Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Stimulus Integration and Parsing in the Primate Auditory Midbrain

Integrating information from multiple sources is a crucial function of the brain. Examples of such integration include multiple stimuli of different modalties, such as visual and auditory, multiple stimuli of the same modality, such as auditory and auditory, and integrating stimuli from the sensory organs (i.e. ears) with stimuli delivered from brain-machine interfaces.

The overall aim of this body of work is to empirically examine stimulus integration in these three domains to inform our broader understanding of how and when the brain combines information from multiple sources.

First, I examine visually-guided auditory, a problem with implications for the general problem in learning of how the brain determines what lesson to learn (and what lessons not to learn). For example, sound localization is a behavior that is partially learned with the aid of vision. This process requires correctly matching a visual location to that of a sound. This is an intrinsically circular problem when sound location is itself uncertain and the visual scene is rife with possible visual matches. Here, we develop a simple paradigm using visual guidance of sound localization to gain insight into how the brain confronts this type of circularity. We tested two competing hypotheses. 1: The brain guides sound location learning based on the synchrony or simultaneity of auditory-visual stimuli, potentially involving a Hebbian associative mechanism. 2: The brain uses a ‘guess and check’ heuristic in which visual feedback that is obtained after an eye movement to a sound alters future performance, perhaps by recruiting the brain’s reward-related circuitry. We assessed the effects of exposure to visual stimuli spatially mismatched from sounds on performance of an interleaved auditory-only saccade task. We found that when humans and monkeys were provided the visual stimulus asynchronously with the sound but as feedback to an auditory-guided saccade, they shifted their subsequent auditory-only performance toward the direction of the visual cue by 1.3-1.7 degrees, or 22-28% of the original 6 degree visual-auditory mismatch. In contrast when the visual stimulus was presented synchronously with the sound but extinguished too quickly to provide this feedback, there was little change in subsequent auditory-only performance. Our results suggest that the outcome of our own actions is vital to localizing sounds correctly. Contrary to previous expectations, visual calibration of auditory space does not appear to require visual-auditory associations based on synchrony/simultaneity.

My next line of research examines how electrical stimulation of the inferior colliculus influences perception of sounds in a nonhuman primate. The central nucleus of the inferior colliculus is the major ascending relay of auditory information before it reaches the forebrain, and thus an ideal target for understanding low-level information processing prior to the forebrain, as almost all auditory signals pass through the central nucleus of the inferior colliculus before reaching the forebrain. Thus, the inferior colliculus is the ideal structure to examine to understand the format of the inputs into the forebrain and, by extension, the processing of auditory scenes that occurs in the brainstem. Therefore, the inferior colliculus was an attractive target for understanding stimulus integration in the ascending auditory pathway.

Moreover, understanding the relationship between the auditory selectivity of neurons and their contribution to perception is critical to the design of effective auditory brain prosthetics. These prosthetics seek to mimic natural activity patterns to achieve desired perceptual outcomes. We measured the contribution of inferior colliculus (IC) sites to perception using combined recording and electrical stimulation. Monkeys performed a frequency-based discrimination task, reporting whether a probe sound was higher or lower in frequency than a reference sound. Stimulation pulses were paired with the probe sound on 50% of trials (0.5-80 µA, 100-300 Hz, n=172 IC locations in 3 rhesus monkeys). Electrical stimulation tended to bias the animals’ judgments in a fashion that was coarsely but significantly correlated with the best frequency of the stimulation site in comparison to the reference frequency employed in the task. Although there was considerable variability in the effects of stimulation (including impairments in performance and shifts in performance away from the direction predicted based on the site’s response properties), the results indicate that stimulation of the IC can evoke percepts correlated with the frequency tuning properties of the IC. Consistent with the implications of recent human studies, the main avenue for improvement for the auditory midbrain implant suggested by our findings is to increase the number and spatial extent of electrodes, to increase the size of the region that can be electrically activated and provide a greater range of evoked percepts.

My next line of research employs a frequency-tagging approach to examine the extent to which multiple sound sources are combined (or segregated) in the nonhuman primate inferior colliculus. In the single-sound case, most inferior colliculus neurons respond and entrain to sounds in a very broad region of space, and many are entirely spatially insensitive, so it is unknown how the neurons will respond to a situation with more than one sound. I use multiple AM stimuli of different frequencies, which the inferior colliculus represents using a spike timing code. This allows me to measure spike timing in the inferior colliculus to determine which sound source is responsible for neural activity in an auditory scene containing multiple sounds. Using this approach, I find that the same neurons that are tuned to broad regions of space in the single sound condition become dramatically more selective in the dual sound condition, preferentially entraining spikes to stimuli from a smaller region of space. I will examine the possibility that there may be a conceptual linkage between this finding and the finding of receptive field shifts in the visual system.

In chapter 5, I will comment on these findings more generally, compare them to existing theoretical models, and discuss what these results tell us about processing in the central nervous system in a multi-stimulus situation. My results suggest that the brain is flexible in its processing and can adapt its integration schema to fit the available cues and the demands of the task.

Evaluating the Impact of the Positive Choices Intervention on Substance Use, Psychological, and Care Engagement Outcomes Relevant to Current National HIV Prevention Goals

The HIV epidemic in the United States continues to be a significant public health problem, with approximately 50,000 new infections occurring each year. National public health priorities have shifted in recent years towards targeted HIV prevention efforts among people living with HIV/AIDS (PLWHA) that include: increasing engagement in and retention in care, improving HIV treatment adherence, and increasing screening for and treatment of substance use and psychological difficulties. This study evaluated the efficacy of Positive Choices (PC), a brief, care-based, theory-driven, 3-session counseling intervention for newly HIV-diagnosed men who have sex with men (MSM), in the context of current national HIV prevention priorities. The study involved secondary analysis of data from a preliminary efficacy trial of the PC intervention (n=102). Descriptive statistics examined baseline substance use, psychological characteristics and strategies, and care engagement and HIV-related biological outcomes. Generalized Estimating Equations (GEE) examined longitudinal changes in these variables by study condition. Results indicated that PC improved adherence to HIV treatment, but increased use of illicit drugs, specifically amyl nitrates and other stimulant drugs; additionally, moderation analyses indicated differences in patterns of change over time in viral load by baseline depression status. Implications of the findings and suggestions for future research are discussed.

New evidence in trauma resuscitation - is 1:1:1 the answer?

Traumatic injury is a common problem, with over five million worldwide deaths from trauma per year. An estimated 10 to 20% of these deaths are potentially preventable with better control of bleeding. Damage control resuscitation involves early delivery of plasma and platelets as a primary resuscitation approach to minimize trauma-induced coagulopathy. Plasma, red blood cell and platelet ratios of 1:1:1 appear to be the best substitution for fresh whole blood; however, the current literature consists only of survivor bias-prone observational studies.