# Probability Commons™

## All Articles in Probability

315 full-text articles. Page 2 of 11.

Golden Arm: A Probabilistic Study Of Dice Control In Craps, 2018 Monmouth University

#### Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii

##### UNLV Gaming Research & Review Journal

This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting ...

2018 Stephen F Austin State University

#### Evaluation Of Using The Bootstrap Procedure To Estimate The Population Variance, Nghia Trong Nguyen

##### Electronic Theses and Dissertations

The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a ...

On Passing The Buck, 2018 Cedarville University

#### On Passing The Buck, Adam J. Hammett, Anna Joy Yang

##### The Research and Scholarship Symposium

Imagine there are n>1 people seated around a table, and person S starts with a fair coin they will flip to decide whom to hand the coin next -- if "heads" they pass right, and if "tails" they pass left. This process continues until all people at the table have "touched" the coin. Curiously, it turns out that all people seated at the table other than S have the same probability 1/(n-1) of being last to touch the coin. In fact, Lovasz and Winkler ("A note on the last new vertex visited by a random walk," J. Graph Theory ...

The Devil You Don’T Know: A Spatial Analysis Of Crime At Newark’S Prudential Center On Hockey Game Days, 2018 Institute for Security and Crime Science - University of Waikato

#### The Devil You Don’T Know: A Spatial Analysis Of Crime At Newark’S Prudential Center On Hockey Game Days, Justin Kurland, Eric Piza

##### Journal of Sport Safety and Security

Inspired by empirical research on spatial crime patterns in and around sports venues in the United Kingdom, this paper sought to measure the criminogenic extent of 216 hockey games that took place at the Prudential Center in Newark, NJ between 2007-2016. Do games generate patterns of crime in the areas beyond the arena, and if so, for what type of crime and how far? Police-recorded data for Newark are examined using a variety of exploratory methods and non-parametric permutation tests to visualize differences in crime patterns between game and non-game days across all of Newark and the downtown area. Change ...

#### Network Structure Sampling In Bayesian Networks Via Perfect Sampling From Linear Extensions, Evan Sidrow

##### Applied Mathematics Graduate Theses & Dissertations

Bayesian networks are widely considered as powerful tools for modeling risk assessment, uncertainty, and decision making. They have been extensively employed to develop decision support systems in a variety of domains including medical diagnosis, risk assessment and management, human cognition, industrial process and procurement, pavement and bridge management, and system reliability. Bayesian networks are convenient graphical expressions for high dimensional probability distributions which are used to represent complex relationships between a large number of random variables. A Bayesian network is a directed acyclic graph consisting of nodes which represent random variables and arrows which correspond to probabilistic dependencies between them ...

2018 Western Kentucky University

#### Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai

##### Masters Theses & Specialist Projects

The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate ...

2018 Louisiana State University and Agricultural and Mechanical College

#### General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

##### LSU Doctoral Dissertations

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory ...

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, 2018 The University of Western Ontario

##### Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case ...

Predicting The Next Us President By Simulating The Electoral College, 2018 New York City College of Technology, CUNY

#### Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

##### Journal of Humanistic Mathematics

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic ...

Sampling Techniques For Big Data Analysis In Finite Population Inference, 2018 Iowa State University

#### Sampling Techniques For Big Data Analysis In Finite Population Inference, Jae Kwang Kim, Zhonglei Wang

##### Statistics Preprints

In analyzing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first method uses a version of inverse sampling by incorporating auxiliary infor- mation from external sources, and the second one borrows the idea of data integration by combining the big data sample with an independent proba- bility sample. Two simulation studies show that the proposed methods are unbiased and have better coverage rates than their alternatives. In addition, the proposed ...

Some Applications Of Sophisticated Mathematics To Randomized Computing, 2018 Selected Works

#### Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg

##### Ronald Greenberg

No abstract provided.

Educational Magic Tricks Based On Error-Detection Schemes, 2018 Loyola University Chicago

#### Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg

##### Ronald Greenberg

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.

Analyzing The Probabilistic Spread Of A Virus On Various Networks, 2018 Bard College

#### Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis

##### Senior Projects Spring 2018

In this project we model the spread of a virus on networks as a probabilistic process. We assume the virus breaks out at one vertex on a network and then spreads to neighboring vertices in each time step with a certain probability. Our objective is to find probability distributions that describe the uncertain number of infected vertices at a given time step. The networks we consider are paths, cycles, star graphs, complete graphs, and broom graphs. Through the use of Markov chains and Jordan Normal Form we analyze the probability distribution of these graphs, characterizing the transition matrix for each ...

2018 University of Montana

#### Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

##### Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of ...

2018 The University of Akron

#### Comparing Various Machine Learning Statistical Methods Using Variable Differentials To Predict College Basketball, Nicholas Bennett

##### Williams Honors College, Honors Research Projects

The purpose of this Senior Honors Project is to research, study, and demonstrate newfound knowledge of various machine learning statistical techniques that are not covered in the University of Akron’s statistics major curriculum. This report will be an overview of three machine-learning methods that were used to predict NCAA Basketball results, specifically, the March Madness tournament. The variables used for these methods, models, and tests will include numerous variables kept throughout the season for each team, along with a couple variables that are used by the selection committee when tournament teams are being picked. The end goal is to ...

2018 The University of Akron

#### A Review Of The Utility Of Bayesian Network Models, Luke Magyar

##### Williams Honors College, Honors Research Projects

Bayesian Networks are probabilistic models built from conditional probability tables that relate two observable instances to one another in parent-child fashion. The networks’ strength lies in their ability to use inferential logic to make likelihood assessments about a parent node based on an observation of its child. Additionally, they make it very easy to combine quantitative data with qualitative knowledge from industry experts. These abilities make them very attractive for use as formulation tools in the paint and rubber industries. Paint and rubber formulation has long proven to be a challenging task because companies have a difficult time compiling the ...

Surprise Vs. Probability As A Metric For Proof, 2018 U.S. Court of Federal Claims

#### Surprise Vs. Probability As A Metric For Proof, Edward K. Cheng, Matthew Ginther

##### Vanderbilt Law School Faculty Publications

In this Symposium issue celebrating his career, Professor Michael Risinger in Leveraging Surprise proposes using "the fundamental emotion of surprise" as a way of measuring belief for purposes of legal proof. More specifically, Professor Risinger argues that we should not conceive of the burden of proof in terms of probabilities such as 51%, 95%, or even "beyond a reasonable doubt." Rather, the legal system should reference the threshold using "words of estimative surprise" -asking jurors how surprised they would be if the fact in question were not true. Toward this goal (and being averse to cardinality), he suggests categories such ...

2018 Michigan Technological University

#### Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara

##### Dissertations, Master's Theses and Master's Reports

Density estimation has wide applications in machine learning and data analysis techniques including clustering, classification, multimodality analysis, bump hunting and anomaly detection. In high-dimensional space, sparsity of data in local neighborhood makes many of parametric and nonparametric density estimation methods mostly inefficient.

This work presents development of computationally efficient algorithms for high-dimensional density estimation, based on Bayesian sequential partitioning (BSP). Copula transform is used to separate the estimation of marginal and joint densities, with the purpose of reducing the computational complexity and estimation error. Using this separation, a parallel implementation of the density estimation algorithm on a 4-core CPU is ...

2018 University of North Florida

#### Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

##### UNF Graduate Theses and Dissertations

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including ...

Can An Influence Graph Driven By Outage Data Determine Transmission Line Upgrades That Mitigate Cascading Blackouts?, 2018 Iowa State University

#### Can An Influence Graph Driven By Outage Data Determine Transmission Line Upgrades That Mitigate Cascading Blackouts?, Kai Zhou, Ian Dobson, Paul D.H. Hines, Zhaoyu Wang

##### Electrical and Computer Engineering Conference Papers, Posters and Presentations

We transform historically observed line outages in a power transmission network into an influence graph that statistically describes how cascades propagate in the power grid. The influence graph can predict the critical lines that are historically most involved in cascading propagation. After upgrading these critical lines, simulating the influence graph suggests that these upgrades could mitigate large blackouts by reducing the probability of large cascades.