Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Can a Broader Education Narrow the Gap? Evidence on Non-Academic Features of Schooling

Empirical studies of education programs and systems, by nature, rely upon use of student outcomes that are measurable. Often, these come in the form of test scores. However, in light of growing evidence about the long-run importance of other student skills and behaviors, the time has come for a broader approach to evaluating education. This dissertation undertakes experimental, quasi-experimental, and descriptive analyses to examine social, behavioral, and health-related mechanisms of the educational process. My overarching research question is simply, which inside- and outside-the-classroom features of schools and educational interventions are most beneficial to students in the long term? Furthermore, how can we apply this evidence toward informing policy that could effectively reduce stark social, educational, and economic inequalities?

The first study of three assesses mechanisms by which the Fast Track project, a randomized intervention in the early 1990s for high-risk children in four communities (Durham, NC; Nashville, TN; rural PA; and Seattle, WA), reduced delinquency, arrests, and health and mental health service utilization in adolescence through young adulthood (ages 12-20). A decomposition of treatment effects indicates that about a third of Fast Track’s impact on later crime outcomes can be accounted for by improvements in social and self-regulation skills during childhood (ages 6-11), such as prosocial behavior, emotion regulation and problem solving. These skills proved less valuable for the prevention of mental and physical health problems.

The second study contributes new evidence on how non-instructional investments – such as increased spending on school social workers, guidance counselors, and health services – affect multiple aspects of student performance and well-being. Merging several administrative data sources spanning the 1996-2013 school years in North Carolina, I use an instrumental variables approach to estimate the extent to which local expenditure shifts affect students’ academic and behavioral outcomes. My findings indicate that exogenous increases in spending on non-instructional services not only reduce student absenteeism and disciplinary problems (important predictors of long-term outcomes) but also significantly raise student achievement, in similar magnitude to corresponding increases in instructional spending. Furthermore, subgroup analyses suggest that investments in student support personnel such as social workers, health services, and guidance counselors, in schools with concentrated low-income student populations could go a long way toward closing socioeconomic achievement gaps.

The third study examines individual pathways that lead to high school graduation or dropout. It employs a variety of machine learning techniques, including decision trees, random forests with bagging and boosting, and support vector machines, to predict student dropout using longitudinal administrative data from North Carolina. I consider a large set of predictor measures from grades three through eight including academic achievement, behavioral indicators, and background characteristics. My findings indicate that the most important predictors include eighth grade absences, math scores, and age-for-grade as well as early reading scores. Support vector classification (with a high cost parameter and low gamma parameter) predicts high school dropout with the highest overall validity in the testing dataset at 90.1 percent followed by decision trees with boosting and interaction terms at 89.5 percent.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.