Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

Determination of Biomolecular Interdomain Motions using Nuclear Magnetic Resonance

Biological macromolecules can rearrange interdomain orientations when binding to various partners. Interdomain dynamics serve as a molecular mechanism to guide the transitions between orientations. However, our understanding of interdomain dynamics is limited because a useful description of interdomain motions requires an estimate of the probabilities of interdomain conformations, increasing complexity of the problem.

Staphylococcal protein A (SpA) has five tandem protein-binding domains and four interdomain linkers. The domains enable Staphylococcus aureus to evade the host immune system by binding to multiple host proteins including antibodies. Here, I present a study of the interdomain motions of two adjacent domains in SpA. NMR spin relaxation experiments identified a 6-residue flexible interdomain linker and interdomain motions. To quantify the anisotropy of the distribution of interdomain orientations, we measured residual dipolar couplings (RDCs) from the two domains with multiple alignments. The N-terminal domain was directly aligned by a lanthanide ion and not influenced by interdomain motions, so it acted as a reference frame to achieve motional decoupling. We also applied {\it de novo} methods to extract spatial dynamic information from RDCs and represent interdomain motions as a continuous distribution on the 3D rotational space. Significant anisotropy was observed in the distribution, indicating the motion populates some interdomain orientations more than others. Statistical thermodynamic analysis of the observed orientational distribution suggests that it is among the energetically most favorable orientational distributions for binding to antibodies. Thus, the affinity is enhanced by a pre-posed distribution of interdomain orientations while maintaining the flexibility required for function.

The protocol described above can be applied to other biological systems in general. Protein molecule calmodulin and RNA molecule trans-activation response element (TAR) also have intensive interdomain motions with relative small intradomain dynamics. Their interdomain motions were studied using our method based on published RDC data. Our results were consistent with literature results in general. The differences could be due to previous studies' use of physical models, which contain assumptions about potential energy and thus introduced non-experimental information into the interpretations.

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.

Data to Decision in a Dynamic Ocean: Robust Species Distribution Models and Spatial Decision Frameworks

Human use of the oceans is increasingly in conflict with conservation of endangered species. Methods for managing the spatial and temporal placement of industries such as military, fishing, transportation and offshore energy, have historically been post hoc; i.e. the time and place of human activity is often already determined before assessment of environmental impacts. In this dissertation, I build robust species distribution models in two case study areas, US Atlantic (Best et al. 2012) and British Columbia (Best et al. 2015), predicting presence and abundance respectively, from scientific surveys. These models are then applied to novel decision frameworks for preemptively suggesting optimal placement of human activities in space and time to minimize ecological impacts: siting for offshore wind energy development, and routing ships to minimize risk of striking whales. Both decision frameworks relate the tradeoff between conservation risk and industry profit with synchronized variable and map views as online spatial decision support systems.

For siting offshore wind energy development (OWED) in the U.S. Atlantic (chapter 4), bird density maps are combined across species with weights of OWED sensitivity to collision and displacement and 10 km2 sites are compared against OWED profitability based on average annual wind speed at 90m hub heights and distance to transmission grid. A spatial decision support system enables toggling between the map and tradeoff plot views by site. A selected site can be inspected for sensitivity to a cetaceans throughout the year, so as to capture months of the year which minimize episodic impacts of pre-operational activities such as seismic airgun surveying and pile driving.

Routing ships to avoid whale strikes (chapter 5) can be similarly viewed as a tradeoff, but is a different problem spatially. A cumulative cost surface is generated from density surface maps and conservation status of cetaceans, before applying as a resistance surface to calculate least-cost routes between start and end locations, i.e. ports and entrance locations to study areas. Varying a multiplier to the cost surface enables calculation of multiple routes with different costs to conservation of cetaceans versus cost to transportation industry, measured as distance. Similar to the siting chapter, a spatial decisions support system enables toggling between the map and tradeoff plot view of proposed routes. The user can also input arbitrary start and end locations to calculate the tradeoff on the fly.

Essential to the input of these decision frameworks are distributions of the species. The two preceding chapters comprise species distribution models from two case study areas, U.S. Atlantic (chapter 2) and British Columbia (chapter 3), predicting presence and density, respectively. Although density is preferred to estimate potential biological removal, per Marine Mammal Protection Act requirements in the U.S., all the necessary parameters, especially distance and angle of observation, are less readily available across publicly mined datasets.

In the case of predicting cetacean presence in the U.S. Atlantic (chapter 2), I extracted datasets from the online OBIS-SEAMAP geo-database, and integrated scientific surveys conducted by ship (n=36) and aircraft (n=16), weighting a Generalized Additive Model by minutes surveyed within space-time grid cells to harmonize effort between the two survey platforms. For each of 16 cetacean species guilds, I predicted the probability of occurrence from static environmental variables (water depth, distance to shore, distance to continental shelf break) and time-varying conditions (monthly sea-surface temperature). To generate maps of presence vs. absence, Receiver Operator Characteristic (ROC) curves were used to define the optimal threshold that minimizes false positive and false negative error rates. I integrated model outputs, including tables (species in guilds, input surveys) and plots (fit of environmental variables, ROC curve), into an online spatial decision support system, allowing for easy navigation of models by taxon, region, season, and data provider.

For predicting cetacean density within the inner waters of British Columbia (chapter 3), I calculated density from systematic, line-transect marine mammal surveys over multiple years and seasons (summer 2004, 2005, 2008, and spring/autumn 2007) conducted by Raincoast Conservation Foundation. Abundance estimates were calculated using two different methods: Conventional Distance Sampling (CDS) and Density Surface Modelling (DSM). CDS generates a single density estimate for each stratum, whereas DSM explicitly models spatial variation and offers potential for greater precision by incorporating environmental predictors. Although DSM yields a more relevant product for the purposes of marine spatial planning, CDS has proven to be useful in cases where there are fewer observations available for seasonal and inter-annual comparison, particularly for the scarcely observed elephant seal. Abundance estimates are provided on a stratum-specific basis. Steller sea lions and harbour seals are further differentiated by ‘hauled out’ and ‘in water’. This analysis updates previous estimates (Williams & Thomas 2007) by including additional years of effort, providing greater spatial precision with the DSM method over CDS, novel reporting for spring and autumn seasons (rather than summer alone), and providing new abundance estimates for Steller sea lion and northern elephant seal. In addition to providing a baseline of marine mammal abundance and distribution, against which future changes can be compared, this information offers the opportunity to assess the risks posed to marine mammals by existing and emerging threats, such as fisheries bycatch, ship strikes, and increased oil spill and ocean noise issues associated with increases of container ship and oil tanker traffic in British Columbia’s continental shelf waters.

Starting with marine animal observations at specific coordinates and times, I combine these data with environmental data, often satellite derived, to produce seascape predictions generalizable in space and time. These habitat-based models enable prediction of encounter rates and, in the case of density surface models, abundance that can then be applied to management scenarios. Specific human activities, OWED and shipping, are then compared within a tradeoff decision support framework, enabling interchangeable map and tradeoff plot views. These products make complex processes transparent for gaming conservation, industry and stakeholders towards optimal marine spatial management, fundamental to the tenets of marine spatial planning, ecosystem-based management and dynamic ocean management.

Dynamic Life Cycle Assessment Modeling Approaches for Transboundary Energy Feedstocks

The rise of the twenty-first century has seen the further increase in the industrialization of Earth’s resources, as society aims to meet the needs of a growing population while still protecting our environmental and natural resources. The advent of the industrial bioeconomy – which encompasses the production of renewable biological resources and their conversion into food, feed, and bio-based products – is seen as an important step in transition towards sustainable development and away from fossil fuels. One sector of the industrial bioeconomy which is rapidly being expanded is the use of biobased feedstocks in electricity production as an alternative to coal, especially in the European Union.

As bioeconomy policies and objectives increasingly appear on political agendas, there is a growing need to quantify the impacts of transitioning from fossil fuel-based feedstocks to renewable biological feedstocks. Specifically, there is a growing need to conduct a systems analysis and potential risks of increasing the industrial bioeconomy, given that the flows within it are inextricably linked. Furthermore, greater analysis is needed into the consequences of shifting from fossil fuels to renewable feedstocks, in part through the use of life cycle assessment modeling to analyze impacts along the entire value chain.

To assess the emerging nature of the industrial bioeconomy, three objectives are addressed: (1) quantify the global industrial bioeconomy, linking the use of primary resources with the ultimate end product; (2) quantify the impacts of the expaning wood pellet energy export market of the Southeastern United States; (3) conduct a comparative life cycle assessment, incorporating the use of dynamic life cycle assessment, of replacing coal-fired electricity generation in the United Kingdom with wood pellets that are produced in the Southeastern United States.

To quantify the emergent industrial bioeconomy, an empirical analysis was undertaken. Existing databases from multiple domestic and international agencies was aggregated and analyzed in Microsoft Excel to produce a harmonized dataset of the bioeconomy. First-person interviews, existing academic literature, and industry reports were then utilized to delineate the various intermediate and end use flows within the bioeconomy. The results indicate that within a decade, the industrial use of agriculture has risen ten percent, given increases in the production of bioenergy and bioproducts. The underlying resources supporting the emergent bioeconomy (i.e., land, water, and fertilizer use) were also quantified and included in the database.

Following the quantification of the existing bioeconomy, an in-depth analysis of the bioenergy sector was conducted. Specifically, the focus was on quantifying the impacts of the emergent wood pellet export sector that has rapidly developed in recent years in the Southeastern United States. A cradle-to-gate life cycle assessment was conducted in order to quantify supply chain impacts from two wood pellet production scenarios: roundwood and sawmill residues. For reach of the nine impact categories assessed, wood pellet production from sawmill residues resulted in higher values, ranging from 10-31% higher.

The analysis of the wood pellet sector was then expanded to include the full life cycle (i.e., cradle-to-grave). In doing to, the combustion of biogenic carbon and the subsequent timing of emissions were assessed by incorporating dynamic life cycle assessment modeling. Assuming immediate carbon neutrality of the biomass, the results indicated an 86% reduction in global warming potential when utilizing wood pellets as compared to coal for electricity production in the United Kingdom. When incorporating the timing of emissions, wood pellets equated to a 75% or 96% reduction in carbon dioxide emissions, depending upon whether the forestry feedstock was considered to be harvested or planted in year one, respectively.

Finally, a policy analysis of renewable energy in the United States was conducted. Existing coal-fired power plants in the Southeastern United States were assessed in terms of incorporating the co-firing of wood pellets. Co-firing wood pellets with coal in existing Southeastern United States power stations would result in a nine percent reduction in global warming potential.

Spatial Relationships among Hydroacoustic, Hydrographic and Top Predator Patterns: Cetacean Distributions in the Mid-Atlantic Bight

Effective conservation and management of top predators requires a comprehensive understanding of their distributions and of the underlying biological and physical processes that affect these distributions. The Mid-Atlantic Bight shelf break system is a dynamic and productive region where at least 32 species of cetaceans have been recorded through various systematic and opportunistic marine mammal surveys from the 1970s through 2012. My dissertation characterizes the spatial distribution and habitat of cetaceans in the Mid-Atlantic Bight shelf break system by utilizing marine mammal line-transect survey data, synoptic multi-frequency active acoustic data, and fine-scale hydrographic data collected during the 2011 summer Atlantic Marine Assessment Program for Protected Species (AMAPPS) survey. Although studies describing cetacean habitat and distributions have been previously conducted in the Mid-Atlantic Bight, my research specifically focuses on the shelf break region to elucidate both the physical and biological processes that influence cetacean distribution patterns within this cetacean hotspot.

In Chapter One I review biologically important areas for cetaceans in the Atlantic waters of the United States. I describe the study area, the shelf break region of the Mid-Atlantic Bight, in terms of the general oceanography, productivity and biodiversity. According to recent habitat-based cetacean density models, the shelf break region is an area of high cetacean abundance and density, yet little research is directed at understanding the mechanisms that establish this region as a cetacean hotspot.

In Chapter Two I present the basic physical principles of sound in water and describe the methodology used to categorize opportunistically collected multi-frequency active acoustic data using frequency responses techniques. Frequency response classification methods are usually employed in conjunction with net-tow data, but the logistics of the 2011 AMAPPS survey did not allow for appropriate net-tow data to be collected. Biologically meaningful information can be extracted from acoustic scattering regions by comparing the frequency response curves of acoustic regions to theoretical curves of known scattering models. Using the five frequencies on the EK60 system (18, 38, 70, 120, and 200 kHz), three categories of scatterers were defined: fish-like (with swim bladder), nekton-like (e.g., euphausiids), and plankton-like (e.g., copepods). I also employed a multi-frequency acoustic categorization method using three frequencies (18, 38, and 120 kHz) that has been used in the Gulf of Maine and Georges Bank which is based the presence or absence of volume backscatter above a threshold. This method is more objective than the comparison of frequency response curves because it uses an established backscatter value for the threshold. By removing all data below the threshold, only strong scattering information is retained.

In Chapter Three I analyze the distribution of the categorized acoustic regions of interest during the daytime cross shelf transects. Over all transects, plankton-like acoustic regions of interest were detected most frequently, followed by fish-like acoustic regions and then nekton-like acoustic regions. Plankton-like detections were the only significantly different acoustic detections per kilometer, although nekton-like detections were only slightly not significant. Using the threshold categorization method by Jech and Michaels (2006) provides a more conservative and discrete detection of acoustic scatterers and allows me to retrieve backscatter values along transects in areas that have been categorized. This provides continuous data values that can be integrated at discrete spatial increments for wavelet analysis. Wavelet analysis indicates significant spatial scales of interest for fish-like and nekton-like acoustic backscatter range from one to four kilometers and vary among transects.

In Chapter Four I analyze the fine scale distribution of cetaceans in the shelf break system of the Mid-Atlantic Bight using corrected sightings per trackline region, classification trees, multidimensional scaling, and random forest analysis. I describe habitat for common dolphins, Risso’s dolphins and sperm whales. From the distribution of cetacean sightings, patterns of habitat start to emerge: within the shelf break region of the Mid-Atlantic Bight, common dolphins were sighted more prevalently over the shelf while sperm whales were more frequently found in the deep waters offshore and Risso’s dolphins were most prevalent at the shelf break. Multidimensional scaling presents clear environmental separation among common dolphins and Risso’s dolphins and sperm whales. The sperm whale random forest habitat model had the lowest misclassification error (0.30) and the Risso’s dolphin random forest habitat model had the greatest misclassification error (0.37). Shallow water depth (less than 148 meters) was the primary variable selected in the classification model for common dolphin habitat. Distance to surface density fronts and surface temperature fronts were the primary variables selected in the classification models to describe Risso’s dolphin habitat and sperm whale habitat respectively. When mapped back into geographic space, these three cetacean species occupy different fine-scale habitats within the dynamic Mid-Atlantic Bight shelf break system.

In Chapter Five I present a summary of the previous chapters and present potential analytical steps to address ecological questions pertaining the dynamic shelf break region. Taken together, the results of my dissertation demonstrate the use of opportunistically collected data in ecosystem studies; emphasize the need to incorporate middle trophic level data and oceanographic features into cetacean habitat models; and emphasize the importance of developing more mechanistic understanding of dynamic ecosystems.

Sensor Planning for Bayesian Nonparametric Target Modeling

Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.

Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.

Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with

little or no prior knowledge

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Dynamic neural networks supporting memory retrieval.

How do separate neural networks interact to support complex cognitive processes such as remembrance of the personal past? Autobiographical memory (AM) retrieval recruits a consistent pattern of activation that potentially comprises multiple neural networks. However, it is unclear how such large-scale neural networks interact and are modulated by properties of the memory retrieval process. In the present functional MRI (fMRI) study, we combined independent component analysis (ICA) and dynamic causal modeling (DCM) to understand the neural networks supporting AM retrieval. ICA revealed four task-related components consistent with the previous literature: 1) medial prefrontal cortex (PFC) network, associated with self-referential processes, 2) medial temporal lobe (MTL) network, associated with memory, 3) frontoparietal network, associated with strategic search, and 4) cingulooperculum network, associated with goal maintenance. DCM analysis revealed that the medial PFC network drove activation within the system, consistent with the importance of this network to AM retrieval. Additionally, memory accessibility and recollection uniquely altered connectivity between these neural networks. Recollection modulated the influence of the medial PFC on the MTL network during elaboration, suggesting that greater connectivity among subsystems of the default network supports greater re-experience. In contrast, memory accessibility modulated the influence of frontoparietal and MTL networks on the medial PFC network, suggesting that ease of retrieval involves greater fluency among the multiple networks contributing to AM. These results show the integration between neural networks supporting AM retrieval and the modulation of network connectivity by behavior.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

Influence of the thalamus on spatial visual processing in frontal cortex.

Each of our movements activates our own sensory receptors, and therefore keeping track of self-movement is a necessary part of analysing sensory input. One way in which the brain keeps track of self-movement is by monitoring an internal copy, or corollary discharge, of motor commands. This concept could explain why we perceive a stable visual world despite our frequent quick, or saccadic, eye movements: corollary discharge about each saccade would permit the visual system to ignore saccade-induced visual changes. The critical missing link has been the connection between corollary discharge and visual processing. Here we show that such a link is formed by a corollary discharge from the thalamus that targets the frontal cortex. In the thalamus, neurons in the mediodorsal nucleus relay a corollary discharge of saccades from the midbrain superior colliculus to the cortical frontal eye field. In the frontal eye field, neurons use corollary discharge to shift their visual receptive fields spatially before saccades. We tested the hypothesis that these two components-a pathway for corollary discharge and neurons with shifting receptive fields-form a circuit in which the corollary discharge drives the shift. First we showed that the known spatial and temporal properties of the corollary discharge predict the dynamic changes in spatial visual processing of cortical neurons when saccades are made. Then we moved from this correlation to causation by isolating single cortical neurons and showing that their spatial visual processing is impaired when corollary discharge from the thalamus is interrupted. Thus the visual processing of frontal neurons is spatiotemporally matched with, and functionally dependent on, corollary discharge input from the thalamus. These experiments establish the first link between corollary discharge and visual processing, delineate a brain circuit that is well suited for mediating visual stability, and provide a framework for studying corollary discharge in other sensory systems.

Coding Strategies and Implementations of Compressive Sensing

This dissertation studies the coding strategies of computational imaging to overcome the limitation of conventional sensing techniques. The information capacity of conventional sensing is limited by the physical properties of optics, such as aperture size, detector pixels, quantum efficiency, and sampling rate. These parameters determine the spatial, depth, spectral, temporal, and polarization sensitivity of each imager. To increase sensitivity in any dimension can significantly compromise the others.

This research implements various coding strategies subject to optical multidimensional imaging and acoustic sensing in order to extend their sensing abilities. The proposed coding strategies combine hardware modification and signal processing to exploiting bandwidth and sensitivity from conventional sensors. We discuss the hardware architecture, compression strategies, sensing process modeling, and reconstruction algorithm of each sensing system.

Optical multidimensional imaging measures three or more dimensional information of the optical signal. Traditional multidimensional imagers acquire extra dimensional information at the cost of degrading temporal or spatial resolution. Compressive multidimensional imaging multiplexes the transverse spatial, spectral, temporal, and polarization information on a two-dimensional (2D) detector. The corresponding spectral, temporal and polarization coding strategies adapt optics, electronic devices, and designed modulation techniques for multiplex measurement. This computational imaging technique provides multispectral, temporal super-resolution, and polarization imaging abilities with minimal loss in spatial resolution and noise level while maintaining or gaining higher temporal resolution. The experimental results prove that the appropriate coding strategies may improve hundreds times more sensing capacity.

Human auditory system has the astonishing ability in localizing, tracking, and filtering the selected sound sources or information from a noisy environment. Using engineering efforts to accomplish the same task usually requires multiple detectors, advanced computational algorithms, or artificial intelligence systems. Compressive acoustic sensing incorporates acoustic metamaterials in compressive sensing theory to emulate the abilities of sound localization and selective attention. This research investigates and optimizes the sensing capacity and the spatial sensitivity of the acoustic sensor. The well-modeled acoustic sensor allows localizing multiple speakers in both stationary and dynamic auditory scene; and distinguishing mixed conversations from independent sources with high audio recognition rate.

Essays on the Dynamic Decisions of Homeowners and Retailers

Urban problems have several features that make them inherently dynamic. Large transaction costs all but guarantee that homeowners will do their best to consider how a neighborhood might change before buying a house. Similarly, stores face large sunk costs when opening, and want to be sure that their investment will pay off in the long run. In line with those concerns, different areas of Economics have made recent advances in modeling those questions within a dynamic framework. This dissertation contributes to those efforts.

Chapter 2 discusses how to model an agent’s location decision when the agent must learn about an exogenous amenity that may be changing over time. The model is applied to estimating the marginal willingness to pay to avoid crime, in which agents are learning about the crime rate in a neighborhood, and the crime rate can change in predictable (Markovian) ways.

Chapters 3 and 4 concentrate on location decision problems when there are externalities between decision makers. Chapter 3 focuses on the decision of business owners to open a store, when its demand is a function of other nearby stores, either through competition, or through spillovers on foot traffic. It uses a dynamic model in continuous time to model agents’ decisions. A particular challenge is isolating the contribution of spillovers from the contribution of other unobserved neighborhood attributes that could also lead to agglomeration. A key contribution of this chapter is showing how we can use information on storefront ownership to help separately identify spillovers.

Finally, chapter 4 focuses on a class of models in which families prefer to live

close to similar neighbors. This chapter provides the first simulation of such a model in which agents are forward looking, and shows that this leads to more segregation than it would have been observed with myopic agents, which is the standard in this literature. The chapter also discusses several extensions of the model that can be used to investigate relevant questions such as the arrival of a large contingent high skilled tech workers in San Francisco, the immigration of hispanic families to several southern American cities, large changes in local amenities, such as the construction of magnet schools or metro stations, and the flight of wealthy residents from cities in the Rust belt, such as Detroit.

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.

RNA Virus Evolution: a Cross-scale, Disease Dynamic Perspective

RNA viruses are an important cause of global morbidity and mortality. The rapid evolutionary rates of RNA virus pathogens, caused by high replication rates and error-prone polymerases, can make the pathogens difficult to control. RNA viruses can undergo immune escape within their hosts and develop resistance to the treatment and vaccines we design to fight them. Understanding the spread and evolution of RNA pathogens is essential for reducing human suffering. In this dissertation, I make use of the rapid evolutionary rate of viral pathogens to answer several questions about how RNA viruses spread and evolve. To address each of the questions, I link mathematical techniques for modeling viral population dynamics with phylogenetic and coalescent techniques for analyzing and modeling viral genetic sequences and evolution. The first project uses multi-scale mechanistic modeling to show that decreases in viral substitution rates over the course of an acute infection, combined with the timing of infectious hosts transmitting new infections to susceptible individuals, can account for discrepancies in viral substitution rates in different host populations. The second project combines coalescent models with within-host mathematical models to identify driving evolutionary forces in chronic hepatitis C virus infection. The third project compares the effects of intrinsic and extrinsic viral transmission rate variation on viral phylogenies.