Statistics and Probability Commons^™

An Introduction To Combinatorics Via Cayley's Theorem, Jaylee Willis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this paper, we explore some of the methods that are often used to solve combinatorial problems by proving Cayley’s theorem on trees in multiple ways. The intended audience of this paper is undergraduate and graduate mathematics students with little to no experience in combinatorics. This paper could also be used as a supplementary text for an undergraduate combinatorics course.

Quantum Computing Simulation Of The Hydrogen Molecule System With Rigorous Quantum Circuit Derivations, Yili Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details.

This report provides a rigorous derivation of simulating quantum chemistry …

A Bayesian Hierarchical Approach For Modeling Virtual Species With Realistic Functional Trait Relationships, Sarah Bogen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Understanding the spatial and temporal dynamics of plant populations has important implications for the fields of ecology and conservation. A rich body of mathematical modeling approaches, including reaction-diffusion equations and integrodifference equations, have been developed to mechanistically model population spread based on species demography and seed dispersal characteristics. However, with over 390,000 plant species on Earth, it is not feasible to collect complete information on all species for the purpose of drawing generalized conclusions. One means of overcoming such a problem is through trait-based modeling, which seeks to represent realistic combinations of organismal traits rather than focusing on individual species. …

Defining Areas Of Interest Using Voronoi And Modified Voronoi Tesselations To Analyze Eye-Tracking Data, Joanna D. Coltrin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a technology used to track where someone is looking. Eye-tracking technology is often used to study what people focus on when looking at a photo of another person. The eye-tracking technology records points on a photo that a person is looking at. When the photo being looked at shows a person, the points can be categorized by body part such as head, right hand, left hand, and torso. This thesis presents the use of partially circular areas to define the body parts of the person in the photo and therefore categorize the points collected by the eye-tracker. …

Contributions To Random Forest Variable Importance With Applications In R, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major focus in statistics is building and improving computational algorithms that can use data to predict a response. Two fundamental camps of research arise from such a goal. The first camp is researching ways to get more accurate predictions. Many sophisticated methods, collectively known as machine learning methods, have been developed for this very purpose. One such method that is widely used across industry and many other areas of investigation is called Random Forests.

The second camp of research is that of improving the interpretability of machine learning methods. This is worthy of attention when analysts desire to optimize …

Geometry- And Accuracy-Preserving Random Forest Proximities With Applications, Jake S. Rhodes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many machine learning algorithms use calculated distances or similarities between data observations to make predictions, cluster similar data, visualize patterns, or generally explore the data. Most distances or similarity measures do not incorporate known data labels and are thus considered unsupervised. Supervised methods for measuring distance exist which incorporate data labels and thereby exaggerate separation between data points of different classes. This approach tends to distort the natural structure of the data. Instead of following similar approaches, we leverage a popular algorithm used for making data-driven predictions, known as random forests, to naturally incorporate data labels into similarity measures known …

Model Averaging In Agriculture And Natural Resources: What Is It? When Is It Useful? When Is It A Distraction?, Philip M. Dixon

Conference on Applied Statistics in Agriculture and Natural Resources

I use two examples to illustrate three methods for model averaging: using AIC weights, using BIC weights, and fully Bayesian analyses. The first example is a capture-recapture study that estimates the population size by averaging over 4 models for capture probabilities. The second is an analysis of a study of logging impacts on Curculionid weevils using a before-after-control-impact (BACI) study design. The estimated impact is averaged over 4 ecologically relevant models.

Both examples demonstrate the sensitivity of model weights, or posterior model probabilities, to the choice of prior model probabilities and prior distributions for parameters. The model averaged estimates and …

A Robust Clustering Method Using Compositional Data Restrictions: Studying Wood Properties In The Reforestation Of Portugal, Pamela M. Chiroque-Solano, Guido A. Moreira

Conference on Applied Statistics in Agriculture and Natural Resources

Classification of multivariate observations while preserving the data’s natural restriction is a challenge. Special properties such as identifiability, interpretability, and others need to be cared for to build a new approach. To avoid these complications, many transformation algorithms have been developed to use traditional models.In this context, the aim of this work is to propose a robust probabilistic distance algorithm to classify compositional data. Based on the probabilistic distance (PD) clustering approach, the proposal identifies clusters minimizing a joint distance function, JDF, which is part of a dissimilarity measure. This measure combines the PD clustering approach with the density of …

Random Regression For Modeling Semen Fertility In Hf Purebred And Crossbred Bulls Using A Bayesian Framework, Vrinda Ambike, R. Venkataramanan, S. M. K. Karthickeyan, K. G. Tirumurugaan, Kaustubh Bhave, M. Swaminathan

Conference on Applied Statistics in Agriculture and Natural Resources

Data on insemination records of Holstein Friesian (HF) purebred (n=45,497) and crossbred (n=58,497) collected from the BAIF Research Foundation were utilized. The conception rate was modeled as a binary trait, using linear repeatability models. Random regression models (RRM) were used to obtain the trajectory of variance components across age of the bulls. Legendre Polynomials up to order of fit of 4 were used for the random effects of additive genetic and permanent environmental effects. 200,000 Gibbs samples were generated with a burn-in of 20,000 and thinning interval of 50 using the THRGIBBS1F90 program. Heritability estimates were very low (0.1) in …

Principal Response Curve Analysis Of Arthropod Community Abundance Data With Sparse Subsets, Changjian Jiang, C. R. Brown, P. Asiimwe, Chen Meng, Adam W. Schapaugh

Conference on Applied Statistics in Agriculture and Natural Resources

Principal response curve (PRC) analysis was applied to an assessment of the ecological impact of the genetically-modified (GM), insect-resistant, cotton MON 88702 on predatory Hemiptera communities in the field. The field community was represented by ten taxa collected ten times across the season at six sites, in which individual taxa were not observed in at least 25% of the time (unique site x collection combinations). These complete absences and those nearly so, called sparse subsets of the data in this investigation, were the result of geoclimatic and seasonal variations, which are both independent of the treatment effect for which the …

Handling Non-Detects With Imputation In A Nested Design: A Simulation Study, Rose Adjei, John R. Stevens

Conference on Applied Statistics in Agriculture and Natural Resources

In this paper, a simulation study was conducted to assess whether it is ideal to address the issue of non-detects in data using a traditional substitution approach for non-detects, imputation, or a non-imputation based approach. Simulated data used were simple nested designs motivated by a real-life data in a study of bumble bee activity in a commercial cherry orchard by Kuivila et al. (2021). The simulated data were generated at different thresholds or censoring levels and at different effect sizes. For each simulated data, seven popular existing techniques to handle non-detects were applied: (i) Zero substitution, (ii) Substitution with half …

Overview Of Optimal Experimental Design And A Survey Of Its Expanse In Application To Agricultural Studies, Stephen J. Walsh

Conference on Applied Statistics in Agriculture and Natural Resources

Optimal Design of Experiments is currently recognized as the modern dominant approach to planning experiments in industrial engineering and manufacturing applications. This approach to design has gained traction among practitioners in the last two decades on two-fronts: 1) optimal designs are the result of a complicated optimization calculation and recent advances in both computing efficiency and algorithms have enabled this approach in real time for practitioners, and 2) such designs are now popular because they allow the researcher to ‘design for the experiment’ by working constraints, cost, number of experiments, and the model of the intended post-hoc data analysis into …

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

Creating Transparent And Accessible Methods For Approximating The Composite Strength Of Concrete Sandwich Wall Panels, Ruth Taylor

Fall Student Research Symposium 2021

Background: The method of designing partially composite sandwich wall panels (SWPs) relies strongly on the use of percent of composite action. Calculating these values proves to be a complex and virtually inaccessible process for practicing engineers, resulting in the reliance on proprietary software or connector-system manufacturers for the necessary values. We simulated percent composite action data, including several relevant variables, to examine the relationship and determine if simple and accessible methods of calculation could be created. Methods: Code from collaborating engineers used to calculate percent composite action with the Iterative Sandwich Beam Theory (ISBT) method was translated into R, a …

Gps-Denied Navigation Using Synthetic Aperture Radar Images And Neural Networks, Teresa White

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout …

Supplementary Files For "Creating A Universal Depth-To-Load Conversion Technique For The Conterminous United States Using Random Forests", Jesse Wheeler, Brennan Bean, Marc Maguire

Browse all Datasets

As part of an ongoing effort to update the ground snow load maps in the United States, this paper presents an investigation into snow densities for the purpose of predicting ground snow loads for structural engineering design with ASCE 7. Despite their importance, direct measurements of snow load are sparse when compared to measurements of snow depth. As a result, it is often necessary to estimate snow load using snow depth and other readily accessible climate variables. Existing depth-to-load conversion methods, each of varying complexity, are well suited for snow load estimation for a particular region or station network, but …

Housing Variables And Immigration: An Exploratory And Predictive Data Analysis In New York City, Jhonatan Medri Cobos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City (NYC). Determining whether immigration status affects home ownership percentage, household rent, or housing cost percentage could help understand the quality of life of NYC residents. Graphical exploration, spatial dependence tests, and spatial autoregressive models of housing and immigration variables provide some insights about their relationships. Our exploration takes place at some geographic subareas of NYC.

Our results first indicate that the housing and immigration data reports spatial dependence; values of a geographic subarea are related to values …

A Phenological Model For A Southern Population Of Mountain Pine Beetle, Catherine E. Wangen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) attacks living Pinus trees across a widespread area of western North America, causing significant ecological and economic damage. The ability to make accurate predictions of how MPB populations across this range will respond to temperatures, which affect MPB progress through life stages, is essential. Northern and southern populations of MPB are genetically different in response to temperature, requiring geographic-specific model parameters. There is not currently a predictive model for the southern MPB life cycle, despite concerns that those populations may be more susceptible to increased numbers of generations per year, which would …

Retail Trading And Stock Volatility: The Case Of Robinhood, Cooper Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We examine the relation between Robinhood usership and stock market volatility. We show that daily fluctuations in Robinhood usership, which is used to proxy retail trading, significantly influence various measures of volatility. These results might suggest that Robinhood users contribute to noise trading as they are generally individuals trading on name recognition, media coverage, popularity, and familiarity of products, rather than on fundamental values. In our empirical approach, we find that the percentage increase in Robinhood usership Granger causes increases in daily stock volatility.

The Effect Of High Elevation Weather Stations On The Usda's Pasture, Rangeland, And Forage Insurance Program, Wyatt Matthew Feuz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper examines the effect of high elevation weather stations on the rainfall index used by the Pasture, Rangeland, and Forage insurance program. Weather station data for the state of Utah is used to identify high elevation weather stations and their location. Utilizing the corresponding rainfall index data, the effect of the high elevation weather stations is determined. This paper finds when high elevation weather stations begin reporting there is a jump up of 19.01–27.88 percentage points on average in the rainfall index for the corresponding grid locations. This indicates the rainfall index may not accurately represent actual precipitation amounts …

Computational Modeling For Decision-Making Under Climate Change Uncertainty: Reservoir Simulation Game, Julianne Quinn

All ECSTATIC Materials

Almost every decision you make is under uncertainty. Will I need a rain jacket in the afternoon? Will they say yes if I ask them out? Is 1 hour enough time to finish this assignment? Oftentimes, we can use computational modeling to simulate different scenarios of what might happen in the future to inform what decisions are best on average, or what decisions minimize the worst case outcome. For example, you could decide what player to draft for your Fantasy Football team by simulating player performance. In this activity, we will simulate how much water to release from a dam …

Survival Analysis: An Exact Method For Rare Events, Kristina Reutzel

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Conventional asymptotic methods for survival analysis work well when sample sizes are at least moderately sufficient. When dealing with small sample sizes or rare events, the results from these methods have the potential to be inaccurate or misleading. To handle such data, an exact method is proposed and compared against two other methods: 1) the Cox proportional hazards model and 2) stratified logistic regression for discrete survival analysis data.

Delta Hedging Of Financial Options Using Reinforcement Learning And An Impossibility Hypothesis, Ronak Tali

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this thesis we take a fresh perspective on delta hedging of financial options as undertaken by market makers. The current industry standard of delta hedging relies on the famous Black Scholes formulation that prescribes continuous time hedging in a way that allows the market maker to remain risk neutral at all times. But the Black Scholes formulation is a deterministic model that comes with several strict assumptions such as zero transaction costs, log normal distribution of the underlying stock prices, etc. In this paper we employ Reinforcement Learning to redesign the delta hedging problem in way that allows us …

A Bayesian Markov Chain Monte Carlo Approach To Uncertainty Quantification, Matthew Isaac

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Uncertainty quantification (UQ) is a framework used frequently in engineering analyses to understand how uncertainty in system inputs lead to uncertainty in the system output. An instability is observed in a UQ method proposed by Roy and Oberkampf and a Bayesian Markov Chain Monte Carlo approach to UQ is offered as an alternative. The Bayesian approach allows analysts to incorporate information from various available sources including observed measurements and expert opinion and to update the analysis and results as more information becomes available. An illustrative engineering example is provided as a platform to demonstrate the Bayesian UQ approach and to …

Simplicity As A New Environmental Virtue, Justin Wheeler

Undergraduate Honors Capstone Projects

This paper argues for the addition of a new environmentally focused virtue, simplicity, to the virtue ethical framework developed by Aristotle. First, relevant background from Aristotle’s virtue ethics are developed including the crucial, “doctrine of the mean”, a balance between excess and deficiency of a specified character trait. The tenets of the new virtue simplicity are developed with practical examples based on Aristotle’s method of developing a virtue of character. Simplicity is proposed as a desire to take the appropriate amount from the natural world and an acceptance of one’s circumstances. Those possessing simplicity will not fall victim to the …

Analysis Of Sat And Isat Scores For Madison School District In Rexburg, Idaho, Holly Dawn Palmer

Undergraduate Honors Capstone Projects

Testing is an integral part of measuring education. If used properly SAT scores can be compared across the nation, and statewide tests can compare different school districts to each other if done properly to avoid certain pitfalls (Fetler, 1991). However, if tests do not have a significant impact on a student, their motivation to take the test will be low and test quality cannot be assumed. When the state funds two separate tests for their students but only one has a significant impact on the student, how should the scores for each test be used, and is it okay to …

The Two Types Of Society: Computationally Revealing Recurrent Social Formations And Their Evolutionary Trajectories, Lux Miranda

Undergraduate Honors Capstone Projects

Comparative social science has a long history of attempts to classify societies and cultures in terms of shared characteristics. However, only recently has it become feasible to conduct quantitative analysis of large historical datasets to mathematically approach the study of social complexity and classify shared societal characteristics. Such methods have the potential to identify recurrent social formations in human societies and contribute to social evolutionary theory. However, in order to achieve this potential, repeated studies are needed to assess the robustness of results to changing methods and data sets. Using an improved derivative of the Seshat: Global History Databank, we …

Demystification Of Graph And Information Entropy, Bryce Frederickson

Undergraduate Honors Capstone Projects

Shannon entropy is an information-theoretic measure of unpredictability in probabilistic models. Recently, it has been used to form a tool, called the von Neumann entropy, to study quantum mechanics and network flows by appealing to algebraic properties of graph matrices. But still, little is known about what the von Neumann entropy says about the combinatorial structure of the graphs themselves. This paper gives a new formulation of the von Neumann entropy that describes it as a rate at which random movement settles down in a graph. At the same time, this new perspective gives rise to a generalization of von …

Applications Of Machine Learning In High-Frequency Trade Direction Classification, Jared E. Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The correct assignment of trades as buyer-initiated or seller-initiated is paramount in many quantitative finance studies. Simple decision rule methods have been used for signing trades since many data sets available to researchers do not include the sign of each trade executed. By utilizing these decision rule methods, as well as engineering new variables from available data, we have demonstrated that machine learning models outperform prior methods for accurately signing trades as buys and sells, achieving state-of-the-art results. The best model developed was 4.5 percentage points more accurate than older methods when predicting onto unseen data. Since finance and economics …

'Lmshapemaker': Utilizing The 'Rmapshaper' R Package To Modify Shapefiles For Use In Linked Micromap Plots, Braden D. Probst

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to effectively create map-based visualizations, some map modifications need to be conducted to ensure the map is readable and interpretable. There are several issues that need to be addressed to achieve this. The boundaries of a country may be overly complex which is particularly true with coastal areas of countries. Regions may be small and not seen in the final plot, as is the case with many capital cities in the world’s countries such as Washington D.C. and the Federal District of Mexico City. In other countries, regions may geographically lie far away from the rest of the …