Probability Commons^™

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 ...

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, 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 ...

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, 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

Octahedral Dice, Todd Estroff, Jeremiah Farrell

Jeremiah Farrell

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be ...

Thinking Poker Through Game Theory, Damian Palafox

Electronic Theses, Projects, and Dissertations

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be ...

Elements Of The Mathematical Formulation Of Quantum Mechanics, Keunjae Go

Senior Honors Papers / Undergraduate Theses

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of ...

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

The Research and Scholarship Symposium

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 ...

Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret

UW Biostatistics Working Paper Series

We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the ...

Using Probabilistic Approach To Joint Clustering And Statistical Inference: Analytics For Big Investment Data, Hua Fang, Honggang Wang, Chonggang Wang, Mahmoud Daneshmand

Hua Julia Fang

This paper proposes a Contrarian Probabilistic Model (CPM) to evaluate the effectiveness of contrarians' investment in preferred stocks using big data from Tradeline. CPM accommodates the unique features of investment data which are often correlated, nested, heterogeneous, non-normal with missing values. The clustering and statistical inference are integrated in CPM, which enables joint investment behavior trajectory pattern recognition and risk analyses based on the entire variance-covariance structure between and within clusters. The empirical study using CPM provides a finer and comprehensive evaluation of contrarian investment in preferred stocks. Two distinctive investment behavior trajectory clusters were identified, showing a few high-risk-seeking ...

A Novel Method For Assessing Co-Monotonicity: An Interplay Between Mathematics And Statistics With Applications, Danang T. Qoyyimi

Electronic Thesis and Dissertation Repository

Numerous problems in econometrics, insurance, reliability engineering, and statistics rely on the assumption that certain functions are monotonic, which may or may not be true in real life scenarios. To satisfy this requirement, from the theoretical point of view, researchers frequently model the underlying phenomena using parametric and semi-parametric families of functions, thus effectively specifying the required shapes of the functions. To tackle these problems in a non-parametric way, when the shape cannot be specified explicitly but only estimated approximately, we suggest indices for measuring the lack of monotonicity in functions. We investigate properties of these indices and offer convenient ...

Probabilistic Reasoning In Cosmology, Yann Benétreau-Dupin

Electronic Thesis and Dissertation Repository

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology.

The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such ...

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

Electronic Thesis and Dissertation Repository

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used ...

Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, Ernest Jum

Doctoral Dissertations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain L^p [the space of measurable functions with a finite p-norm], for p greater than or equal to ...

Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li

Doctoral Dissertations

This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.

Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a ...

Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, Tiffany Kolba, Avanti Athreya, Jonathan Mattingly

Tiffany N Kolba

No abstract provided.

Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu

UNLV Gaming Research & Review Journal

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such non-standard knowledge ...

The Relationship Between Self-Determination And Client Outcomes Among The Homeless, Samuel M. Hanna

Electronic Theses, Projects, and Dissertations

This paper has attempted to determine if there is a significant relationship between self-determination and client outcomes among the homeless. The study has been based upon the conceptual framework set forth in Self-Determination Theory. The purpose of the study was to explore the relationship between self-determination and client outcomes among the homeless. Using a data collection instrument, based on empirically validated instrumentation, clients from several homeless service providers in the City of San Bernardino were assessed for the level of self-determination and autonomy support they experience within these agencies. Outcome measures included such things as whether the client was going ...

Estimated Probability Of Becoming A Case Of Drug Dependence In Relation To Duration Of Drug-Taking Experience: A Function Approach, Olga Vsevolozhskaya, James Anthony

Olga A. Vsevolozhskaya

Measured as elapsed time from first use to dependence syndrome onset, the estimated 'induction interval' for cocaine clearly is short relative to the cannabis interval, but little is known about risk of becoming dependent when use persists. Published estimates for this facet of drug dependence epidemiology are from life histories elicited years after first use. To improve estimation, we turn to new data from nationally representative samples of newly incident drug users identified via probability sampling and confidential computer-assisted self-interviews for the National Surveys on Drug Use and Health, 2004-2013. Standardized modules assess first and most recent use, and dependence ...