Statistics and Probability Commons^™

Applications Of Ornstein-Uhlenbeck Type Stochastic Differential Equations, Osei Kofi Tweneboah

Open Access Theses & Dissertations

In this Dissertation, we show with plausible arguments that the Stochastic Differential Equations (SDEs) arising on the superposition and coupling system of independent Ornstein-Uhlenbeck process is a new method available in modern literature that takes the properties and behavior of the data into consideration when performing the statistical analysis of the time series.

The time series to be analyzed is thought of as a source of fluctuations, and thus we need a model that takes this behavior into consideration when performing such analysis. Most of the standard methods fail to take into account the physical behavior of the time series, …

Spatially Adaptive Estimation Of Spectrum, Yi None Xie

Open Access Theses & Dissertations

When analyzing a stationary time series, one of the questions we are often interested in is how to estimate its spectrum. Many approaches have been proposed to this end. Most are focused on smoothing the periodogram using a single smoothing parameter across all Fourier frequencies. In this paper, we smooth the log periodogram by placing a spatially adaptive prior called the dynamic shrinkage prior, so that varying degrees of smoothing may be applied to different intervals of Fourier frequencies, resulting in less biased estimates of the spectrum. Further research will extend this approach to spectral estimation for nonstationary time series.

Psychometric Analysis Of Forensic Examiner Behavior, Amanda Luby, A. Mazumder, B. Junker

Mathematics & Statistics Faculty Works

Forensic science often involves the comparison of crime-scene evidence to a known-source sample to determine if the evidence and the reference sample came from the same source. Even as forensic analysis tools become increasingly objective and automated, final source identifications are often left to individual examiners’ interpretation of the evidence. Each source identification relies on judgements about the features and quality of the crime-scene evidence that may vary from one examiner to the next. The current approach to characterizing uncertainty in examiners’ decision-making has largely centered around the calculation of error rates aggregated across examiners and identification tasks, without taking …

Association Between Baseline Abundance Of Peptoniphilus, A Gram-Positive Anaerobic Coccus, And Wound Healing Outcomes Of Dfus, Kyung R. Min, Adriana Galvis, Katherine L. Baquerizo Nole, Rohita Sinha, Jennifer Clarke, Robert S. Kirsner, Dragana Ajdic

Department of Statistics: Faculty Publications

Diabetic foot ulcers (DFUs) lead to nearly 100,000 lower limb amputations annually in the United States. DFUs are colonized by complex microbial communities, and infection is one of the most common reasons for diabetes-related hospitalizations and amputations. In this study, we examined how DFU microbiomes respond to initial sharp debridement and off- loading and how the initial composition associates with 4 week healing outcomes. We employed 16S rRNA next generation sequencing to perform microbial profiling on 50 sam- ples collected from 10 patients with vascularized neuropathic DFUs. Debrided wound sam- ples were obtained at initial visit and after one week …

Representation Of Features As Images With Neighborhood Dependencies For Compatibility With Convolutional Neural Networks, Omid Bazgir, Ruibo Zhang, Saugato Rahman Dhruba, Raziur Rahman, Souparno Ghosh, Ranadip Pal

Department of Statistics: Faculty Publications

Deep learning with Convolutional Neural Networks has shown great promise in image-based classification and enhancement but is often unsuitable for predictive modeling using features without spatial correlations. We present a feature representation approach termed REFINED (REpresentation of Features as Images with NEighborhood Dependencies) to arrange high-dimensional vectors in a compact image form conducible for CNN-based deep learning. We consider the similarities between features to generate a concise feature map in the form of a two-dimensional image by minimizing the pairwise distance values following a Bayesian Metric Multidimensional Scaling Approach. We hypothesize that this approach enables embedded feature extraction and, integrated …

Perceived Neighborhood: Preferences Versus Actualities, Saeed Moradi, Ali Nejat, Da Hu, Souparno Ghosh

Department of Statistics: Faculty Publications

Housing recovery plays a key role in the overall restoration of a community. A multitude of factors affect housing recovery, many of which are associated with interactions of residents with their perceived neighborhoods. Targeting perceived neighborhoods rather than administratively defined measures of land helps with devising recovery plans that could better address social preferences of the residents. However, such measures are commonly subject to collection of information via expensive and time-consuming surveys. The current research aims to contribute to the domain by exploring the relationship between perception of households of their neighborhood anchors (perceived anchors) and the anchors that exist …

In Praise Of Partially Interpretable Predictors, Tri Le, Bertrand S. Clarke

Department of Statistics: Faculty Publications

Often there is an uninterpretable model that is statistically as good as, if not better than, a successful interpretable model. Accordingly, if one restricts attention to interpretable models, then one may sacrifice predictive power or other desirable properties. A minimal condition for an interpretable, usually parametric, model to be better than another model is that the first should have smallermean-squared error or integratedmean-squared error.We show through a series of examples that this is often not the case and give the asymptotic forms of a variety of interpretable, partially interpretable, and noninterpretable methods. We find techniques that combine aspects of both …

Tumor Ablation Due To Inhomogeneous Anisotropic Diffusion In Generic Three-Dimensional Topologies, Erdi Kara, Aminur Rahman, Eugenio Aulisa, Souparno Ghosh

Department of Statistics: Faculty Publications

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal …

Statistical Downscaling With Spatial Misalignment: Application To Wildland Fire Pm2.5 Concentration Forecasting, Suman Majumder, Yawen Guan, Brian J. Reich, Susan O’Neill, Ana G. Rappold

Department of Statistics: Faculty Publications

Fine particulate matter, PM_2.5, has been documented to have adverse health effects, and wildland fires are a major contributor to PM_2.5 air pollution in the USA. Forecasters use numerical models to predict PM_2.5 concentrations to warn the public of impending health risk. Statistical methods are needed to calibrate the numerical model forecast using monitor data to reduce bias and quantify uncertainty. Typical model calibration techniques do not allow for errors due to misalignment of geographic locations. We propose a spatiotemporal downscaling methodology that uses image registration techniques to identify the spatial misalignment and accounts for and …

การเปรียบเทียบวิธีบูตสแตรปในการประมาณช่วงความเชื่อมั่นของค่าสัมประสิทธิ์การถดถอยเชิงเส้นที่มีมิติสูง, ภูวกร นิธิศนทีกุล

Chulalongkorn University Theses and Dissertations (Chula ETD)

งานวิจัยฉบับนี้มีวัตถุประสงค์เพื่อศึกษาและเปรียบเทียบช่วงความเชื่อมั่นสำหรับค่าสัมประสิทธิ์การถดถอยโดยแนวทางบูตสแตรปที่แตกต่างกัน (1) วิธีสุ่มตัวแปรตามและตัวแปรอิสระ (2) วิธีสุ่มส่วนเหลือ และ (3) วิธีสุ่มค่าถ่วงน้ำหนัก ผู้วิจัยได้จำลองชุดข้อมูลขนาดมิติต่ำและมิติสูงขึ้น และ นำมาวิเคราะห์เปรียบเทียบด้วยวิธีบูตสแตปที่แตกต่างกัน 3 วิธี โดยการวัดค่าเฉลี่ยเปอร์เซ็นต์ช่วงความเชื่อมั่นที่ครอบคลุมค่าสัมประสิทธิ์การถดถอยค่าจริง ค่าเฉลี่ยความกว้าง ค่าเฉลี่ยอัตราผลบวกเทียม และค่าเฉลี่ยอัตราผลลบเทียม ระหว่าง 1,000 ข้อมูล การวิเคราะห์ของเราพบว่าบูตสแตรปที่ใช้สุ่มตัวแปรตามและตัวแปรอิสระดีที่สุดในแง่ของทั้งค่าเฉลี่ยเปอร์เซ็นต์ช่วงความเชื่อมั่นที่ครอบคลุมค่าสัมประสิทธิ์การถดถอยค่าจริงและค่าเฉลี่ยอัตราผลบวกเทียม บูตสแตรปที่ใช้สุ่มส่วนเหลือดีที่สุดในแง่ของค่าเฉลี่ยความกว้าง และบูตสแตรปที่ใช้สุ่มค่าถ่วงน้ำหนักดีที่สุดในแง่ของค่าเฉลี่ยอัตราผลลบเทียม

Novel Random Forest Methods And Algorithms For Autism Spectrum Disorders Research, Afrooz Jahedi

CGU Theses & Dissertations

Random Forest (RF) is a flexible, easy to use machine learning algorithm that was proposed by Leo Breiman in 2001 for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Its superior prediction accuracy has made it the most used algorithms in the machine learning field. In this dissertation, we use the random forest as the main building block for creating a proximity matrix for multivariate matching and diagnostic classification problems that are used for autism research (as an exemplary application). In observational studies, matching is used to optimize the balance …

A Multinational Study Of The Etiology And Clinical Teleology Of Moral Evaluations Of Patient Behaviors, Anna Yu Lee

CGU Theses & Dissertations

This dissertation is a collection of four studies which collectively explore a hypothesized construct of ‘moral evaluation of patient behaviors’ (MEPB) as a driver of health professionals’ readiness to interact humanistically with their patients. In these studies, ‘humanistic interactions’ refer to the non-technical, intangible skills and factors of clinical competence; the factors specifically explored in these studies were compassion toward patients, self-efficacy for treating patients, and optimism toward patient treatment. For the purpose of specificity, all factors were examined as they pertained to patients with substance use disorders. Survey data from a convenience sample of 524 health professionals (i.e. physicians, …

Enhancing Models And Measurements Of Traffic-Related Air Pollutants For Health Studies Using Dispersion Modeling And Bayesian Data Fusion, Stuart A. Batterman, Veronica J. Berrocal, Chad Milando, Owais Gilani, Saravanan Arunachalam, K. Max Zhang

Faculty Journal Articles

Research Report 202 describes a study led by Dr. Stuart Batterman at the University of Michigan, Ann Arbor and colleagues. The investigators evaluated the ability to predict traffic-related air pollution using a variety of methods and models, including a line source air pollution dispersion model and sophisticated spatiotemporal Bayesian data fusion methods. Exposure assessment for traffic-related air pollution is challenging because the pollutants are a complex mixture and vary greatly over space and time. Because extensive direct monitoring is difficult and expensive, a number of modeling approaches have been developed, but each model has its own limitations and errors.

Dr. …

Bread Dough Experiment, Collin Stivala

Student Research Poster Presentations 2020

This is my Final Poster for Design of Experiments. My poster explains the process and results of my experiment, in which I made bread dough, and tested the effects that Flour and Temperature have on bread dough.

Does Water Boil Faster With Salt?, Soumyadip Acharyya

Student Research Poster Presentations 2020

Whether water boils faster with salt is perhaps a never-ending question. My study has addressed this topic from a statistical perspective. Additionally, I have also investigated whether the water quantity affects the boiling time. I used the two-way Analysis of variance (ANOVA) to analyze and interpret the data.

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Causal Effect Random Forest Of Interaction Trees For Learning Individualized Treatment Regimes In Observational Studies: With Applications To Education Study Data, Luo Li

CGU Theses & Dissertations

Learning individualized treatment regimes (ITR) using observational data holds great interest in various fields, as treatment recommendations based on individual characteristics may improve individual treatment benefits with a reduced cost. It has long been observed that different individuals may respond to a certain treatment with significant heterogeneity. ITR can be defined as a mapping between individual characteristics to a treatment assignment. The optimal ITR is the treatment assignment that maximizes expected individual treatment effects. Rooted from personalized medicine, many studies and applications of ITR are in medical fields and clinical practice. Heterogeneous responses are also well documented in educational interventions. …

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% …

Rickettsialpox – A Rare But Not Extinct Disease: A Review Of The Literature And New Directions, Marina Eremeeva, Kamalich Muniz-Rodriguez

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

Smallpox rickettsia is an urban zoonosis caused by Rickettsia akari. To date, R. akari is the only characterized representative of the group of spotted fevers transmitted by the gamasid mite Liponyssoides sanguineus, which is common among peridomic rodents. This disease was first described in New York in 1946, and a few years later a similar outbreak occurred in the Ukrainian SSR. Numerous serological studies and diagnostics of sporadic cases of smallpox rickettsiosis suggest its widespread occurrence on the planet; however, the current geography and incidence of smallpox rickettsiosis is unknown. Smallpox rickettsiosis is characterized by the classic clinical triad of …

Chase-Escape On Sparse Networks, Emma Sylvie Bernstein

Senior Projects Spring 2020

Chase-escape is a competitive growth process in which prey spread through an environment while being chased and consumed by predators. The environment is typically modeled by a graph—such as a lattice, tree, or clique—and the species by particles competing to occupy sites. It is arguably more natural to study these dynamics in heterogeneous environments. To this end, we consider chase-escape on a canonical sparse random graph called the Erdo ̋s-R ́enyi graph. We show that if prey spreads too slowly then both species quickly die out. On the other hand, if prey spreads fast enough, then coexistence occurs. Concrete bounds …