might sample and choose a mate from a distribution of prospective partners. The strategy involves a threshold criterion against which prospective mates are evaluated. The optimal threshold depends on the attributes of prospective mates, which are likely to vary across generations or within the lifetime of searchers due to stochastic environmental events. The extent of this variability and the cost to acquire information on the distribution of the quality of prospective mates determine whether a learned or environmentally canalized threshold is likely …

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.

Next-Peak: A Normal-Exponential Two-Peak Model For Peak-Calling In Chip-Seq Data, Nak-Kyeong Kim, Rasika V. Jayatillake, John L. Spouge

Mathematics & Statistics Faculty Publications

Background: Chromatin immunoprecipitation followed by high-throughput sequencing (ChIP-seq) can locate transcription factor binding sites on genomic scale. Although many models and programs are available to call peaks, none has dominated its competition in comparison studies.

Results: We propose a rigorous statistical model, the normal-exponential two-peak (NEXT-peak) model, which parallels the physical processes generating the empirical data, and which can naturally incorporate mappability information. The model therefore estimates total strength of binding (even if some binding locations do not map uniquely into a reference genome, effectively censoring them); it also assigns an error to an estimated binding location. The comparison study …

Probability Of Identification: A Statistical Model For The Validation Of Qualitative Botanical Identification Methods, Robert A. Labudde, James M. Harnly

Mathematics & Statistics Faculty Publications

A qualitative botanical identification method (BIM) is an analytical procedure that returns a binary result (1 = Identified, 0 = Not Identified). A BIM may be used by a buyer, manufacturer, or regulator to determine whether a botanical material being tested is the same as the target (desired) material, or whether it contains excessive nontarget (undesirable) material. The report describes the development and validation of studies for a BIM based on the proportion of replicates identified, or probability of identification (POI), as the basic observed statistic. The statistical procedures proposed for data analysis follow closely those of the probability of …

Alternatives To Mixture Model Analysis Of Correlated Binomial Data, N. Rao Chaganty, Roy Sabo, Yihao Deng

Mathematics & Statistics Faculty Publications

While univariate instances of binomial data are readily handled with generalized linear models, cases of multivariate or repeated measure binomial data are complicated by the possibility of correlated responses. Likelihood-based estimation can be applied by using mixture distribution models, though this approach can present computational challenges. The logistic transformation can be used to bypass these concerns and allow for alternative estimating procedures. One popular alternative is the generalized estimating equation (GEE) method, though systematic errors can lead to infeasible correlation estimates or nonconvergence problems. Our approach is the coupling of quasileast squares (QLSs) method with a rarely used matrix factorization, …

Weighted Scores Method For Regression Models With Dependent Data, Aristidis K. Nikoloulopoulos, Harry Joe, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a "weighted scores method", which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our …

Probability Models For Blackjack Poker, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in order …

The Joint Distribution Of Bivariate Exponential Under Linearly Related Model, Norou Diawara, Kumer Pial Das

Mathematics & Statistics Faculty Publications

In this paper, fundamental results of the joint distribution of the bivariate exponential distributions are established. The positive support multivariate distribution theory is important in reliability and survival analysis, and we applied it to the case where more than one failure or survival is observed in a given study. Usually, the multivariate distribution is restricted to those with marginal distributions of a specified and familiar lifetime family. The family of exponential distribution contains the absolutely continuous and discrete case models with a nonzero probability on a set of measure zero. Examples are given, and estimators are developed and applied to …

Linear Dependency For The Difference In Exponential Regression, Indika Sathish, Norou Diawara

Mathematics & Statistics Faculty Publications

In the field of reliability, a lot has been written on the analysis of phenomena that are related. Estimation of the difference of two population means have been mostly formulated under the no-correlation assumption. However, in many situations, there is a correlation involved. This paper addresses this issue. A sequential estimation method for linearly related lifetime distributions is presented. Estimations for the scale parameters of the exponential distribution are given under square error loss using a sequential prediction method. Optimal stopping rules are discussed using concepts of mean criteria, and numerical results are presented.

Professor Gopal Kanji's Retirement As Editor Of Journal Of Applied Statistics, M. C. Agrawal, Steven B. Caudill, S. Chakraborti, Norman Draper, Ian Dryden, Joe Gani, Steven G. Gilmour, Z. Govindarajulu, David J. Hand, Dayanand Naik

Mathematics & Statistics Faculty Publications

(First paragraph) This. issue of Journal of Applied Statistics marks the first in its history which does not fall under the editorship of its founder Professor Gopal Kanji. Following his retirement from the role we would like to use this editorial to outline the history and development of the Journal and pay tribute to the many achievements of Gopal’s career.

Symptoms Of Gastro-Oesophageal Reflux Disease And The Severity Of Obstructive Sleep Apnoea Syndrome Are Not Related In Sleep Disorders Center Patients, H.-N. Kim, R. D. Vorona, M. P. Winn, M. Doviak, D. A. Johnson, J. Catesby Ware

Mathematics & Statistics Faculty Publications

Background: Studies suggest obstructive sleep apnea syndrome (OSAS) frequently manifests in patients with gastroesophageal reflux disease (GERD) and that there may be a causal relationship.

Aim: To determine the relationship between OSAS and symptoms of GERD.

Methods: Consecutive patients referred to the Sleep Disorders Center (SDC) 18 years and older with polysomnographically defined OSAS were evaluated prospectively for GERD using a validated symptoms questionnaire. The GERD and OSAS relationship was assessed by 1) determining frequency of GERD in patients with and without OSAS; 2) ascertaining the relationship between OSAS severity categories and presence of GERD; 3) examining GERD score in …

A Comparison Of Esomeprazole And Lansoprazole For Control Of Intragastric Ph In Patients With Symptoms Of Gastro-Oesophageal Reflux Disease, D. A. Johnson, T. Stacy, M. Ryan, T. Wootton, J. Willia, K. Hornbuckle, W. Brooks, M. Doviak

Mathematics & Statistics Faculty Publications

Background: Intragastric acid suppression is the most direct measure of the pharmacodynamic efficacy of proton pump inhibitors, which are the most effective drugs for acid-related diseases.

Aim: To compare the effectiveness of once and twice daily dosing of lansoprazole and esomeprazole in controlling intragastric acidity ( target gastric pH > 4.0) over a 24-hour period.

Methods: In an open-label, two-way crossover study, 45 Helicobacter pylori-negative patients with gastro-oesophageal reflux disease were randomized to receive one of two regimens: 30 mg lansoprazole or esomeprazole 40 mg once daily. Intragastric pH was assessed by 24-hour pH monitoring on day 5 of each regimen. …

Wishartness And Independence Of Matrix Quadratic Forms For Kronecker Product Covariance Structures, Akhil K. Vaish, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Let X be distributed as matrix normal with mean M and covariance matrix W⊗V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran’s theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor. © 2003 Elsevier Inc. All rights reserved.

Strong Large Deviation And Local Limit Theorms, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

Most large deviation results give asymptotic expressions for log P(Y_n ≥ y_n), where the event {Y_n ≥ y_n} is a large deviation event, that is, P(Y_n ≥ y_n) goes to 0 exponentially fast. We refer to such results as weak large deviation results. In this paper we obtain strong large deviation results for arbitrary random variables {Y_n}, that is, we obtain asymptotic expressions for P(Y_n ≥ y_n), where {Y_n ≥ y_n} is a large deviation event. These strong large deviation results …