DRUM Collection: Computer Science Theses and Dissertationshttp://hdl.handle.net/1903/27562014-12-19T07:56:43Z2014-12-19T07:56:43ZHierarchical Bayes Analysis of Behavioral ExperimentsDong, Chenhttp://hdl.handle.net/1903/158192014-10-12T02:36:27Z2014-01-01T00:00:00ZTitle: Hierarchical Bayes Analysis of Behavioral Experiments
Authors: Dong, Chen
Abstract: In this dissertation, we develop generalized hierarchical Bayesian ANOVA, to assist experimental researchers in the behavioral and social sciences in the analysis of the effects of experimentally manipulated within- and between-subjects factors. The method alleviates several limitations of classical ANOVA, still commonly employed in those fields. An accompanying R package for hierarchical Bayesian ANOVA is developed. It offers statistical routines and several easy-to-use functions for esti- mation of hierarchical Bayesian ANOVA models that are tailored to the analysis of experimental research. Markov chain Monte Carlo (MCMC) simulation is used to simulate posterior samples of the parameters of each model specified by the user. The core program of all models is written in R and JAGS (Just Another Gibbs Sam- pler) which is very similar to the famous software WinBUGS. After preparing the data in the required format, users simply select an appropriate model, and estimate it without any advanced coding. The main aim of the R package is to offer freely accessible resources for hierarchical Bayesian ANOVA analysis, which makes it easy to use for behavioral researchers. We also develop generalized Bayesian mediation models for analysis of mediation effects. By using Bayesian analysis, inference is straightforward and exact, which makes it appealing for experimental studies with small samples. The Bayesian approach is also conceptually simpler for any model with a complicated structure, especially for multilevel mediation analysis. Analysis of several data sets are used to illustrate the proposed methods.2014-01-01T00:00:00ZROBUSTNESS OF ATTRACTING ORBITSJoglekar, Madhura R.http://hdl.handle.net/1903/158172014-10-12T02:36:18Z2014-01-01T00:00:00ZTitle: ROBUSTNESS OF ATTRACTING ORBITS
Authors: Joglekar, Madhura R.
Abstract: Understanding the transition to turbulence is a long-lasting problem in fluid dynamics, particularly in the case of simple flows in which the base laminar flow does not become linearly unstable. For flows at a low Reynolds number, all initial conditions decay to the laminar profile. At higher Reynolds numbers, above a critical value, turbulence is observed, often in the form of a chaotic saddle. The magnitude of the perturbation that disrupts the laminar flow into the turbulent region depends on the Reynolds number and on the direction of the perturbation. In Chapter 2, we investigate the robustness of the laminar attractor to perturbations in a 9-dimensional sinusoidal shear flow model. We examine the geometry of the `edge of chaos', where the edge denotes the boundary of the chaotic saddle, which is embedded in the basin of attraction of the laminar state, and is accessible from that state.
For a smooth dynamical system $x_{n+1} = F(C, x_n)$ (depending on a parameter C), there may be infinitely many periodic windows, that is, intervals in C having a region of stable periodic behavior. However, the smaller of these windows are easily destroyed with tiny perturbations, so that only finitely many of the windows can be detected for a given level of noise. For a fixed perturbation size $\epsilon$, we consider the system behavior in the presence of noise. In this Chapter, we look at the ``$\epsilon$-robust windows'', that is, those periodic windows such that for the superstable parameter value C in that window, the general periodic behavior persists despite noise of amplitude $\le \epsilon$. We focus on the quadratic map, and numerically compute the number of periodic windows that are $\epsilon$-robust. In Chapter 3, we obtain a robustness-exponent $\alpha \approx .51 \pm .03$, which characterizes the robustness of periodic windows in the presence of noise.
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$ can convert an attractor from chaotic to non-chaotic or vice-versa. We call a parameter value where this can happen $\epsilon$-uncertain. The probability that a random choice of the parameter is $\epsilon$-uncertain commonly scales like a power law in $\epsilon$. Surprisingly, two seemingly similar ways of defining this scaling, both of physical interest, yield different numerical values for the scaling exponent. In Chapter 4, we show why this happens and present a quantitative analysis of this phenomenon.
Many dynamical systems reach a level of maximum topological entropy as the system parameter is increased followed by a decrease to zero entropy. In Chapter 5, we give an example such that the number of cascades continues to increase for arbitrarily large values of the parameter. We investigate the map $S_{\mu}:[0,1] \rightarrow [0,1)$ defined by $S_{\mu}(x) := \mu \sin(2\pi x) \bmod{1}.$ For this map, the entropy increases without bound as $\mu \rightarrow \infty$, and the system has an ever-increasing
number of solitary cascades for $\mu \in [0,m]$ as $m$ is increased to higher and higher integer values. Specifically, we calculate the number of period-$k$ cascades of the map, for $k>1$, for positive integer values of $\mu \in [0,m]$, where $m \in \mathbb{N}$.2014-01-01T00:00:00ZCrowdsourcing decision support: frugal human computation for efficient decision input acquisitionQuinn, Alexander Jameshttp://hdl.handle.net/1903/158162014-10-12T02:36:12Z2014-01-01T00:00:00ZTitle: Crowdsourcing decision support: frugal human computation for efficient decision input acquisition
Authors: Quinn, Alexander James
Abstract: When faced with data-intensive decision problems, individuals, businesses, and governmental decision-makers must balance trade-offs between optimality and the high cost of conducting a thorough decision process. The unprecedented availability of information online has created opportunities to make well-informed, near-optimal decisions more efficiently. A key challenge that remains is the difficulty of efficiently gathering the requisite details in a form suitable for making the decision.
Human computation and social media have opened new avenues for gathering relevant information or opinions in support of a decision-making process. It is now possible to coordinate paid web workers from online labor markets such as Amazon Mechanical Turk and others in a distributed search party for the needed information. However, the strategies that individuals employ when confronted with too much information--satisficing, information foraging, etc.--are more difficult to apply with a large, distributed group. Consequently, current distributed approaches are inherently wasteful of human time and effort.
This dissertation offers a method for coordinating workers to efficiently enter the inputs for spreadsheet decision models. As a basis for developing and understanding the idea, I developed AskSheet, a system that uses decision models represented as spreadsheets. The user provides a spreadsheet model of a decision, the formulas of which are analyzed to calculate the value of information for each of the decision inputs. With that, it is able to prioritize the inputs and make the decision input acquisition process more frugal. In doing so, it trades machine capacity for analyzing the model for a reduction in the cost and burden to the humans providing the needed information.2014-01-01T00:00:00ZNew Notions and Mechanisms for Statistical PrivacyGroce, Adam Dowlinhttp://hdl.handle.net/1903/158132014-10-12T02:35:53Z2014-01-01T00:00:00ZTitle: New Notions and Mechanisms for Statistical Privacy
Authors: Groce, Adam Dowlin
Abstract: Many large databases of personal information currently exist in the hands of corporations, nonprofits, and governments. The data in these databases could be used to answer any number of important questions, aiding in everything from basic research to day-to-day corporate decision-making. These questions must be answered while respecting the privacy of the individuals whose data are being used. However, even defining privacy in this setting can be difficult. The standard definition in the field is differential privacy. During the years since its introduction, a wide variety of query algorithms have been found that can achieve meaningful utility while at the same time protecting the privacy of individuals. However, differential privacy is a very strong definition, and in some settings it can seem too strong. Given the difficulties involved in getting differentially private output to all desirable queries, many have looked for ways to weaken differential privacy without losing its meaningful privacy guarantees.
Here we discuss two such weakenings. The first is computational differential privacy, originally defined by Mironov et al. We find the promise of this weakening to be limited. We show two results that severely curtail the potential for computationally private mechanisms to add any utility over those that achieve standard differential privacy when working in the standard setting with all data held by a single entity.
We then propose our own weakening, coupled-worlds privacy. This definition is meant to capture the cases where reasonable bounds can be placed on the adversary's certainty about the data (or, equivalently, the adversary's auxiliary information). We discuss the motivation for the definition, its relationship to other definitions in the literature, and its useful properties. Coupled-worlds privacy is actually a framework with which specific definitions can be instantiated, and we discuss a particular instantiation, distributional differential privacy, which we believe is of particular interest.
Having introduced this definition, we then seek new distributionally differentially private query algorithms that can release useful information without the need to add noise, as is necessary when satisfying differential privacy. We show that one can release a variety of query output with distributional differential privacy, including histograms, sums, and least-squares regression lines.2014-01-01T00:00:00Z