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Articles 1 - 14 of 14
Full-Text Articles in Probability
Analysis And Implementation Of The Maximum Likelihood Expectation Maximization Algorithm For Find, Angus Boyd Jameson
Analysis And Implementation Of The Maximum Likelihood Expectation Maximization Algorithm For Find, Angus Boyd Jameson
Student Research Projects
This thesis presents an organized explanation and breakdown of the Maximum Likelihood Expectation Maximization image reconstruction algorithm. This background research was used to develop a means of implementing the algorithm into the imaging code for UNH's Field Deployable Imaging Neutron Detector to improve its ability to resolve complex neutron sources. This thesis provides an overview for this implementation scheme, and include the results of a couple of reconstruction tests for the algorithm. A discussion is given on the current state of the algorithm and its integration with the neutron detector system, and suggestions are given for how the work and …
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently …
A Brief On Optimal Transport, Austin G. Vandegriffe
A Brief On Optimal Transport, Austin G. Vandegriffe
Graduate Student Research & Creative Works
Optimal transport is an interesting and exciting application of measure theory to optimization and analysis. In the following, I will bring you through a detailed treatment of random variable couplings, transport plans, basic properties of transport plans, and finishing with the Wasserstein distance on spaces of probability measures with compact support. No detail is left out in this presentation, but some results have further generality and more intricate consequences when tools like measure disintegration are used. But this is left for future work.
A Brief On Characteristic Functions, Austin G. Vandegriffe
A Brief On Characteristic Functions, Austin G. Vandegriffe
Graduate Student Research & Creative Works
Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust in …
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
All HMC Faculty Publications and Research
Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability - continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods …
Video Game Genre Classification Based On Deep Learning, Yuhang Jiang
Video Game Genre Classification Based On Deep Learning, Yuhang Jiang
Masters Theses & Specialist Projects
Video games have played a more and more important role in our life. While the genre classification is a deeply explored research subject by leveraging the strength of deep learning, the automatic video game genre classification has drawn little attention in academia. In this study, we compiled a large dataset of 50,000 video games, consisting of the video game covers, game descriptions and the genre information. We explored three approaches for genre classification using deep learning techniques. First, we developed five image-based models utilizing pre-trained computer vision models such as MobileNet, ResNet50 and Inception, based on the game covers. Second, …
Autoassociative-Heteroassociative Neural Network, Claudia V. Kropas-Hughes, Steven K. Rogers, Mark E. Oxley, Matthew Kabrisky
Autoassociative-Heteroassociative Neural Network, Claudia V. Kropas-Hughes, Steven K. Rogers, Mark E. Oxley, Matthew Kabrisky
AFIT Patents
An efficient neural network computing technique capable of synthesizing two sets of output signal data from a single input signal data set. The method and device of the invention involves a unique integration of autoassociative and heteroassociative neural network mappings, the autoassociative neural network mapping enabling a quality metric for assessing the generalization or prediction accuracy of the heteroassociative neural network mapping.
On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.
Personal Foul: How Head Trauma And The Insurance Industry Are Threatening Sports, Zachary Cooler
Personal Foul: How Head Trauma And The Insurance Industry Are Threatening Sports, Zachary Cooler
Senior Honors Theses
This thesis will investigate the growing problem of head trauma in contact sports like football, hockey, and soccer through medical studies, implications to the insurance industry, and ongoing litigation. The thesis will investigate medical studies that are finding more evidence to support the claim that contact sports players are more likely to receive head trauma symptoms such as memory loss, mood swings, and even Lou Gehrig’s disease in extreme cases. The thesis will also demonstrate that these medical symptoms and monetary losses from medical claims are convincing insurance companies to withdraw insurance coverage for sports leagues, which they are justifying …
Dynamic Control Of Probabilistic Simple Temporal Networks, James C. Boerkoel Jr., Michael Gao, Lindsay Popowski
Dynamic Control Of Probabilistic Simple Temporal Networks, James C. Boerkoel Jr., Michael Gao, Lindsay Popowski
All HMC Faculty Publications and Research
The controllability of a temporal network is defined as an agent’s ability to navigate around the uncertainty in its schedule and is well-studied for certain networks of temporal constraints. However, many interesting real-world problems can be better represented as Probabilistic Simple Temporal Networks (PSTNs) in which the uncertain durations are represented using potentially-unbounded probability density functions. This can make it inherently impossible to control for all eventualities. In this paper, we propose two new dynamic controllability algorithms that attempt to maximize the likelihood of successfully executing a schedule within a PSTN. The first approach, which we call MIN-LOSS DC, finds …
Dice Questions Answered, Warren Campbell, William P. Dolan
Dice Questions Answered, Warren Campbell, William P. Dolan
SEAS Faculty Publications
Superstitious discussion of fair and unfair dice has pervaded the tabletop gaming industry since its inception. Many of these are not based on any quantitative data or studies. Consequently, misconceptions have been spread widely. One dice float test video on Youtube currently has 925,000 views (Fisher, 2015a). To combat the flood of misconceptions we investigated the following questions: 1) Are dice cursed? 2) Are D20s (20-sided dice) less fair than D6s (6-sided dice)? 3) Do float tests tell anything about the fairness of dice? 4) Are some dice systems inherently fairer than others? 5) Are density differences or dimensions more …
Inferences For Weibull-Gamma Distribution In Presence Of Partially Accelerated Life Test, Mahmoud Mansour, M A W Mahmoud Prof., Rashad El-Sagheer
Inferences For Weibull-Gamma Distribution In Presence Of Partially Accelerated Life Test, Mahmoud Mansour, M A W Mahmoud Prof., Rashad El-Sagheer
Basic Science Engineering
In this paper, the point at issue is to deliberate point and interval estimations for the parameters of Weibull-Gamma distribution (WGD) using progressively Type-II censored (PROG-II-C) sample under step stress partially accelerated life test (SSPALT) model. The maximum likelihood (ML), Bayes, and four parametric bootstrap methods are used to obtain the point estimations for the distribution parameters and the acceleration factor. Furthermore, the approximate confidence intervals (ACIs), four bootstrap confidence intervals and credible intervals of the estimators have been gotten. The results of Bayes estimators are computed under the squared error loss (SEL) function using Markov Chain Monte Carlo (MCMC) …
Some New Results On Stochastic Comparisons Of Coherent Systems Using Signatures, Ebrahim Amini-Seresht, Baha-Eldin Khaledi, Subhash C. Kochar
Some New Results On Stochastic Comparisons Of Coherent Systems Using Signatures, Ebrahim Amini-Seresht, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
We consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed …
Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang
Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang
The University of Michigan Department of Biostatistics Working Paper Series
This paper outlines a new class of shrinkage priors for Bayesian isotonic regression modeling a binary outcome against a predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The predictor is categorized into a large number of groups, and the set of differences between outcome probabilities in consecutive categories is equipped with a multivariate prior having support over the set of simplexes. The Dirichlet distribution, which can be derived from a normalized cumulative sum of gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that …