Making Sense of Noisy Data: Theory and Applications

This thesis introduces a novel and interpretable index of increase which is mathematically defined based on the distance between a given function and a set of non-increasing functions. Unlike the widely used traditional statistical methods for analyzing relationships between variables, the index does not rely on assumptions such as linearity, normality, and monotonicity, which may not be satisfied. Hence, it has the flexibility to be applied directly on pairs of data points to measure and compare non-linear, asymmetric, and non-monotonic relationships between two variables. We begin with a review of the literature and background knowledge in Chapter 2. In Chapter 3, we propose a distance-based index of increase, describe its properties in detail, and show its benefits through applying it to an educational dataset. In this way, we see the interpretability of the index of increase and how it can be applied. We also propose several modifications for different scenarios, such as subgroup analysis. Lastly, we provide a step-by-step implementation guideline for non-statistical researchers or practitioners. In Chapter 4, we investigate two extensions of the index of increase, which quantify the interchangeability between variables. We discuss the usage of them in the context of developing curricula, accompanied with extensive graphical and numerical illustrations. In Chapter 5, we introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the empirical index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision. We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic. Finally, in Chapter 6, we summarize our main results and give an outline of potential future works

Coordinated Transit Response Planning and Operations Support Tools for Mitigating Impacts of All-Hazard Emergency Events

This report summarizes current computer simulation capabilities and the availability of near-real-time data sources allowing for a novel approach of analyzing and determining optimized responses during disruptions of complex multi-agency transit system. The authors integrated a number of technologies and data sources to detect disruptive transit system performance issues, analyze the impact on overall system-wide performance, and statistically apply the likely traveler choices and responses. The analysis of unaffected transit resources and the provision of temporary resources are then analyzed and optimized to minimize overall impact of the initiating event

Nonparametric Statistical Inference with an Emphasis on Information-Theoretic Methods

This book addresses contemporary statistical inference issues when no or minimal assumptions on the nature of studied phenomenon are imposed. Information theory methods play an important role in such scenarios. The approaches discussed include various high-dimensional regression problems, time series and dependence analyses