Probability Commons^™

Statistical Inference For Networks Of High-Dimensional Point Processes, Xu Wang, Mladen Kolar, Ali Shojaie

UW Biostatistics Working Paper Series

Fueled in part by recent applications in neuroscience, high-dimensional Hawkes process have become a popular tool for modeling the network of interactions among multivariate point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work have only focused on estimation. To bridge this gap, this paper proposes a high-dimensional statistical inference procedure with theoretical guarantees for multivariate Hawkes process. Key to this inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarizes the entire history of the process. We apply this …

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Probabilistic Models For Order-Picking Operations With Multiple In-The-Aisle Pick Positions, Jingming Liu

Graduate Theses and Dissertations

The development of probability density functions (pdfs) for travel time of a narrow aisle lift truck (NALT) and an automated storage and retrieval (AS/R) machine is the focus of the dissertation. The multiple in-the-aisle pick positions (MIAPP) order picking system can be modeled as an M/G/1 queueing problem in which storage and retrieval requests are the customers and the vehicle (NALT or AS/R machine) is the server. Service time is the sum of travel time and the deterministic time to pick up and deposit a pallet (TPD).

Our first contribution is the development of travel time pdfs for retrieval operations …

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …

A Statistical Analysis Of The Roulette Martingale System: Examples, Formulas And Simulations With R, Peter Pflaumer

International Conference on Gambling & Risk Taking

Some gamblers use a martingale or doubling strategy as a way of improving their chances of winning. This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. A computer simulation study with R of the doubling strategy is presented. The results of doubling to gambling with a constant sized bet on simple chances (red or black numbers, even or odd numbers, and low (1 – 18) or high (19 – 36) numbers) and …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Machine Learning Pipeline For Exoplanet Classification, George Clayton Sturrock, Brychan Manry, Sohail Rafiqi

SMU Data Science Review

Planet identification has typically been a tasked performed exclusively by teams of astronomers and astrophysicists using methods and tools accessible only to those with years of academic education and training. NASA’s Exoplanet Exploration program has introduced modern satellites capable of capturing a vast array of data regarding celestial objects of interest to assist with researching these objects. The availability of satellite data has opened up the task of planet identification to individuals capable of writing and interpreting machine learning models. In this study, several classification models and datasets are utilized to assign a probability of an observation being an exoplanet. …

Leveraging Natural Language Processing Applications And Microblogging Platform For Increased Transparency In Crisis Areas, Ernesto Carrera-Ruvalcaba, Johnson Ekedum, Austin Hancock, Ben Brock

SMU Data Science Review

Through microblogging applications, such as Twitter, people actively document their lives even in times of natural disasters such as hurricanes and earthquakes. While first responders and crisis-teams are able to help people who call 911, or arrive at a designated shelter, there are vast amounts of information being exchanged online via Twitter that provide real-time, location-based alerts that are going unnoticed. To effectively use this information, the Tweets must be verified for authenticity and categorized to ensure that the proper authorities can be alerted. In this paper, we create a Crisis Message Corpus from geotagged Tweets occurring during 7 hurricanes …

Predictive Distributions Via Filtered Historical Simulation For Financial Risk Management, Tyson Clark

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

Filtered historical simulation with an underlying GARCH process can be used as a valuable tool in VaR analysis, as it derives risk estimates that are sensitive to the distributional properties of the historical data of the produced predictive density. I examine the applications to risk analysis that filtered historical simulation can provide, as well as an interpretation of the predictive density as a poor man’s Bayesian posterior distribution. The predictive density allows us to make associated probabilistic statements regarding the results for VaR analysis, giving greater measurement of risk and the ability to maintain the optimal level of risk per …

Generalizations Of The Arcsine Distribution, Rebecca Rasnick

Electronic Theses and Dissertations

The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first …

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 …

Ergodicity For The 3d Stochastic Navier-Stokes Equations Perturbed By Lévy Noise, Manil T. Mohan, K. Sakthivel, Sivaguru S. Sritharan

Faculty Publications

In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using the Kolmogorov equations of integrodifferential type associated with the SNSE perturbed by Lévy noise, we construct a transition semigroup and establish the existence of a unique invariant measure. We also show that it is ergodic and strongly mixing.
/="/">Abstract © Wiley.

Dice Mythbusters, C. Warren Campbell, William P. Dolan

Student Research Conference Select Presentations

All dice are unfair because they cannot be manufactured with absolute precision. However, some dice are more unfair than others. Each year hundreds of millions of dice are sold worldwide. Dice commonly used in role playing games are 4-sided (D4), 6-sided (D6), 8-sided (D8), 10-sided (D10), 12-sided (D12), and 20-sided (D20). Most of these are manufactured using plastic mold injection and rock tumbler methods. This method can result in dimensional inaccuracies in the dice and sometimes density inhomogeneities. In 3000-roll tests of eleven D20 dice only three tested fair. In a running chi square test it was shown that for …

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

COBRA Preprint Series

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards …

Non Parametric Test For Testing Exponentiality Against Exponential Better Than Used In Laplace Transform Order, Mahmoud Mansour, M A W Mahmoud Prof.

Basic Science Engineering

In this paper, the test statistic for testing exponentiality against exponential better than used in Laplace transform order (EBUL) based on the Laplace transform technique is proposed. Pitman’s asymptotic efficiency of our test is calculated and compared with other tests. The percentiles of this test are tabulated. The powers of the test are estimated for famously used distributions in aging problems. In the case of censored data, our test is applied and the percentiles are also calculated and tabulated. Finally, real examples in different areas are utilized as practical applications for the proposed test.

One-Dimensional Excited Random Walk With Unboundedly Many Excitations Per Site, Omar Chakhtoun

Dissertations, Theses, and Capstone Projects

We study a discrete time excited random walk on the integers lattice requiring a tail decay estimate on the number of excitations per site and extend the existing framework, methods, and results to a wider class of excited random walks.

We give criteria for recurrence versus transience, ballisticity versus zero linear speed, completely classify limit laws in the transient regime, and establish a functional limit laws in the recurrence regime.

Counting And Coloring Sudoku Graphs, Kyle Oddson

Mathematics and Statistics Dissertations, Theses, and Final Project Papers

A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n² × n² sudoku grid for all n ∈ ℤ^≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n; we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …

The Dark Sky Character Of Archaeological Landscapes: Cultural Meaning And Conservation Strategies, Frank Prendergast

Book/Book Chapter

This paper presents the first ever study of light pollution at selected Irish prehistoric archaeological landscapes. The concepts of cosmology and landscape are first briefly described and followed by a summary of early human settlement of the island. Building on this, the extant corpus of early prehistoric megalithic burial tombs is illustrated to show their contrasting distribution patterns and typology. Analysis of tomb locations using nearest-neighbour statistical methods reveals evidence of intentional clustering. Further geo-statistical analysis identifies the geographical locations and the density ranking of these nucleated clusters - a feature especially evident in the passage tomb tradition on this …

Statistical Inference For The Transformed Rayleigh Lomax Distribution With Progressive Type-Ii Right Censorship, Amani Alghami, Wei Ning, Arjun K. Gupta

Mathematics and Statistics Faculty Publications

In this paper, we study the transformed Rayleigh Lomax (Trans-RL) distribution which belongs to a certain family of two parameters lifetime distributions given by Wang et al (2010). Confidence intervals and inverse estimators of the Trans-RL parameters are derived in terms of order statistics. A simulation study is conducted to report the coverage probabilities, the average biases and the average relative mean square errors for the maximum likelihood, L-moments and inverse estimators. We compare the performance of these methods under different schemes of progressively Type-II right censoring. Finally, an illustrative example is provided to demonstrate the proposed methods.

High Dimensional Outlier Detection, Omid Khormali

Graduate Student Theses, Dissertations, & Professional Papers

In statistics and data science, outliers are data points that differ greatly from other observations in a data set. They are important attributes of the data because they can dramatically influence patterns and relationships manifested by non-outliers. It is therefore very important to detect and adequately deal with outliers. Recently, a novel algorithm, the ROMA algorithm, has been proposed [11]. In this paper, we propose a modification of the ROMA algorithm that reduces its computational complexity from $O(n^2 m)$ to $O((n/(2^m-o(1)))^2 m)$ where $n$ is the number of data points and $m$ is the dimension of the space. And as …

Biodiversity And Distribution Of Benthic Foraminifera In Harrington Sound, Bermuda: The Effects Of Physical And Geochemical Factors On Dominant Taxa, Nam Le

Honors Theses

Harrington Sound, Bermuda, is a nearly enclosed lagoon acting as a subtropical/tropical, carbonate-rich basin in which carbonate sediments, reef patches, and carbonate-producing organisms accumulate. Here, one of the most important calcareous groups is the Foraminifera. Analyses of common benthic orders, including miliolids (Quinqueloculina and Triloculina spp.) and rotaliids (Homotrema rubrum, Elphidium spp., and Ammonia beccarii), are essential in understanding past and present environmental conditions affecting the island's coastal environment. These taxa have been studied previously; however, factors explaining their individual patterns of abundance in the Sound are not well detailed. The goal of this study is …

Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane

Statistical Science Theses and Dissertations

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?

We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …

An Overview And Evaluation Of Synthetc: A Statistical Model For Extra-Tropical Cyclones, Rafael Uryayev

Dissertations and Theses

Extratropical cyclones (ETCs) are the most common weather phenomena affecting the United States, Canada, and Europe. They can pose serious hazards over large swaths of area. In this thesis, a statistical model of ETCs, called SynthETC, is discussed. The model accounts for the for genesis, track path, termination, and intensity of statistically generated ETCs. Genesis is modeled as a Poisson process, whose mean is determined by climate and historical information. Tracks are modeled as a regression-mean determined by climate and historical information plus a stochastic component. Lysis is modeled using logistic regression, with climate states as covariates. Intensity is modeled …

Snap Scholar: The User Experience Of Engaging With Academic Research Through A Tappable Stories Medium, Ieva Burk

CMC Senior Theses

With the shift to learn and consume information through our mobile devices, most academic research is still only presented in long-form text. The Stanford Scholar Initiative has explored the segment of content creation and consumption of academic research through video. However, there has been another popular shift in presenting information from various social media platforms and media outlets in the past few years. Snapchat and Instagram have introduced the concept of tappable “Stories” that have gained popularity in the realm of content consumption.

To accelerate the growth of the creation of these research talks, I propose an alternative to video: …