Assuming a set of variates are independent and normally distributed is commonplace in statistics. In this thesis, we consider the consequences of these assumptions as they pertain to global sensitivity analysis. We begin by illustrating how the notion of sensitivity becomes distorted in the presence of codependent model inputs. This observation motivates us to develop a new methodology which accommodates for input codependencies. Our methodology can be summarized through three points: First, a new form of sensitivity is presented which performs as well as the classical form but can be obtained at a fraction of the computational cost. Second, we define a measure which quantifies the extent of distortion caused by codependent inputs. The third point is regarding the modelling of said codependencies. The multivariate normal distribution is a natural choice for modelling codependent inputs; however, our methodology uses a copula-based approach instead. Copulas are a contemporary strategy for constructing multivariate distributions whereby the marginal and joint behaviours are treated separately. As a result, a practitioner has more flexibility when modelling inputs. / Thesis (Master, Chemical Engineering) -- Queen's University, 2013-12-05 10:16:26.81

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International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / A significant problem in the processing chain of a low resolution quantization system is the Analog to Digital converter quantization error. The classical model of quantization treats the error generated as a random additive process that is independent of the input and uniformly distributed. This model is valid for complex or random input signals that are large relative to a least significant bit. But the model fails catastrophically for small, simple signals applied to high resolution quantization systems, and in addition, the model fails for simple signals applied to low resolution quantization systems, i.e. one to 6 bits resolution. This paper will discuss a means of correcting this problem by the application of dither. Two methods of dither will be discussed as well as a real-life implementation of the techniques.

Class of 2009 Abstract / OBJECTIVES: The purpose of this study was to determine the perceptions of the general public in Arizona regarding random drug screening and obtaining and maintaining health care benefits. METHODS: Individuals entering and leaving a grocery store in Chandler, Arizona on one day were invited to voluntarily participate in the study by reviewing a subject disclosure form and completing an 11 item questionnaire. The Likert scale varied from 1 = Strongly Disagree to 6 = Strongly Agree. Individuals were eligible to participate if they were adults and living in Arizona. RESULTS: One hundred adults participated in the study. The results of the study showed general agreement for passing a drug test for illegal substances before being hired (5.0 ± 1.5, mean ± SD), and if testing positive for illegal drugs, being allowed to enroll in a drug treatment program to keep their health care benefits (4.8 ±1.6). Respondents agreed that employers should require random drug testing to maintain employment (4.4 ± 1.8). However, respondents neither agreed or disagreed that people should be required to pass a drug test to be eligible to receive health care benefits (3.9 ± 2.0) or that they should be required to pass a periodic drug test to maintain their health care benefits (3.7 ± 2.0). CONSLUSIONS: Respondents agreed with drug testing to obtain and maintain employment; however, respondents neither agreed or disagreed with the concept of obtaining or maintaining health care benefits with passing a drug test for illegal substances.

Approved for public release; distribution is unlimited / Includes supplementary material / Reissued 30 May 2017 with correction to degree on title page. / Randomness is at the heart of today's computing. There are two categorical methods to generate random numbers: pseudorandom number generation (PRNG) methods and true random number generation (TRNG) methods. While PRNGs operate orders of magnitude faster than TRNGs, the strength of PRNGs lies in their initial seed. TRNGs can function to generate such a seed. This thesis will focus on studying the feasibility of using the next generation Naval Postgraduate School Femto Satellite (NPSFS) as a TRNG. The hardware for the next generation will come from the Intel Quark D2000 along with its onboard BMC150 6-axis eCompass. We simulated 3-dimensional motion to see if any raw data from the BMC150 could be used as an entropy source for random number generation.We studied various "schemes" on how to select and output specific data bits to determine if more entropy and increased bitrate could be reached. Data collected in this thesis suggests that the BMC150 contains certain bits that could be considered good sources of entropy. Various schemes further utilized these bits to yield a strong entropy source with higher bitrate. We propose the NPSFS be studied further to find other sources of entropy. We also propose a prototype be sent into space for experimental verification of these results. / Lieutenant, United States Navy

Random number generator is a key component for strengthening and securing the confidentiality of electronic communications. Random number generators can be divided as either pseudo random number generators or true random number generators. A pseudo random number generator produces a stream of numbers that appears to be random but actually follow predefined sequence. A true random number generator produces a stream of unpredictable numbers that have no defined pattern. There has been growing interest to design true random number generator in past few years. Several Field Programmable Gate Array (FPGA) and Application Specific Integrated Circuit (ASIC) based approaches have been used to generate random data that requires analog circuit. RNGs having analog circuits demand for more power and area. These factors weaken hardware analog circuit-based RNG systems relative to hardware completely digital-based RNGs systems. This thesis is focused on the design of completely digital true random number generator ASIC.

Traditional skill ratings are not suitable for new types of games. We developed a general skill rating framework for games which do not discriminate players based on their skill. This class of games is widely present in the world. We use Bayesian statistics to convert aggregate data about the player's performance to a percentile rank describing his skill. The system is applicable to both single-player and multiplayer games with binary and non-binary endings. The rating formulas do not contain any arbitrary constants. We have tested the system in simulations and on real game data, and we outline its possible applications.

The present work aims to contribute to the study of networks by mapping the temporal evolution of the degree to a random walk in degree space. We analyzed how and when the degree approximates a pre-established value through a parallel with the first-passage problem of random walks. The mean time for the first-passage was calculated for the dynamical versions the Watts-Strogatz and Erdos-Renyi models. We also analyzed the degree variance for the random recursive tree and Barabasi-Albert models / O presente trabalho visa contribuir com a pesquisa na área de redes através do mapeamento da evolução temporal do grau com um passeio aleatório no espaço do mesmo. Para tanto, foi feita uma análise de quando e como a quantidade de ligações do vértice se aproxima de um valor pré-estabelecido, mediante um paralelo com o problema da primeira passagem de passeios aleatórios. O tempo médio para a primeira passagem para as versões dinâmicas dos modelos Watts-Strogatz e Erdos-Rényi foram calculados. Além disso, foi realizado um estudo da variância do grau para os modelos da árvore recursiva aleatória e Barabási-Albert

This thesis is composed of three main parts. Each chapter is concerned with characterizing some properties of a random ensemble or stochastic process. The properties of interest and the methods for investigating them di er between chapters. We begin by establishing some asymptotic results regarding zeros of random harmonic mappings, a topic of much interest to mathematicians and astrophysicists alike. We introduce a new model of harmonic polynomials based on the so-called "Weyl ensemble" of random analytic polynomials. Building on the work of Li and Wei [28] we obtain precise asymptotics for the average number of zeros of this model. The primary tools used in this section are the famous Kac-Rice formula as well as classical methods in the asymptotic analysis of integrals such as the Laplace method. Continuing, we characterize several topological properties of this model of harmonic polynomials. In chapter 3 we obtain experimental results concerning the number of connected components of the orientation-reversing region as well as the geometry of the distribution of zeros. The tools used in this section are primarily Monte Carlo estimation and topological data analysis (persistent homology). Simulations in this section are performed within MATLAB with the help of a computational homology software known as Perseus. While the results in this chapter are empirical rather than formal proofs, they lead to several enticing conjectures and open problems. Finally, in chapter 4 we address an industry problem in applied mathematics and machine learning. The analysis in this chapter implements similar techniques to those used in chapter 3. We analyze data obtained by observing CAN tra c. CAN (or Control Area Network) is a network for allowing micro-controllers inside of vehicles to communicate with each other. We propose and demonstrate the e ectiveness of an algorithm for detecting malicious tra c using an approach that discovers and exploits the natural geometry of the CAN surface and its relationship to random walk Markov chains. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

We consider the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such equations arise, for example, in stochastic groundwater ow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, lack uniform coercivity and boundedness with respect to the random parameter and have only limited spatial regularity. To give a rigorous bound on the cost of the multilevel Monte Carlo estimator to reach a desired accuracy, one needs to quantify the bias of the estimator. The bias, in this case, is the spatial discretisation error in the numerical solution of the partial differential equation. This thesis is concerned with establishing bounds on this discretisation error in the practically relevant and technically demanding case of coefficients which are not uniformly coercive or bounded with respect to the random parameter. Under mild assumptions on the regularity of the coefficient, we establish new results on the regularity of the solution for a variety of model problems. The most general case is that of a coefficient which is piecewise Hölder continuous with respect to a random partitioning of the domain. The established regularity of the solution is then combined with tools from classical discretisation error analysis to provide a full convergence analysis of the bias of the multilevel estimator for finite element and finite volume spatial discretisations. Our analysis covers as quantities of interest several spatial norms of the solution, as well as point evaluations of the solution and its gradient and any continuously Fréchet differentiable functional. Lastly, we extend the idea of multilevel Monte Carlo estimators to the framework of Markov chain Monte Carlo simulations. We develop a new multilevel version of a Metropolis Hastings algorithm, and provide a full convergence analysis.