First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing non-separable structures should be accounted for in the model construction. We propose three different tests to investigate this hypothesis as a step of preliminary data analysis. The first two tests are exact or asymptotically exact for Poisson processes. The first test based on permutations and global envelopes allows us to detect at which spatial and temporal locations or lags the data deviate from the null hypothesis. The second test is a simple and computationally cheap $χ^2$-test. The third test is based on statistical reconstruction method and can be generally applied for non-Poisson processes. The performance of the first two tests is studied in a simulation study for Poisson and non-Poisson models. The third test is applied to the real data of the UK 2001 epidemic foot and mouth disease.
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that assume a simpler spatio-temporal dependence structure with separability and full symmetry. However, it is challenging to visualize and assess separability and full symmetry from spatio-temporal observations. In this work, we propose a functional data analysis approach that constructs test functions using the cross-covariances from time series observed at each pai…
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular approach to Dirichlet processes in a spatial setting relies on a stick-breaking representation of the process, where the dependence over space is described in the definition of the stick-breaking probabilities. Extensions to include temporal dependence are still limited, however it is important, in particular for those phenomena which may change rapidly over time a…
Environmental monitoring is a task that requires to surrogate system-wide information with limited sensor readings. Under the proximity principle, an environmental monitoring system can be based on the virtual sensing logic and then rely on distance-based prediction methods, such as $k$-nearest-neighbors, inverse distance weighted regression and spatio-temporal kriging. The last one is cumbersome with large datasets, but we show that a suitable separability assumption reduces its computational cost to an extent broader than considered insofar. Only spatial interpolation needs to be performed i…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, inc…
Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes does not scale with data volume and requires strong assumptions about stationarity, separability, and distance measures of covariance functions that are often unrealistic for global data. Only very few modeling approaches suitably model spatiotemporal correlations while addressing both computational scalability as well as flexible covariance models. In this…
Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Credible models of the correlations in longitudinal imaging require two or more pattern components. Valid inference requires enough flexibility of the correlation model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the correlation structure. For many one-dimensional spatial or temporal arrays, the linear expon…
Introduction The tau statistic is a recent second-order correlation function that can assess the magnitude and range of global spatiotemporal clustering from epidemiological data containing geolocations of individual cases and, usually, disease onset times. This is the first review of its use, and the aspects of its computation and presentation that could affect inferences drawn and bias estimates of the statistic. Methods Using Google Scholar we searched papers or preprints that cited the papers that first defined/reformed the statistic. We tabulated their key characteristics to understand th…
We present a new methodology and accompanying theory to test for separability of spatio-temporal functional data. In spatio-temporal statistics, separability is a common simplifying assumption concerning the covariance structure which, if true, can greatly increase estimation accuracy and inferential power. While our focus is on testing for the separation of space and time in spatio-temporal data, our methods can be applied to any area where separability is useful, including biomedical imaging. We present three tests, one being a functional extension of the Monte Carlo likelihood method of Mit…
In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so far since classical implementations lead to unscalable algorithms. We then propose a novel procedure to address this problem by coupling GP regression and Kalman filtering. In particular, assuming space…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting distributions of these test statistics under null hypotheses are always normal distributions, and they can be implemented easily for practical use. If null hypotheses are false, as the sample size goes to infinity, they diverge to infinity and consequently are consistent tests for any alternative. The approach can be applied to various null hypotheses such as the indep…
Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606（索邦大学、巴黎第六大学、法国国家科学研究中心、巴黎第六大学计算机科学实验室（UMR 7606））；Vedecom Institute（维德科姆研究所）
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts the observations from the latent representations. We consider several variants of this model, corresponding to different prior hypothesis about the spatial relations between the series. The model is evaluated and compared to state-of-the-art baselines, on a variety of forecasting …
An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or floods, or heavy-metal levels are dangerously high. Identifying these regions in a spatial or spatio-temporal setting is an important responsibility in environmental monitoring. Exceedance regions are often estimated by finding the areas where predictions from a statistical model exceed some threshold. Even when estimation error is quantifiable at individual l…
This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs, with applications to spatio-temporal models having non-trivial properties. Within the framework of Generalized Random Fields, a criterion for existence and uniqueness of stationary solutions for this class of SPDEs is proposed and proven. Their covariance are then obtained through their spectral measure. We present a result relating the covariance in the ca…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability and positive otherwise. The measure can be estimated without calculating the full non-separable covaria…
Geometric Identification and Consistent Estimation of Source Apportionment with Application to Greenland Summit Aerosols
Colorado School of Mines（科罗拉多矿业学院）；University of California, Davis（加州大学戴维斯分校）；Colorado State University（科罗拉多州立大学）；Stockholm University（斯德哥尔摩大学）；University of Colorado（科罗拉多大学）；National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局）；Johns Hopkins University（约翰斯·霍普金斯大学）
University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）
The effect of bias on hypothesis formation is characterized for an automated data-driven projection pursuit neural network to extract and select features for binary classification of data streams. This intelligent exploratory process partitions a complete vector state space into disjoint subspaces to create working hypotheses quantified by similarities and differences observed between two groups of labeled data streams. Data streams are typically time sequenced, and may exhibit complex spatio-temporal patterns. For example, given atomic trajectories from molecular dynamics simulation, the mach…
Deformable registration of spatiotemporal Cone-Beam Computed Tomography (CBCT) images taken sequentially during the radiation treatment course yields a deformation field for a pair of images. The Jacobian of this field at any voxel provides a measure of the expansion or contraction of a unit volume. We analyze the Jacobian at different sections of the tumor volumes obtained from delineation done by radiation oncologists for lung cancer patients. The delineations across the temporal sequence are compared post registration to compute tumor areas namely, unchanged (U), newly grown (G), and reduce…
For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated spatially stationary functional field. The asymptotic distribution of the test statistic that adapts to potentially diverging ra…
University College London（伦敦大学学院）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）
As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited in their ability to explain dynamic state changes in the brain which occurs spontaneously as a result of normal brain function. Hidden Markov Models (HMMs) trained on neuroimaging time series data have since arisen as a method to produce dynamical models that are easy to train but can be difficult to fully parametrise or analyse. We propose an interpretation …
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons, or due to a small sample size. However, inferential tools to verify this assumption are somewhat lacking in high-dimensional or functional {data analysis} settings, where this assumption is most relevant. We propose here to test separability by focusing on $K$-dimensional projections of the difference between the covariance o…
This paper concerns the modeling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose a formal test for the weak separability hypothesis, where the asymptotic null distribution of the test statistic is a chi-…
Indian Institute of Technology Kharagpur（印度理工学院卡拉克普尔分校）；Tata Medical Center, Kolkata（塔塔医疗中心（加尔各答））；Arden Cancer Centre（阿登癌症中心）；Department of Computer Science and Engineering（计算机科学与工程系）；Department of Radiation Oncology（放射肿瘤学系）；Department of Nuclear Medicine（核医学系）；Department of Medical Physics（医学物理系）
We report a model to predict patient's radiological response to curative radiation therapy (RT) for non-small-cell lung cancer (NSCLC). Cone-Beam Computed Tomography images acquired weekly during the six-week course of RT were contoured with the Gross Tumor Volume (GTV) by senior radiation oncologists for 53 patients (7 images per patient). Deformable registration of the images yielded six deformation fields for each pair of consecutive images per patient. Jacobian of a field provides a measure of local expansion/contraction and is used in our model. Delineations were compared post-registratio…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach is adequate for univariate classification tasks, it is especially advantageous for filter-type variable selection. It constitutes a robust and nonparametric method which may identify important otherwise neglected variables. It can incorporate the operating conditions of the classification task. Last but not least, the exact finite sample distribution of the…
Identifying mobility behaviors in rich trajectory data is of great economic and social interest to various applications including urban planning, marketing and intelligence. Existing work on trajectory clustering often relies on similarity measurements that utilize raw spatial and/or temporal information of trajectories. These measures are incapable of identifying similar moving behaviors that exhibit varying spatio-temporal scales of movement. In addition, the expense of labeling massive trajectory data is a barrier to supervised learning models. To address these challenges, we propose an uns…
Current literature suggests that urban heat-islands and their consequences are intensifying under climate change and urbanization. Here we explore the relatively unexplored hypothesis that emerging urban corridors (UCs) spawn megaregions of intense heat which are evident from observations. A delineation of the eleven United States UCs relative to their underlying climatological regions (non-UCs) suggest a surprisingly mixed trend. Medians and trends of winter temperatures over the last 60-years are generally higher in the UCs but no such general trends are observed in the summer. Heat wave met…
In many data scientific problems, we are interested in inferring causal relationships in the data generating mechanism. Here, we consider the following real-world question: how has the Colombian conflict influenced tropical forest loss? There is evidence for both enhancing and reducing impacts. Answering such questions requires the use of causal models. In this work, we propose a class of causal models for spatio-temporal stochastic processes. It allows us to formally define and quantify the causal effect of a vector of covariates $X$ on a real-valued response $Y$, even if the causal backgroun…
