Longitudinal Data Analysis and Time Series Commons^™

Leveraging Deep Learning Recurrence And Attention Mechanisms For Flood Forecasting And Assessment, Elnaz Heidari

All Dissertations

Predicting how much water will flow in rivers and streams is important for managing floods, water supply, and the environment. Traditionally, government agencies have used complex models, such as the National Water Model (NWM), which simulate how much water moves through landscapes using physical laws and real-world data. However, recent advances in Artificial Intelligence (AI) have enabled new ways to make these predictions. This research explored whether AI-based models could predict river discharge more accurately. These AI models learn patterns from past data instead of relying only on physical rules. To find out how well they work, the AI models …

Efficient Fully Bayesian Approaches To Brain Activity Mapping With Complex-Valued Fmri Data: Analysis Of Real And Imaginary Components In A Cartesian Model And Extension To Magnitude And Phase In A Polar Model, Zhengxin Wang

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Functional magnetic resonance imaging (fMRI) plays a crucial role in neuroimaging, enabling the exploration of brain activity through complex-valued signals. Traditional fMRI analyses have largely focused on magnitude information, often overlooking the potential insights offered by phase data, and therefore, lead to underutilization of available data and flawed statistical assumptions. This dissertation proposes two efficient, fully Bayesian approaches for the analysis of complex-valued functional magnetic resonance imaging (cv-fMRI) time series.

Chapter 2 introduces the model, referred to as CV-sSGLMM, using the real and imaginary components of cv-fMRI data and sparse spatial generalized linear mixed model prior. This model extends the …

Estimating Financial And Environmental Risk: Some New Developments And Comparison Study., Fnu Kamronnaher

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This dissertation delves into the concept of risk, specifically focusing on two prominent categories: financial risk and environmental risk.

Financial risk is the probability of unfavorable outcomes of an investment while environmental risk refers to the possible harm to the environment resulting from extreme weather events. More specifically, risk is the high (low) quantiles of the distribution of variables of interest. \\ To quantify and assess uncertainties in financial and environmental risk, robust and reliable methodologies are needed. The aim of this dissertation is to develop some risk assessment methods and compare them with the widely used methodologies in both …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

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Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Statistical Methods For Modern Threats, Brandon Lumsden

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More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research …

Penalized Estimation Of Autocorrelation, Xiyan Tan

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This dissertation explored the idea of penalized method in estimating the autocorrelation (ACF) and partial autocorrelation (PACF) in order to solve the problem that the sample (partial) autocorrelation underestimates the magnitude of (partial) autocorrelation in stationary time series. Although finite sample bias corrections can be found under specific assumed models, no general formulae are available. We introduce a novel penalized M-estimator for (partial) autocorrelation, with the penalty pushing the estimator toward a target selected from the data. This both encapsulates and differs from previous attempts at penalized estimation for autocorrelation, which shrink the estimator toward the target value of zero. …