The Battle Against Malaria: A Teachable Moment, 2017 Schoolcraft College

#### The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

*Journal of Humanistic Mathematics*

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to ...

Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, 2017 University of San Francisco

#### Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, Nathaniel Stevens, C. M. Anderson-Cook

*Mathematics*

When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. New graphical summaries provide strategies for visualizing the results.

Stochastic Processes And Integrals, 2017 Wayne State University

#### Stochastic Processes And Integrals, Jose L. Menaldi

*Mathematics Faculty Research Publications*

Stochastic integrals with respect to Wiener process and Poisson measures are discusses, beginning from stochastic processes.

Quantifying The Effect Of The Shift In Major League Baseball, 2017 Bard College

#### Quantifying The Effect Of The Shift In Major League Baseball, Christopher John Hawke Jr.

*Senior Projects Spring 2017*

Baseball is a very strategic and abstract game, but the baseball world is strangely obsessed with statistics. Modern mainstream statisticians often study offensive data, such as batting average or on-base percentage, in order to evaluate player performance. However, this project observes the game from the opposite perspective: the defensive side of the game. In hopes of analyzing the game from a more concrete perspective, countless mathemeticians - most famously, Bill James - have developed numerous statistical models based on real life data of Major League Baseball (MLB) players. Large numbers of metrics go into these models, but what this project attempts to ...

Kinetic Monte Carlo Methods For Computing First Capture Time Distributions In Models Of Diffusive Absorption, 2017 Harvey Mudd College

#### Kinetic Monte Carlo Methods For Computing First Capture Time Distributions In Models Of Diffusive Absorption, Daniel Schmidt

*HMC Senior Theses*

In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches ...

Numerical Calculus Of Probability Density Functions, 2017 University of Colorado at Boulder

#### Numerical Calculus Of Probability Density Functions, Ignas V. Satkauskas

*Applied Mathematics Graduate Theses & Dissertations*

In this thesis we construct novel functional representations for the Probability Density Functions (PDFs) of random variables and develop efficient and accurate algorithms for computing the PDFs of their sums, products and quotients, again in the same representation. We consider two important cases of random variables: non-negative random variables and random variables taking both positive and negative values. For the first case, we use approximations by decaying exponentials with complex exponents, while for the second case we develop a Gaussian-based multiresolution analysis (GMRA).

The need to represent distributions of products and quotients of random variables appear in many areas of ...

Inference In Networking Systems With Designed Measurements, 2017 University of Massachusetts Amherst

#### Inference In Networking Systems With Designed Measurements, Chang Liu

*Doctoral Dissertations*

Networking systems consist of network infrastructures and the end-hosts have been essential in supporting our daily communication, delivering huge amount of content and large number of services, and providing large scale distributed computing. To monitor and optimize the performance of such networking systems, or to provide flexible functionalities for the applications running on top of them, it is important to know the internal metrics of the networking systems such as link loss rates or path delays. The internal metrics are often not directly available due to the scale and complexity of the networking systems. This motivates the techniques of inference ...

Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, 2017 University of Kentucky

#### Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman

*Theses and Dissertations--Education Science*

Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate ...

Set-Theoretic Reconstructability Of Elementary Cellular Automata, 2016 Portland State University

#### Set-Theoretic Reconstructability Of Elementary Cellular Automata, Martin Zwick, Hui Shu

*Martin Zwick*

Set-theoretic reconstructability analysis is used to characterize the structures of the mappings of elementary cellular automata. The minimum complexity structure for each ECA mapping, indexed by parameter σ, is more effective than the λ parameter of Langton as a predictor of chaotic dynamics.

Multi-Level Decomposition Of Probalistic Relations, 2016 Portland State University

#### Multi-Level Decomposition Of Probalistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski

*Martin Zwick*

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.

Control Uniqueness In Reconstructability Analysis, 2016 Portland State University

#### Control Uniqueness In Reconstructability Analysis, Martin Zwick

*Martin Zwick*

When the reconstructability analysis of a directed system yields a structure in which a generated variable appears in more than one subsystem, information from all of the subsystems can be used in modeling the relationship between generating and generated variables. The conceptualization and procedure proposed here is discussed in relation to Klir's concept of control uniqueness.

Reconstructability Analysis With Fourier Transforms, 2016 Portland State University

#### Reconstructability Analysis With Fourier Transforms, Martin Zwick

*Martin Zwick*

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the ...

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, 2016 Washington University in St. Louis

#### A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

*Doctor of Business Administration Dissertations*

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with ...

On A Multiple-Choice Guessing Game, 2016 Bethel College - Mishawaka

#### On A Multiple-Choice Guessing Game, Ryan Cushman, Adam J. Hammett

*Adam J. Hammett, Ph.D.*

We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability ...

Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, 2016 University of Tennessee, Knoxville

#### Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, Kai Kang

*Doctoral Dissertations*

The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this ...

Numerical Solutions Of Stochastic Differential Equations, 2016 University of Tennessee, Knoxville

#### Numerical Solutions Of Stochastic Differential Equations, Liguo Wang

*Doctoral Dissertations*

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to ...

Newsvendor Models With Monte Carlo Sampling, 2016 East Tennessee State University

#### Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

*Electronic Theses and Dissertations*

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected proﬁt. Finally, this method will be used ...

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, 2016 University of Georgia

#### Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

*Journal of Humanistic Mathematics*

This review-essay on the mother-and-daughter collaboration *Math on Trial* stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, 2016 Hofstra University

#### Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, Justus R. Riek

*Journal of Humanistic Mathematics*

This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems

Stochastic Processes And Their Applications To Change Point Detection Problems, 2016 Graduate Center, City University of New York

#### Stochastic Processes And Their Applications To Change Point Detection Problems, Heng Yang

*All Dissertations, Theses, and Capstone Projects*

This dissertation addresses the change point detection problem when either the post-change distribution has uncertainty or the post-change distribution is time inhomogeneous. In the case of post-change distribution uncertainty, attention is drawn to the construction of a family of composite stopping times. It is shown that the proposed composite stopping time has third order optimality in the detection problem with Wiener observations and also provides information to distinguish the different values of post-change drift. In the case of post-change distribution uncertainty, a computationally efficient decision rule with low-complexity based on Cumulative Sum (CUSUM) algorithm is also introduced. In the time ...