Statistics and Probability Commons^™

Spatio-Temporal Analysis Of Point Patterns, Abdul-Nasah Soale

Electronic Theses and Dissertations

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

Journal of Humanistic Mathematics

This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, Justus R. Riek

Journal of Humanistic Mathematics

This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems

Apoe Ε4 Allele Modifies The Association Of Lead Exposure With Age-Related Cognitive Decline In Older Individuals, Diddier Prada, Elena Colicino, Melinda C. Power, Marc G Weisskopf, Jia Zhong, Lifang Hou, Avron Spiro, Pantel Vokonas, Plus 4 Others...

Epidemiology Faculty Publications

BACKGROUND: Continuing chronic and sporadic high-level of lead exposure in some regions in the U.S. has directed public attention to the effects of lead on human health. Long-term lead exposure has been associated with faster cognitive decline in older individuals; however, genetic susceptibility to lead-related cognitive decline during aging has been poorly studied.

METHODS: We determined the interaction of APOE-epsilon variants and environmental lead exposure in relation to age-related cognitive decline. We measured tibia bone lead by K-shell-x-ray fluorescence, APOE-epsilon variants by multiplex PCR and global cognitive z-scores in 489 men from the VA-Normative Aging Study. To determine global cognitive …

Update On Schizophrenia And Bipolar Disorder: Focus On Cariprazine, Rona Jeannie Roberts, Lillian Jan Findlay, Peggy El-Mallakh, Rif S. El-Mallakh

Nursing Faculty Publications

Schizophrenia and bipolar disorder are severe psychiatric disorders that are frequently associated with persistent symptoms and significant dysfunction. While there are a multitude of psychopharmacologic agents are available for treatment of these illnesses, suboptimal response and significant adverse consequences limit their utility. Cariprazine is a new, novel antipsychotic medication with dopamine D2 and D3 partial agonist effects. Its safety and efficacy have been investigated in acute psychosis of schizophrenia, bipolar mania, bipolar depression, and unipolar depression. Efficacy has been demonstrated in schizophrenia and mania. It is unclear if cariprazine is effective in depression associated with unipolar or bipolar illness. Adverse …

Retention Of Mothers And Infants In The Prevention Of Mother-To-Child Transmission Of Hiv Programme Is Associated With Individual And Facility-Level Factors In Rwanda., Godfrey B Woelk, Dieudonne Ndatimana, Sally Behan, Martha Mukaminega, Epiphanie Nyirabahizi, Heather J. Hoffman, Placidie Mugwaneza, Muhayimpundu Ribakare, Anouk Amzel, B Ryan Phelps

Epidemiology Faculty Publications

OBJECTIVES: Investigate levels of retention at specified time periods along the prevention of mother-to-child transmission (PMTCT) cascade among mother-infant pairs as well as individual- and facility-level factors associated with retention.

METHODS: A retrospective cohort of HIV-positive pregnant women and their infants attending five health centres from November 2010 to February 2012 in the Option B programme in Rwanda was established. Data were collected from several health registers and patient follow-up files. Additionally, informant interviews were conducted to ascertain health facility characteristics. Generalized estimating equation methods and modelling were utilized to estimate the number of mothers attending each antenatal care visit …

Self-Similar Random Process And Chaotic Behavior In Serrated Flow Of High Entropy Alloys, Shuying Chen, Liping Yu, Jingli Ren, Xie Xie, Xueping Li, Ying Xu, Guangfeng Zhao, Peizhen Li, Fuqian Yang, Yang Ren, Peter K. Liaw

Chemical and Materials Engineering Faculty Publications

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al_0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and …

Variable Selection For Estimating The Optimal Treatment Regimes In The Presence Of A Large Number Of Covariate, Baqun Zhang, Min Zhang

The University of Michigan Department of Biostatistics Working Paper Series

Most of existing methods for optimal treatment regimes, with few exceptions, focus on estimation and are not designed for variable selection with the objective of optimizing treatment decisions. In clinical trials and observational studies, often numerous baseline variables are collected and variable selection is essential for deriving reliable optimal treatment regimes. Although many variable selection methods exist, they mostly focus on selecting variables that are important for prediction (predictive variables) instead of variables that have a qualitative interaction with treatment (prescriptive variables) and hence are important for making treatment decisions. We propose a variable selection method within a general classification …

Theorems On Boundedness Of Solutions To Stochastic Delay Differential Equations, Youssef Raffoul, Dan Ren

Mathematics Faculty Publications

In this report, we provide general theorems about boundedness or bounded in probability of solutions to nonlinear delay stochastic differential systems. Our analysis is based on the successful construction of suitable Lyapunov functionals. We offer several examples as application of our theorems.

Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, Mudassar Imran

Mathematics Faculty Publications

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.

The Influence Of Model Resolution On The Simulated Sensitivity Of North Atlantic Tropical Cyclone Maximum Intensity To Sea Surface Temperature, Sarah Strazzo, James Elsner, Timothy Larow, Hiroyuki Murakami, Michael Wehner, Ming Zhao

Publications

No abstract provided.

Practical Targeted Learning From Large Data Sets By Survey Sampling, Patrice Bertail, Antoine Chambaz, Emilien Joly

U.C. Berkeley Division of Biostatistics Working Paper Series

We address the practical construction of asymptotic confidence intervals for smooth (i.e., pathwise differentiable), real-valued statistical
parameters by targeted learning from independent and identically
distributed data in contexts where sample size is so large that it poses
computational challenges. We observe some summary measure of all data and select a sub-sample from the complete data set by Poisson rejective sampling with unequal inclusion probabilities based on the summary measures. Targeted learning is carried out from the easier to handle sub-sample. We derive a central limit theorem for the targeted minimum loss estimator (TMLE) which enables the construction of …

How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary …

Effects Of Growth Mindset Training On Undergraduate Statistics Students, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Undergraduate introductory statistics courses have experienced numerous changes in the past century, for instance, increased enrollment and diversification of students required to take the courses. Promising research has been conducted on mathematical mindsets, however, no research is available for introductory statistics courses. This presentation addresses the effect of growth mindset training on students in mathematics.

Complex-Valued Time-Series Correlation Increases Sensitivity In Fmri Analysis, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.

Materials and Methods

The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform …

Computational Modeling Of Facial Response For Detecting Differential Traits In Autism Spectrum Disorders, Manar D. Samad

Electrical & Computer Engineering Theses & Dissertations

This dissertation proposes novel computational modeling and computer vision methods for the analysis and discovery of differential traits in subjects with Autism Spectrum Disorders (ASD) using video and three-dimensional (3D) images of face and facial expressions. ASD is a neurodevelopmental disorder that impairs an individual’s nonverbal communication skills. This work studies ASD from the pathophysiology of facial expressions which may manifest atypical responses in the face. State-of-the-art psychophysical studies mostly employ na¨ıve human raters to visually score atypical facial responses of individuals with ASD, which may be subjective, tedious, and error prone. A few quantitative studies use intrusive sensors on …

Analysis Off Dependent Discrete Choices Using Gaussian Copula, Arjun Poddar

Mathematics & Statistics Theses & Dissertations

A popular tool for analyzing product choices of consumers is the well-known conditional logit discrete choice model. Originally publicized by McFadden (1974), this model assumes that the random components of the underlying latent utility functions of the consumers follow independent Gumbel distributions. However, in practice the independence assumption may be violated and a more reasonable model should account for the dependence of the utilities. In this dissertation we use the Gaussian copula with compound symmetric and autoregressive of order one correlation matrices to construct a general multivariate model for the joint distribution of the utilities. The induced correlations on the …

Improved Estimation Of Optimal Cut-Off Point Associated With Youden Index Using Ranked Set Sampling, Jingjing Yin, Hani M. Samawi, Daniel Linder

Biostatistics: Faculty Publications

A diagnostic cut-off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut-off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity −1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut-off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is …

Guidelines For Assessment And Instruction In Statistics Education (Gaise) College Report 2016, Robert Carver, Michelle Everson, John Gabrosek, Nicholas Horton, Robin Lock, Megan Mocko, Allan Rossman, Ginger Holmes Roswell, Paul Velleman, Jeffrey Witmer, Beverly Wood

Publications

In 2005 the American Statistical Association (ASA) endorsed the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report. This report has had a profound impact on the teaching of introductory statistics in two- and four-year institutions, and the six recommendations put forward in the report have stood the test of time. Much has happened within the statistics education community and beyond in the intervening 10 years, making it critical to re-evaluate and update this important report. For readers who are unfamiliar with the original GAISE College Report or who are new to the statistics education community, the full …