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Description
Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of stream dependence can be missed by each approach because neither one fully addresses the multivariate nature of the accumulated data when generators are run in parallel. This dissertation identifies these potential faults in the parallel testing methodologies of TestU01 and investigates two different methods to better detect inter-stream dependencies: correlation motivated multivariate tests and vector time series based tests. These methods have been implemented in an extension to TestU01 built in C++ and the unique aspects of this extension are discussed. A variety of different generation scenarios are then examined using the TestU01 suite in concert with the extension. This enhanced software package is found to better detect certain forms of inter-stream dependencies than the original TestU01 suites of tests.
ContributorsIsmay, Chester (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
Description
By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a 1 by 1 saddle square), which was rediscovered by many authors including Thorp (1979). Thorp gave two proofs of the probability of a saddle point, one using combinatorics and one using a beta integral. In 1965, Falk and Thrall investigated the integrals required for the probabilities of a 2 by 2 saddle square for 2 × n and m × 2 games with iid uniform (0,1) payoffs, but they were not able to evaluate the integrals. This dissertation generalizes Thorp's beta integral proof of Goldman's probability of a saddle point, establishing an integral formula for the probability that a m × n game with iid uniform (0,1) payoffs has a k by k saddle square (k ≤ m,n). Additionally, the probabilities of a 2 by 2 and a 3 by 3 saddle square for a 3 × 3 game with iid uniform(0,1) payoffs are found. For these, the 14 integrals observed by Falk and Thrall are dissected into 38 disjoint domains, and the integrals are evaluated using the basic properties of the dilogarithm function. The final results for the probabilities of a 2 by 2 and a 3 by 3 saddle square in a 3 × 3 game are linear combinations of 1, π2, and ln(2) with rational coefficients.
ContributorsManley, Michael (Author) / Kadell, Kevin W. J. (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Lohr, Sharon (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2011
Description
There are multiple mathematical models for alignment of individuals moving within a group. In a first class of models, individuals tend to relax their velocity toward the average velocity of other nearby neighbors. These types of models are motivated by the flocking behavior exhibited by birds. Another class of models have been introduced to describe rapid changes of individual velocity, referred to as jump, which better describes behavior of smaller agents (e.g. locusts, ants). In the second class of model, individuals will randomly choose to align with another nearby individual, matching velocities. There are several open questions concerning these two type of behavior: which behavior is the most efficient to create a flock (i.e. to converge toward the same velocity)? Will flocking still emerge when the number of individuals approach infinity? Analysis of these models show that, in the homogeneous case where all individuals are capable of interacting with each other, the variance of the velocities in both the jump model and the relaxation model decays to 0 exponentially for any nonzero number of individuals. This implies the individuals in the system converge to an absorbing state where all individuals share the same velocity, therefore individuals converge to a flock even as the number of individuals approach infinity. Further analysis focused on the case where interactions between individuals were determined by an adjacency matrix. The second eigenvalues of the Laplacian of this adjacency matrix (denoted ƛ2) provided a lower bound on the rate of decay of the variance. When ƛ2 is nonzero, the system is said to converge to a flock almost surely. Furthermore, when the adjacency matrix is generated by a random graph, such that connections between individuals are formed with probability p (where 0
1/N. ƛ2 is a good estimator of the rate of convergence of the system, in comparison to the value of p used to generate the adjacency matrix..
ContributorsTrent, Austin L. (Author) / Motsch, Sebastien (Thesis director) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Modeling human survivorship is a core area of research within the actuarial com
munity. With life insurance policies and annuity products as dominant financial
instruments which depend on future mortality rates, there is a risk that observed
human mortality experiences will differ from projected when they are sold. From an
insurer’s portfolio perspective, to curb this risk, it is imperative that models of hu
man survivorship are constantly being updated and equipped to accurately gauge and
forecast mortality rates. At present, the majority of actuarial research in mortality
modeling involves factor-based approaches which operate at a global scale, placing
little attention on the determinants and interpretable risk factors of mortality, specif
ically from a spatial perspective. With an abundance of research being performed
in the field of spatial statistics and greater accessibility to localized mortality data,
there is a clear opportunity to extend the existing body of mortality literature to
wards the spatial domain. It is the objective of this dissertation to introduce these
new statistical approaches to equip the field of actuarial science to include geographic
space into the mortality modeling context.
First, this dissertation evaluates the underlying spatial patterns of mortality across
the United States, and introduces a spatial filtering methodology to generate latent
spatial patterns which capture the essence of these mortality rates in space. Second,
local modeling techniques are illustrated, and a multiscale geographically weighted
regression (MGWR) model is generated to describe the variation of mortality rates
across space in an interpretable manner which allows for the investigation of the
presence of spatial variability in the determinants of mortality. Third, techniques for
updating traditional mortality models are introduced, culminating in the development
of a model which addresses the relationship between space, economic growth, and
mortality. It is through these applications that this dissertation demonstrates the
utility in updating actuarial mortality models from a spatial perspective.
munity. With life insurance policies and annuity products as dominant financial
instruments which depend on future mortality rates, there is a risk that observed
human mortality experiences will differ from projected when they are sold. From an
insurer’s portfolio perspective, to curb this risk, it is imperative that models of hu
man survivorship are constantly being updated and equipped to accurately gauge and
forecast mortality rates. At present, the majority of actuarial research in mortality
modeling involves factor-based approaches which operate at a global scale, placing
little attention on the determinants and interpretable risk factors of mortality, specif
ically from a spatial perspective. With an abundance of research being performed
in the field of spatial statistics and greater accessibility to localized mortality data,
there is a clear opportunity to extend the existing body of mortality literature to
wards the spatial domain. It is the objective of this dissertation to introduce these
new statistical approaches to equip the field of actuarial science to include geographic
space into the mortality modeling context.
First, this dissertation evaluates the underlying spatial patterns of mortality across
the United States, and introduces a spatial filtering methodology to generate latent
spatial patterns which capture the essence of these mortality rates in space. Second,
local modeling techniques are illustrated, and a multiscale geographically weighted
regression (MGWR) model is generated to describe the variation of mortality rates
across space in an interpretable manner which allows for the investigation of the
presence of spatial variability in the determinants of mortality. Third, techniques for
updating traditional mortality models are introduced, culminating in the development
of a model which addresses the relationship between space, economic growth, and
mortality. It is through these applications that this dissertation demonstrates the
utility in updating actuarial mortality models from a spatial perspective.
ContributorsCupido, Kyran (Author) / Jevtic, Petar (Thesis advisor) / Fotheringham, A. Stewart (Committee member) / Lanchier, Nicolas (Committee member) / Páez, Antonio (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2020
Description
In baseball, a starting pitcher has historically been a more durable pitcher capable of lasting long into games without tiring. For the entire history of Major League Baseball, these pitchers have been expected to last 6 innings or more into a game before being replaced. However, with the advances in statistics and sabermetrics and their gradual acceptance by professional coaches, the role of the starting pitcher is beginning to change. Teams are experimenting with having starters being replaced quicker, challenging the traditional role of the starting pitcher. The goal of this study is to determine if there is an exact point at which a team would benefit from replacing a starting or relief pitcher with another pitcher using statistical analyses. We will use logistic stepwise regression to predict the likelihood of a team scoring a run if a substitution is made or not made given the current game situation.
ContributorsBuckley, Nicholas J (Author) / Samara, Marko (Thesis director) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Information Systems (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
As the impacts of climate change worsen in the coming decades, natural hazards are expected to increase in frequency and intensity, leading to increased loss and risk to human livelihood. The spatio-temporal statistical approaches developed and applied in this dissertation highlight the ways in which hazard data can be leveraged to understand loss trends, build forecasts, and study societal impacts of losses. Specifically, this work makes use of the Spatial Hazard Events and Losses Database which is an unparalleled source of loss data for the United States. The first portion of this dissertation develops accurate loss baselines that are crucial for mitigation planning, infrastructure investment, and risk communication. This is accomplished thorough a stationarity analysis of county level losses following a normalization procedure. A wide variety of studies employ loss data without addressing stationarity assumptions or the possibility for spurious regression. This work enables the statistically rigorous application of such loss time series to modeling applications. The second portion of this work develops a novel matrix variate dynamic factor model for spatio-temporal loss data stratified across multiple correlated hazards or perils. The developed model is employed to analyze and forecast losses from convective storms, which constitute some of the highest losses covered by insurers. Adopting factor-based approach, forecasts are achieved despite the complex and often unobserved underlying drivers of these losses. The developed methodology extends the literature on dynamic factor models to matrix variate time series. Specifically, a covariance structure is imposed that is well suited to spatio-temporal problems while significantly reducing model complexity. The model is fit via the EM algorithm and Kalman filter. The third and final part of this dissertation investigates the impact of compounding hazard events on state and regional migration in the United States. Any attempt to capture trends in climate related migration must account for the inherent uncertainties surrounding climate change, natural hazard occurrences, and socioeconomic factors. For this reason, I adopt a Bayesian modeling approach that enables the explicit estimation of the inherent uncertainty. This work can provide decision-makers with greater clarity regarding the extent of knowledge on climate trends.
ContributorsBoyle, Esther Sarai (Author) / Jevtic, Petar (Thesis advisor) / Lanchier, Nicolas (Thesis advisor) / Lan, Shiwei (Committee member) / Cheng, Dan (Committee member) / Fricks, John (Committee member) / Gall, Melanie (Committee member) / Cutter, Susan (Committee member) / McNicholas, Paul (Committee member) / Arizona State University (Publisher)
Created2023