Indiana University-Purdue University Indianapolis (IUPUI) / Spatio-temporal data is becoming very popular in the recent times, as there are large number of datasets that collect both location and temporal information in the real time. The main challenge is that extracting useful insights from such large data set is extremely complex and laborious. In this thesis, we have proposed a novel 2D technique to visualize the spatio-temporal big data. The visualization of the combined interaction between the spatial and temporal data is of high importance to uncover the insights and identify the trends within the data. Maps have been a successful way to represent the spatial information. Addition- ally, in this work, colors are used to represent the temporal data. Every data point has the time information which is converted into relevant color, based on the HSV color model. The variation in the time is represented by transition from one color to another and hence provide smooth interpolation. The proposed solution will help the user to quickly understand the data and gain insights.

Knowledge discovery on spatio-temporal datasets has attracted<br />growing interests. Recent advances on remote sensing technology mean<br />that massive amounts of spatio-temporal data are being collected,<br />and its volume keeps increasing at an ever faster pace. It becomes<br />critical to design efficient algorithms for identifying novel and<br />meaningful patterns from massive spatio-temporal datasets. Different<br />from the other data sources, this data exhibits significant<br />space-time statistical dependence, and the assumption of i.i.d. is<br />no longer valid. The exact modeling of space-time dependence will<br />render the exponential growth of model complexity as the data size<br />increases. This research focuses on the construction of efficient<br />and effective approaches using approximate inference techniques for<br />three main mining tasks, including spatial outlier detection, robust<br />spatio-temporal prediction, and novel applications to real world<br />problems.<br /><br />Spatial novelty patterns, or spatial outliers, are those data points<br />whose characteristics are markedly different from their spatial<br />neighbors. There are two major branches of spatial outlier detection<br />methodologies, which can be either global Kriging based or local<br />Laplacian smoothing based. The former approach requires the exact<br />modeling of spatial dependence, which is time extensive; and the<br />latter approach requires the i.i.d. assumption of the smoothed<br />observations, which is not statistically solid. These two approaches<br />are constrained to numerical data, but in real world applications we<br />are often faced with a variety of non-numerical data types, such as<br />count, binary, nominal, and ordinal. To summarize, the main research<br />challenges are: 1) how much spatial dependence can be eliminated via<br />Laplace smoothing; 2) how to effectively and efficiently detect<br />outliers for large numerical spatial datasets; 3) how to generalize<br />numerical detection methods and develop a unified outlier detection<br />framework suitable for large non-numerical datasets; 4) how to<br />achieve accurate spatial prediction even when the training data has<br />been contaminated by outliers; 5) how to deal with spatio-temporal<br />data for the preceding problems.<br /><br />To address the first and second challenges, we mathematically<br />validated the effectiveness of Laplacian smoothing on the<br />elimination of spatial autocorrelations. This work provides<br />fundamental support for existing Laplacian smoothing based methods.<br />We also discovered a nontrivial side-effect of Laplacian smoothing,<br />which ingests additional spatial variations to the data due to<br />convolution effects. To capture this extra variability, we proposed<br />a generalized local statistical model, and designed two fast forward<br />and backward outlier detection methods that achieve a better balance<br />between computational efficiency and accuracy than most existing<br />methods, and are well suited to large numerical spatial datasets.<br /><br />We addressed the third challenge by mapping non-numerical variables<br />to latent numerical variables via a link function, such as logit<br />function used in logistic regression, and then utilizing<br />error-buffer artificial variables, which follow a Student-t<br />distribution, to capture the large valuations caused by outliers. We<br />proposed a unified statistical framework, which integrates the<br />advantages of spatial generalized linear mixed model, robust spatial<br />linear model, reduced-rank dimension reduction, and Bayesian<br />hierarchical model. A linear-time approximate inference algorithm<br />was designed to infer the posterior distribution of the error-buffer<br />artificial variables conditioned on observations. We demonstrated<br />that traditional numerical outlier detection methods can be directly<br />applied to the estimated artificial variables for outliers<br />detection. To the best of our knowledge, this is the first<br />linear-time outlier detection algorithm that supports a variety of<br />spatial attribute types, such as binary, count, ordinal, and<br />nominal.<br /><br />To address the fourth and fifth challenges, we proposed a robust<br />version of the Spatio-Temporal Random Effects (STRE) model, namely<br />the Robust STRE (R-STRE) model. The regular STRE model is a recently<br />proposed statistical model for large spatio-temporal data that has a<br />linear order time complexity, but is not best suited for<br />non-Gaussian and contaminated datasets. This deficiency can be<br />systemically addressed by increasing the robustness of the model<br />using heavy-tailed distributions, such as the Huber, Laplace, or<br />Student-t distribution to model the measurement error, instead of<br />the traditional Gaussian. However, the resulting R-STRE model<br />becomes analytical intractable, and direct application of<br />approximate inferences techniques still has a cubic order time<br />complexity. To address the computational challenge, we reformulated<br />the prediction problem as a maximum a posterior (MAP) problem with a<br />non-smooth objection function, transformed it to a equivalent<br />quadratic programming problem, and developed an efficient<br />interior-point numerical algorithm with a near linear order<br />complexity. This work presents the first near linear time robust<br />prediction approach for large spatio-temporal datasets in both<br />offline and online cases. / Ph. D.

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The statistical modeling of spatial extreme events, augmented by graphical models, provides a comprehensive framework for the development of techniques and models to describe natural phenomena in a variety of environmental, geoscience, and climate science applications. In a changing climate, the impact of natural hazards, such as wildfires, is believed to have evolved in frequency, size, and spatial extent, although regional responses may vary. The aforementioned impacts are of great significance due to their association with air pollution, irreversible harm to the environment and atmosphere, and the fact that they put human lives at risk. The prediction of wildfires holds significant importance within the realm of wildfire management due to its influence on the allocation of resources, the mitigation of detrimental consequences, and the subsequent recovery endeavors. Therefore, the development of robust statistical methodologies that can accurately forecast extreme wildfire occurrences across spatial and temporal dimensions is of great significance. In this thesis, we develop new spatial statistical models, combined with popular machine learning techniques, as well as novel extreme-value methods to enhance the prediction of wildfire risk using graphical models. First, in order to jointly efficiently model high-dimensional wildfire counts and burnt areas over the whole continguous United States, we propose a four-stage zero-inflated bivariate spatiotemporal model combining low-rank spatial models and random forests. Second, to model high values of the McArthur Forest Fire Danger Index over Australia, we develop a novel spatial extreme-value model based on mixtures of tree-based multivariate Pareto distributions. Our new methodology combines theoretically justified spatial extreme models with a computationally convenient graphical model framework to spatial problems in high dimensions efficiently. Third, we exploit recent advancements in deep learning and build a parametric regression model using graphic convolutional neural networks and the extended Generalized Pareto distribution, allow us to jointly model moderate and extreme wildfires observed on irregular spatial grid. We work with a novel dataset of Australian wildfires from 1999 to 2019, and analyse monthly spread over areas correspond to Statistical Area Level 1 regions. We highlight the efficacy of our newly proposed model and perform risk assessment for Australia and dense communities.

Flood risk management in the U.S. has contributed to overdevelopment in at-risk areas, increases in flood losses over time, significant deficits in federal emergency programs, and inequitable outcomes to households and communities. Addressing these issues in a cost-effective and socially equitable manner relies on the ability of policy analysts to identify and understand complex interactions that characterize coupled natural-human systems, and tools for accurate estimates of the risks that arise from these interactions. This dissertation addresses this need by developing and investigating a flood risk analysis system that integrates data on property locations, assessments and transactions, high resolution flood hazard models, and flood risk policy and impacts across the coterminous United States. We focus on the degree to which markets accurately value their exposure to flooding and its impacts, and the accuracy of procedures and tools to estimate flood losses. In the first chapter, we identify heterogeneous valuation of storm risk in the Florida Keys that depends on the presence of structural defense and proximity to damaged homes after Hurricane Irma. This result suggests that stranded assets, properties with increasing vulnerability to storms but unable to rebuild structures and recover wealth, and overvalued assets at risk, which raise disaster costs, can occur simultaneously. This runs counter to the common framing of competing drivers of observed market valuation. In the second, we show that conventional methods employed in flood loss assessments to achieve large spatial scales introduce large aggregation bias by sacrificing spatial resolution in inputs. This investigation adds important context to published risk assessments and highlights opportunities to improve flood loss estimation uncertainty quantification which can support more cost effective and equitable management. In the final chapter, we conduct a nationwide study to contrast the predictive accuracy of predominantly used U.S. agency flood damage prediction models and empirical alternatives using data on 846 K observed flood losses to single-family homes from 446 flood events. We find that U.S. agency models mischaracterize the relationships of losses at the lowest low and high inundation depths, for high-valued structures, and structures with basements. Evaluated alternatives improve mean accuracy on these dimensions. In extrapolation to 72.4 M single-family homes in the U.S., these differences translate into markedly different predictions of U.S.-wide flood damages to single-family homes. The results from this dissertation provide an improved empirical foundation for flood risk management that relies on the valuation and estimation of flood risk from county to continental scales.

Recently, increased attention has been given to the social and environmental context in which crimes occur (Wells & Weisheit 2004). This new interest in the human ecology of crime is largely demographic, both in terms of subject matter and increasingly in terms of the analytic methods used. Building on existing literature on the social ecology of crime, this study introduces a new approach to studying sub-county geographies of reported crime using existing census place and county definitions coupled with spatial demographic methods. Spatially decomposing counties into Census places and what Esselstyn (1953) earlier called “open country,” or non-places, allows for the development of a unique but phenomenological meaningful sub-county geography that substantively holds meaning in conceptualizing rural and urban localities in the demographic analysis of crime. This decomposition allows for the examination of core-periphery relationships at the sub-county level, which are hypothesized to act similarly to those at the national level (Agnew 1993; Lightfoot and Martinez 1995). Using 1990 to 2000 Agency-level UCR data within this approach, I propose to use spatial statistics to describe and explain patterns of crime across differing localities. Potential processes of spatial mobility in regards to the spread of criminal activity from places to non-place localities are also examined. In order to adequately understand these spatial patterns of crime while testing the usability of the new place-level geography, several of the generally accepted theories of crime and a number of explanatory factors and covariates are tested. Furthermore, using this sub-county geography, significant patterns of spatial diffusion and contagion are through the implementation and modification of the spatio-temporal model, which provides the current point of departure and put forth by Cohen and Tita (1999). The results are promising and suggest a meaningful contribution to the ecological analysis of crime and the larger sub-discipline of spatial demography.

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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.

Spatio-temporal data analysis involves modeling a variable observed at different locations over time. A key component of space-time modeling is determining the spatial scale of the data. This dissertation addresses the following three questions: 1) How does spatial aggregation impact the properties of the variable and its model? 2) What spatial scale of the data produces more accurate forecasts of the aggregate variable? 3) What properties lead to the smallest information loss due to spatial aggregation? Answers to these questions involve a thorough examination of two common space-time models: the STARMA and GSTARMA models. These results are helpful to researchers seeking to understand the impact of spatial aggregation on temporal and spatial correlation as well as to modelers interested in determining a spatial scale for the data. Two data examples are included to illustrate the findings, and they concern states' annual labor force totals and monthly burglary counts for police districts in the city of Philadelphia. / Statistics

No / It's all long gone now...they've closed the shop on the corner of Athlone Street...it was a rough one with a pub on the corner...my dad ran it a long time ago...that time... Within the dominant biomedical discourse, late-life dementia is regarded as a pathological condition characterised by disorientation in time and space, word finding difficulties and 'problem behaviours' such as 'wandering' and 'repetitive questioning'. Once taken out of its biomedical straightjacket, however, dementia emerges as a condition which has much in common with the conscious projects of surrealist and situationist arts movements. This includes the subversion of the idea of time (and history) as linear, unidirectional progress. People diagnosed with dementia frequently state a desire to return (or indeed a fear of returning) to places from the past which no longer exist in physical space, but which remain real as remembered worlds and sources of nostalgia (literally 'the pain of returning'). These are also issues central to the field of psychogeography - an interdisciplinary approach to exploring the emotional and sensory impact of specific, particularly urban, locations. Informed by the work of poets such as Blake, Baudelaire, and Rimbaud, as theorised by, for example, Walter Benjamin and Guy Debord, psychogeography privileges undirected 'wandering' through its emphasis on concepts such as the flaneur, and the dérive (or 'drift'). In this paper, such concepts will be used as a way of exploring the spatio-temporal experiences of people with dementia, using extracts from film and narrative life stories.