Statistical Models Commons^™

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Relationship Between High School Math Course Selection And Retention Rates At Otterbein University, Lauren A. Fisher

Undergraduate Honors Thesis Projects

Binary logistic regression was used to study the relationship between high school math course selection and retention rates at Otterbein University. Graduation rates from postsecondary institutions are low in the United States and, more specifically, at Otterbein. This study is important in helping to determine what can raise retention rates, and ultimately, graduation rates. It directs focus toward high school math course selection and what should be changed before entering a post-secondary institution. Otterbein will have a better idea of what type of students to recruit and which students may be good candidates with some extra help. Recruiting is expensive, …

Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone

Department of Management: Faculty Publications

Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …

Spin Glass Reflection Of The Decoding Transition For Quantum Error Correcting Codes, Alexey Kovalev, Leonid P. Pryadko

Department of Physics and Astronomy: Faculty Publications

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z₂ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of "post-topological" extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Modelling And Analysis On Noisy Financial Time Series, Jinsong Leng

Research outputs 2014 to 2021

Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models to make the prediction of the possible trends and cycles. Even though many statistical or machine learning (ML) models have been proposed, however, there are no universal solutions available to resolve such particular prob-lem. In this paper, the powerful forward-backward non-linear filter and wavelet-based denoising method are introduced to remove the high level of noise embedded in financial time series. With the filtered time series, the statistical …

Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky

Publications and Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …

A Superposed Log-Linear Failure Intensity Model For Repairable Artillery Systems, Byeong Min Mun, Suk Joo Bae, Paul Kvam

Department of Math & Statistics Faculty Publications

This article investigates complex repairable artillery systems that include several failure modes. We derive a superposed process based on a mixture of nonhomogeneous Poisson processes in a minimal repair model. This allows for a bathtub-shaped failure intensity that models artillery data better than currently used methods. The method of maximum likelihood is used to estimate model parameters and construct confidence intervals for the cumulative intensity of the superposed process. Finally, we propose an optimal maintenance policy for repairable systems with bathtub-shaped intensity and apply it to the artillery-failure data.

A Normal Truncated Skewed-Laplace Model In Stochastic Frontier Analysis, Junyi Wang

Masters Theses & Specialist Projects

Stochastic frontier analysis is an exciting method of economic production modeling that is relevant to hospitals, stock markets, manufacturing factories, and services. In this paper, we create a new model using the normal distribution and truncated skew-Laplace distribution, namely the normal-truncated skew-Laplace model. This is a generalized model of the normal-exponential case. Furthermore, we compute the true technical efficiency and estimated technical efficiency of the normal-truncated skewed-Laplace model. Also, we compare the technical efficiencies of normal-truncated skewed-Laplace model and normal-exponential model.

Flexible Distributed Lag Models Using Random Functions With Application To Estimating Mortality Displacement From Heat-Related Deaths, Roger D. Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

No abstract provided.

Generalized Bathtub Hazard Models For Binary-Transformed Climate Data, James Polcer

Masters Theses & Specialist Projects

In this study, we use a hazard-based modeling as an alternative statistical framework to time series methods as applied to climate data. Data collected from the Kentucky Mesonet will be used to study the distributional properties of the duration of high and low-energy wind events relative to an arbitrary threshold. Our objectiveswere to fit bathtub models proposed in literature, propose a generalized bathtub model, apply these models to Kentucky Mesonet data, and make recommendations as to feasibility of wind power generation. Using two different thresholds (1.8 and 10 mph respectively), results show that the Hjorth bathtub model consistently performed better …

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

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 …

Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel

COBRA Preprint Series

Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a …

A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski

Developmental Cognitive Neuroscience Laboratory: Faculty Publications

The power properties of traditional repeated measures and hierarchical linear models have not been clearly determined in the balanced design for longitudinal studies in the current literature. A Monte Carlo power analysis of traditional repeated measures and hierarchical multivariate linear models are presented under three variance-covariance structures. Results suggest that traditional repeated measures have higher power than hierarchical linear models for main effects, but lower power for interaction effects. Significant power differences are also exhibited when power is compared across different covariance structures. Results also supplement more comprehensive empirical indexes for estimating model precision via bootstrap estimates and the approximate …

A Method For Visualizing Multivariate Time Series Data, Roger D. Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

Visualization and exploratory analysis is an important part of any data analysis and is made more challenging when the data are voluminous and high-dimensional. One such example is environmental monitoring data, which are often collected over time and at multiple locations, resulting in a geographically indexed multivariate time series. Financial data, although not necessarily containing a geographic component, present another source of high-volume multivariate time series data. We present the mvtsplot function which provides a method for visualizing multivariate time series data. We outline the basic design concepts and provide some examples of its usage by applying it to a …

Bayesian Analysis For Penalized Spline Regression Using Win Bugs, Ciprian M. Crainiceanu, David Ruppert, M.P. Wand

Johns Hopkins University, Dept. of Biostatistics Working Papers

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. MCMC mixing is substantially improved from the previous versions by using low{rank thin{plate splines instead of truncated polynomial basis. Simulation time …

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge

Articles

This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based …

Spatio-Temporal Analysis Of Areal Data And Discovery Of Neighborhood Relationships In Conditionally Autoregressive Models, Subharup Guha, Louise Ryan

Harvard University Biostatistics Working Paper Series

No abstract provided.

Bayesian Smoothing Of Irregularly-Spaced Data Using Fourier Basis Functions, Christopher J. Paciorek

Harvard University Biostatistics Working Paper Series

No abstract provided.

Gauss-Seidel Estimation Of Generalized Linear Mixed Models With Application To Poisson Modeling Of Spatially Varying Disease Rates, Subharup Guha, Louise Ryan

Harvard University Biostatistics Working Paper Series

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases.

This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM …

Computational Techniques For Spatial Logistic Regression With Large Datasets, Christopher J. Paciorek, Louise Ryan

Harvard University Biostatistics Working Paper Series

In epidemiological work, outcomes are frequently non-normal, sample sizes may be large, and effects are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. We focus on binary outcomes, with the risk surface a smooth function of space. We compare penalized likelihood models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation.

A Bayesian model using a spectral basis representation of the spatial surface provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial …

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models, Larry Leon, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are …

A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan

The University of Michigan Department of Biostatistics Working Paper Series

Case-cohort designs are increasingly commonly used in large epidemiological cohort studies. Nan, Yu, and Kalbeisch (2004) provided the asymptotic results for censored linear regression models in case-cohort studies. In this article, we consider computational aspects of their proposed rank based estimating methods. We show that the rank based discontinuous estimating functions for case-cohort studies are monotone, a property established for cohort data in the literature, when generalized Gehan type of weights are used. Though the estimating problem can be formulated to a linear programming problem as that for cohort data, due to its easily uncontrollable large scale even for a …

Semiparametric Regression In Capture-Recapture Modelling, O. Gimenez, C. Barbraud, Ciprian M. Crainiceanu, S. Jenouvrier, B.T. Morgan

Johns Hopkins University, Dept. of Biostatistics Working Papers

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in the survival process may be explained by incorporating relevant covariates. We develop nonparametric and semiparametric regression models for estimating survival in capture-recapture models. A fully Bayesian approach using MCMC simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adelie.

A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch

The University of Michigan Department of Biostatistics Working Paper Series

A goal of radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal, however complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe a relationship between dose and observed functional complication, however only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication …