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Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Recent applications in machine learning favor approximate, optimization-based inference for fast predictions, but applications to computer surrogate modeling - with an eye towards downstream tasks like Bayesian optimization and reliability analysis - demand broader uncertainty quantification (UQ). I prioritize UQ through full posterior integration in a Bayesian scheme, hinging on elliptical slice sampling of latent layers. I demonstrate how my DGP's non-stationary flexibility, combined with appropriate UQ, allows for active learning: a virtuous cycle of data acquisition and model updating that departs from traditional space-filling designs and yields more accurate surrogates for fixed simulation effort. I propose new sequential design schemes that rely on optimization of acquisition criteria through evaluation of strategically allocated candidates instead of numerical optimizations, with a motivating application to contour location in an aeronautics simulation. Alternatively, when simulation runs are cheap and readily available, large datasets present a challenge for full DGP posterior integration due to cubic scaling bottlenecks. For this case I introduce the Vecchia approximation, popular for ordinary GPs in spatial data settings. I show that Vecchia-induced sparsity of Cholesky factors allows for linear computational scaling without compromising DGP accuracy or UQ. I vet both active learning and Vecchia-approximated DGPs on numerous illustrative examples and real computer experiments. I provide open-source implementations in the "deepgp" package for R on CRAN. / Doctor of Philosophy / Scientific research hinges on experimentation, yet direct experimentation is often impossible or infeasible (practically, financially, or ethically). For example, engineers designing satellites are interested in how the shape of the satellite affects its movement in space. They cannot create whole suites of differently shaped satellites, send them into orbit, and observe how they move. Instead they rely on carefully developed computer simulations. The complexity of such computer simulations necessitates a statistical model, termed a "surrogate", that is able to generate predictions in place of actual evaluations of the simulator (which may take days or weeks to run). Gaussian processes (GPs) are a common statistical modeling choice because they provide nonlinear predictions with thorough estimates of uncertainty, but they are limited in their flexibility. Deep Gaussian processes (DGPs) offer a more flexible alternative while still reaping the benefits of traditional GPs. I provide an implementation of DGP surrogates that prioritizes prediction accuracy and estimates of uncertainty. For computer simulations that are very costly to run, I provide a method of sequentially selecting input configurations to maximize learning from a fixed budget of simulator evaluations. I propose novel methods for selecting input configurations when the goal is to optimize the response or identify regions that correspond to system "failures". When abundant simulation evaluations are available, I provide an approximation which allows for faster DGP model fitting without compromising predictive power. I thoroughly vet my methods on both synthetic "toy" datasets and real aeronautic computer experiments.

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The modeling of spatio-temporal and multivariate spatial random fields has been an important and growing area of research due to the increasing availability of spacetime-referenced data in a large number of scientific applications. In geostatistics, the covariance function plays a crucial role in describing the spatio-temporal dependence in the data and is key to statistical modeling, inference, stochastic simulation and prediction. Therefore, the development of flexible covariance models, which can accomodate the inherent variability of the real data, is necessary for an advantageous modeling of random fields. This thesis is composed of four significant contributions in the development and applications of new covariance models for stationary multivariate spatial processes, and nonstationary spatial and spatio-temporal processes. The first focus of the thesis is on modeling of stationary multivariate spatial random fields through flexible multivariate covariance functions. Chapter 2 proposes a semiparametric approach for multivariate covariance function estimation with flexible specification of the cross-covariance functions via their spectral representations. The proposed method is applied to model and predict the bivariate data of particulate matter concentration (PM2.5) and wind speed (WS) in the United States. Chapter 3 introduces a parametric class of multivariate covariance functions with asymmetric cross-covariance functions. The proposed covariance model is applied to analyze the asymmetry and perform prediction in a trivariate data of PM2.5, WS and relative humidity (RH) in the United States. The second focus of the thesis is on nonstationary spatial and spatio-temporal random fields. Chapter 4 presents a space deformation method which imparts nonstationarity to any stationary covariance function. The proposed method utilizes the functional data registration algorithm and classical multidimensional scaling to estimate the spatial deformation. The application of the proposed method is demonstrated on a precipitation data. Finally, chapter 5 proposes a parametric class of time-varying spatio-temporal covariance functions, which are nonstationary in time. The proposed class is a time-varying generalization of an existing nonseparable stationary class of spatio-temporal covariance functions. The proposed time-varying model is then used to study the seasonality effect and perform space-time predictions in the daily PM2.5 data from Oregon, United States.

The optic tectum of the leopard frog has long been known to process visual information about prey and looming threats, stimuli characterized by their movement in the visual field. However, atectal frogs can still respond to the stationary visual environment, which therefore constitutes a separate visual subsystem in the frog. The present work seeks to characterize the stationary visual environment module in the leopard frog, beginning with the hypothesis that this module is located in the anterior thalamus, among two retinorecipient neuropil regions known as neuropil of Bellonci (NB) and corpus geniculatum (CG). First, the puzzle of how a stationary frog can see the stationary environment, in the absence of the eye movements necessary for persistence of vision, is resolved, as we show that whole-head movements caused by the frog's respiratory cycles keep the retinal image in motion. Next, the stationary visual environment system is evaluated along behavioral, anatomic, and physiological lines, and connections to other brain areas are elucidated. When the anterior thalamic visual center is disconnected, frogs show behavioral impairments in visually navigating the stationary world. Under electrophysiological probing, neurons in the NB/CG region show response properties consistent with their proposed role in processing information about the stationary visual environment: they respond to light/dark and color information, as well as reverse-engineered "stationary" stimuli (reproducing the movement on the retina of the visual backdrop caused by the frog's breathing movements), and they do not habituate. We show that there is no visuotopic map in the anterior thalamus but rather a nasal-ward constriction in the receptive fields of progressively more caudal cell groups in the NB/CG region. Furthermore, each side of the anterior thalamic visual region receives information from only the contralateral half of the visual field, as defined by the visual midline, resulting from a pattern of partial crossing over of optic nerve fibers that is also seen in the mammalian thalamic visual system, a commonality with unknown evolutionary implications. We show that the anterior thalamic visual region shares reciprocal connections with the same area on the opposite side of the brain, as well as with the posterior thalamus on both sides; there is also an anterograde ipsilateral projection from the NB/CG toward the medulla and presumably pre-motor areas. / Biology

In this dissertation, a variable selection method for spatial data is developed. It is assumed that the spatial process is non-stationary as a whole but is piece-wise stationary. The pieces where the spatial process is stationary are called regions. The variable selection approach accounts for two sources of correlation: (1) the spatial correlation of the data within the regions, and (2) the correlation of adjacent regions. The variable selection is carried out by including indicator variables that characterize the significance of the regression coefficients. The Ising distribution as prior for the vector of indicator variables, models the dependence of adjacent regions. We present a case study on brook trout data where the response of interest is the presence/absence of the fish at sites in the eastern United States. We find that the method outperforms the case of the probit regression where the spatial field is assumed stationary and isotropic. Additionally, the method outperformed the case where multiple regions are assumed independent of their neighbors. / Ph. D.

Advances in micro-electro-mechanical-systems (MEMS) along with nanotechnology based methods have enabled the miniaturization of analytical chemistry instrumentation. The broader aim is to provide a portable, low-cost, and low-power platform for the real-time detection and identification of organic compounds in a wide variety of applications. A benchtop gas chromatography (GC) system is considered a gold standard for chemical analysis by analytical chemists. Similarly, miniaturization of key GC components (preconcentrator, separation column, detector, and pumps) using micro- and nanotechnology based techniques is an on-going research field. This dissertation specifically deals with the design, fabrication, coating, and chromatographic testing of microfabricated separation columns for GC. This work can be broadly categorized into three research areas: design and development of new column designs, introduction of new stationary phases and the development of novel fabrication methodologies for integrating functionalized thin-film into microchannels for chromatographic separations. As a part of this research, two high performance new micro column designs namely width-modulated and high-density semi-packed columns are introduced for the first time. Similarly, two new types of functionalized stationary phases are also demonstrated i.e. a highly stable and homogenous silica nanoparticles coating deposited using a layer-by-layer self-assembly scheme and a highly conformal functionalized thin aluminum oxide film deposited using atomic layer deposition. Moreover, novel thin-film patterning methods using different microfabrication technologies are also demonstrated for high-aspect ratio multicapillary and semi-packed columns. / Ph. D.

No / Streptococcus agalactiae is a major neonatal pathogen that is able to colonise various host environments and is associated with both gastrointestinal and vaginal maternal carriage. Maternal vaginal carriage represents the major source for transmission of S. agalactiae to the foetus/neonate and thus is a significant risk factor for neonatal disease. In order to understand factors influencing maternal carriage we have investigated growth and long term survival of S. agalactiae under conditions of low pH and nutrient stress in vitro. Surprisingly, given that vaginal pH is normally <4.5, S. agalactiae was found to survive poorly at low pH and failed to grow at pH 4.3. However, biofilm growth, although also reduced at low pH, was shown to enhance survival of S. agalactiae. Proteomic analysis identified 26 proteins that were more abundant under nutrient stress conditions (extended stationary phase), including a RelE family protein, a universal stress protein family member and four proteins that belong to the Gls24 (PF03780) stress protein family. Cumulatively, these data indicate that novel mechanisms are likely to operate that allow S. agalactiae survival at low pH and under nutrient stress during maternal vaginal colonisation and/or that the bacteria may access a more favourable microenvironment at the vaginal mucosa. As current in vitro models for S. agalactiae growth appear unsatisfactory, novel methods need to be developed to study streptococcal colonisation under physiologically-relevant conditions.