Spatio-temporal Correlation Structure Research Articles

Optimizing spatio-temporal correlation structures for modeling food security in Africa: a simulation-based investigation

This study investigates the impact of spatio- temporal correlation using four spatio-temporal models: Spatio-Temporal Poisson Linear Trend Model (SPLTM), Poisson Temporal Model (TMS), Spatio-Temporal Poisson Anova Model (SPAM), and Spatio-Temporal Poisson Separable Model (STSM) concerning food security and nutrition in Africa. Evaluating model goodness of fit using the Watanabe Akaike Information Criterion (WAIC) and assessing bias through root mean square error and mean absolute error values revealed a consistent monotonic pattern. SPLTM consistently demonstrates a propensity for overestimating food security, while TMS exhibits a diverse bias profile, shifting between overestimation and underestimation based on varying correlation settings. SPAM emerges as a beacon of reliability, showcasing minimal bias and WAIC across diverse scenarios, while STSM consistently underestimates food security, particularly in regions marked by low to moderate spatio-temporal correlation. SPAM consistently outperforms other models, making it a top choice for modeling food security and nutrition dynamics in Africa. This research highlights the impact of spatial and temporal correlations on food security and nutrition patterns and provides guidance for model selection and refinement. Researchers are encouraged to meticulously evaluate the biases and goodness of fit characteristics of models, ensuring their alignment with the specific attributes of their data and research goals. This knowledge empowers researchers to select models that offer reliability and consistency, enhancing the applicability of their findings.

Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure

AbstractSpatiotemporal measurements observed through river networks have two distinct characteristics: a spatiotemporal correlation under the flow‐connected structure and the existence of heterogeneous covariances, which require a careful approach to implement principal component analysis (PCA). This paper focuses on developing a PCA method to reflect the unique characteristics of river networks. We propose a novel method combining flow‐directed PCA and geographically weighted PCA for the domain of river networks. The strengths of our approach are that it can (i) reduce dimensionality for streamflow data while effectively removing correlation among them and (ii) identify the group structure of data. It is possible to find essential patterns and sources of variation that may not be disclosed due to the attributes of flow‐connected networks. We apply the proposed method to the daily monitoring records of total organic carbon in the Geum River catchment area in South Korea. The results show that the proposed method successfully adjusts for the topological structure of the network and temporal correlation among observations while considering the spatial heterogeneity, enabling a more concrete understanding of monitoring networks.

Dynamic spatio-temporal correlation and hierarchical directed graph structure based ultra-short-term wind farm cluster power forecasting method

Accurate wind farm cluster power forecasting is of great significance for the safe operation of the power system with high wind power penetration. However, most of the current neural network methods used for wind farm cluster power forecasting have the following three problems: (1) lack of consideration of dynamic spatio-temporal correlation among adjacent wind farms; (2) simultaneously forecasting all wind farms’ power to obtain the total power will produce numerous error sources; (3) ignoring the causal relationship among input variables. Therefore, to solve the above problems, this paper proposes an ultra-short-term wind farm cluster power forecasting method based on dynamic spatio-temporal correlation and hierarchical directed graph structure. Firstly, three different types of nodes (wind speed nodes, wind power nodes, and target node) and input samples are defined, and then the spatio-temporal correlation matrices that can describe the correlation of adjacent wind farms are also calculated. Secondly, directed edges are defined to connect different nodes in order to obtain the hierarchical directed graph structure. Finally, this graph structure with dynamic spatio-temporal correlation information is used to train the forecasting model. In case study, compared with other benchmark methods, the proposed method shows excellent performance in improving accuracy of power forecasting.

New spatio-temporal complex covariance functions for vectorial data through positive mixtures

In the literature, the theory of complex-valued random fields is usually recalled to describe the evolution of vector data in space, without including the temporal dimension. However, as in the real case, the development of the complex formalism in a spatio-temporal context and the construction of some new classes of spatio-temporal complex covariance models are of sure interest for the scientific community partly due to the ongoing explosion in the availability of vector observations in space–time. In this paper, after presenting the fundamental aspects of the complex formalism of a spatio-temporal random field in a complex domain and the extension of some classes of complex-valued covariance models from a spatial domain to a spatio-temporal one, a new family of spatio-temporal complex-valued models obtained through a positive mixture of an infinite number of terms is proposed and various examples are discussed. A case study on modeling the spatio-temporal complex correlation structure of vectorial data is also provided.

Advancing Space‐Time Simulation of Random Fields: From Storms to Cyclones and Beyond

AbstractRealistic stochastic simulation of hydro‐environmental fluxes in space and time, such as rainfall, is challenging yet of paramount importance to inform environmental risk analysis and decision making under uncertainty. Here, we advance random fields simulation by introducing the concepts of general velocity fields and general anisotropy transformations. This expands the capabilities of the so‐called Complete Stochastic Modeling Solution (CoSMoS) framework enabling the simulation of random fields (RF's) preserving: (a) any non‐Gaussian marginal distribution, (b) any spatiotemporal correlation structure (STCS), (c) general advection expressed by velocity fields with locally varying speed and direction, and (d) locally varying anisotropy. We also introduce new copula‐based STCS's and provide conditions guaranteeing their positive definiteness. To illustrate the potential of CoSMoS, we simulate RF's with complex patterns and motion mimicking rainfall storms moving across an area, spiraling fields resembling weather cyclones, fields converging to (or diverging from) a point, and colliding air masses. The proposed methodology is implemented in the freely available CoSMoS R package.

Rainfall spatio-temporal correlation and intermittency structure from micro-γ to meso-β scale in the Netherlands

AbstractWe investigate the spatio-temporal structure of rainfall at spatial scales from 7m to over 200 km in the Netherlands. We used data from two networks of laser disdrometers with complementary interstation distances in two Dutch cities (comprising five and six disdrometers, respectively) and a Dutch nationwide network of 31 automatic rain gauges. The smallest aggregation interval for which raindrop size distributions were collected by the disdrometers was 30 s, while the automatic rain gauges provided 10-min rainfall sums. This study aims to supplement other micro-γ investigations (usually performed in the context of spatial rainfall variability within a weather radar pixel) with new data, while characterizing the correlation structure across an extended range of scales. To quantify the spatio-temporal variability, we employ a two-parameter exponential model fitted to the spatial correlograms and characterize the parameters of the model as a function of the temporal aggregation interval. This widely used method allows for a meaningful comparison with seven other studies across contrasting climatic settings all around the world. We also separately analyzed the intermittency of the rainfall observations. We show that a single parameterization, consisting of a two-parameter exponential spatial model as a function of interstation distance combined with a power-law model for decorrelation distance as a function of aggregation interval, can coherently describe rainfall variability (both spatial correlation and intermittency) across a wide range of scales. Limiting the range of scales to those typically found in micro-γ variability studies (including four of the seven studies to which we compare our results) skews the parameterization and reduces its applicability to larger scales.

Stochastic modeling of gridded short-term rainstorms

Abstract This study aims to develop a stochastic method (SM_GSTR) for generating short-time (i.e., hourly) rainstorm events at all grids (named gridded rainstorm events) in a region. The proposed SM_GSTR model is developed by the non-normal correlated multivariate Monte Carlo simulation (MMCS) method with the statistical properties and spatiotemporal correlation structures of the four event-based gridded rainfall characteristics. The radar-based rainfall data on 20 typhoon events at 336 grids in a basin located in north Taiwan, Nankan River watershed, are used in the model development and demonstration. The results from the model demonstration indicate that the proposed SM_GSTR model can reproduce a great number of gridded rainfall characteristics, of which, the statistical properties in time and space have a good fit to those from the observations in association with the acceptable deviation; thus, it can reasonably emulate the behavior of the rain field in both time and space. It is expected that the resulting massive rainfall-induced disasters (e.g., inundation and landslide) from the physical-based numerical model with the simulated gridded rainstorms by the proposed SM_GSTR model can be applied to establish an alternative artificial intelligence (AI) model for effectively forecasting the hydrologic variables (e.g., runoff and water-level).

FMRI and Artifact computation and Analysis

Over the years, the field of Medical Imagology has gained considerable importance. The number of neuroimaging studies conducted using functional magnetic resonance imaging (fMRI) has been exploding in recent years. fMRI survey gives to rise to large amounts of noisy data with a complex spatiotemporal correlation structure. Statistics play great role in clarifying the features of the data and gain results that can be used and explain by neuroscientists. Several types of artifacts can happen through a functional magnetic resonance imaging (fMRI) scanner Because of software or hardware problems, physical limitation or human physiologic phenomenon. Several of them can negatively affect diagnostic image goodness, and confused with various pathology. Artificial Characteristics is show in an image not found in the real actual object it is the necessary to recognize these artifacts according to a basic perception of their origin, especially those simulating pathology, as they can be sing to wrong diagnostic medical. As a result, it causes dangerous effects on the patient’s health. We discuss the study of fMRI data in this paper; we highlight important and significant problems where statistics already play a major role. It is include a sequence of programs for processing, analysing, and offer fMRI data. Of special regard to statisticians might be its use of functions from the statistical software package. The conventional methods are FSL and SPM. The most generally applied software is SPM (Statistical Parametric Mapping), which include groups of MATLAB functions for pre-processing, analysing, and display fMRI data.

Spatiotemporal variation in maturation: a case study with American plaice (Hippoglossoides platessoides) on the Grand Bank off Newfoundland

Fisheries management usually does not explicitly account for spatial variation in life history traits within populations. However, for some stocks this spatial variation may be substantial. We develop a spatiotemporal generalized linear model and fit the model to a long time series of maturation data for American plaice (Hippoglossoides platessoides) on the Grand Bank off Newfoundland and Labrador. The spatiotemporal correlation structure improves estimation of small-scale spatiotemporal variation in maturity across locations and times with limited or few samples. We test how American plaice maturity varies at three different spatial resolutions. We find improvements in model fit when decreasing spatial scales for higher spatial resolution due to high levels of spatial heterogeneity in American plaice maturity at age and size. Modeling variation in life history traits at the appropriate spatial and temporal scales is necessary for understanding population dynamics and developing appropriate fisheries management strategies.

A general mathematical method for predicting spatio-temporal correlations emerging from agent-based models.

Agent-based models are used to study complex phenomena in many fields of science. While simulating agent-based models is often straightforward, predicting their behaviour mathematically has remained a key challenge. Recently developed mathematical methods allow the prediction of the emerging spatial patterns for a general class of agent-based models, whereas the prediction of spatio-temporal pattern has been thus far achieved only for special cases. We present a general and mathematically rigorous methodology that allows deriving the spatio-temporal correlation structure for a general class of individual-based models. To do so, we define an auxiliary model, in which each agent type of the primary model expands to three types, called the original, the past and the new agents. In this way, the auxiliary model keeps track of both the initial and current state of the primary model, and hence the spatio-temporal correlations of the primary model can be derived from the spatial correlations of the auxiliary model. We illustrate the agreement between analytical predictions and agent-based simulations using two example models from theoretical ecology. In particular, we show that the methodology is able to correctly predict the dynamical behaviour of a host–parasite model that shows spatially localized oscillations.

WEED-MC: Wavelet Transform for Energy Efficient Data Gathering and Matrix Completion

Compressed sensing based data gathering is in-efficient in small scale wireless sensor networks because of uncorrelated observations at the sink. Failure to exploit the low rank and suitable transform domain to explore the correlation structure of sensor data, results in significantly low recovery accuracy in such matrix completion algorithms for small scale networks. Targeting the spatio temporal correlation structure of the data, a novel data gathering and matrix completion scheme, which exploits the low rank property and compactness of sensor data which exists in wavelet transform domain, is proposed in this work. The compactness of the sensor data in wavelet transform domain is used for recovering the missing entries of the matrix. Experiments and simulations, for single-node and multi-node scenarios, prove the efficacy of the proposed approach over existing schemes significantly in terms of recovery accuracy even at extremely low sampling rate.

Bayesian spatio-temporal inference of trace gas emissions using an integrated nested Laplacian approximation and Gaussian Markov random fields

Abstract. We present a method to infer spatially and spatio-temporally correlated emissions of greenhouse gases from atmospheric measurements and a chemical transport model. The method allows fast computation of spatial emissions using a hierarchical Bayesian framework as an alternative to Markov chain Monte Carlo algorithms. The spatial emissions follow a Gaussian process with a Matérn correlation structure which can be represented by a Gaussian Markov random field through a stochastic partial differential equation approach. The inference is based on an integrated nested Laplacian approximation (INLA) for hierarchical models with Gaussian latent fields. Combining an autoregressive temporal correlation and the Matérn field provides a full spatio-temporal correlation structure. We first demonstrate the method on a synthetic data example and follow this using a well-studied test case of inferring UK methane emissions from tall tower measurements of atmospheric mole fraction. Results from these two test cases show that this method can accurately estimate regional greenhouse gas emissions, accounting for spatio-temporal uncertainties that have traditionally been neglected in atmospheric inverse modelling.

Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity

AbstractNature manifests itself in space and time. The spatiotemporal complexity of processes such as precipitation, temperature, and wind, does not allow purely deterministic modeling. Spatiotemporal random fields have a long history in modeling such processes, and yet a single unified framework offering the flexibility to simulate processes that may differ profoundly does not exist. Here we introduce a blueprint to efficiently simulate spatiotemporal random fields that preserve any marginal distribution, any valid spatiotemporal correlation structure, and intermittency. We suggest a set of parsimonious yet flexible marginal distributions and provide a rule of thumb for their selection. We propose a new and unified approach to construct flexible spatiotemporal correlation structures by combining copulas and survival functions. The versatility of our framework is demonstrated by simulating conceptual cases of intermittent precipitation, double‐bounded relative humidity, and temperature maxima fields. As a real‐word case we simulate daily precipitation fields. In all cases, we reproduce the desired properties. In an era characterized by advances in remote sensing and increasing availability of spatiotemporal data, we deem that this unified approach offers a valuable and easy‐to‐apply tool for modeling complex spatiotemporal processes.

Latency Analysis for Sequential Detection in Low-Complexity Binary Radio Systems

We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital data streams available for statistical processing are binary and exhibit temporal and spatial dependencies. To handle the intractable multivariate binary data model, we first consider sequential tests for exponential family distributions. Within this generic probabilistic framework, we identify adaptive approximations for the log-likelihood ratio and the Kullback-Leibler divergence. The results allow designing sequential detectors for binary radio systems and analyzing their average run-time along classical arguments of Wald. In particular, the derived tests exploit the spatio-temporal correlation structure of the analog sensor signals engraved into the binary measurements. As an application, we consider the specification of binary sensing architectures for cognitive radio and GNSS spectrum monitoring where our results characterize the sequential detection latency as a function of the temporal oversampling and the number of antennas. Finally, we evaluate the efficiency of the proposed algorithms and illustrate the accuracy of our analysis via Monte-Carlo simulations.

A Bayesian spatiotemporal approach to inform management unit appropriateness

One prerequisite for sustainable fisheries management is to match management actions with biological processes. Stocks are fundamental units for fisheries management. Understanding the spatial structure of fish stocks is critical for conducting defensible stock assessments, applying efficient management strategies, and ensuring the sustainability of fish stocks. Yellow perch (Perca flavescens) is an important fishery in the Great Lakes. The appropriateness of its management units (MUs) has been identified as of high concern by the Great Lakes Fisheries Commission. Here we established integrated nested Laplace approximations and stochastic partial differential equations as two powerful tools for modeling spatiotemporal patterns of fish relative biomass. These fast computational approaches were applied to fit a Bayesian hierarchical hurdle model to occurrence and positive mass of yellow perch caught in gill-net surveys. Yellow perch relative biomass index has clear temporal variation and spatial heterogeneity, with the two middle MUs for yellow perch within Lake Erie merging together. The method explicitly models the spatiotemporal correlation structure inherent in biomass survey data at a reasonable computational cost, and the estimated spatiotemporal correlation informs stock structure.

Angular Positions Estimation of Spatially Extended Targets for MIMO Radar Using Complex Spatiotemporal Sparse Bayesian Learning

Aiming at the problem of scattering centers resolving and angular positions estimation of spatially extended targets, a high-resolution and high-accuracy angle estimation method based on multi-task group sparse model and collocated MIMO radar is proposed, which is helpful to obtain the structure information of targets and improve the success rate of target recognition. Characterized by sparse and clustered distribution in space, angular positions estimation of multiple closely-spaced and correlated point scattering targets belonging to a spatially extended target can be modeled as a multi-task group sparse problem and can be solved by multi-task group sparse recovery. To overcome the sparse recovery performance degradation caused by the high correlation in group sparse solution matrix and to improve the accuracy and robustness of angle estimation, a complex spatiotemporal sparse Bayesian learning (CST-SBL) algorithm which exploits spatiotemporal correlation structures of the solution matrix is proposed to reconstruct angular positions. Compared with previous work, the proposed approach achieves high-resolution and high-accuracy estimation performance, especially in cases of low SNR and few snapshots. The theoretical analysis and simulation results validate the effectiveness of the proposed technique.

Spatio-temporal modeling of destination choice behavior through the Bayesian hierarchical approach

Trip purpose inference is critical in transportation demand management (TDM) as well as traffic congestion alleviation. However, destination choice can be affected by a variety of factors, many of which are difficult to determine (e.g. socio-demographics). Besides, the spatio-temporal variation and correlation inherent in travel patterns further intensify the difficulty of understanding destination choice behavior. To this end, this research proposes a Bayesian hierarchical approach for modeling the destination choice behavior through time and space. The proposed method can take into account both the unavailable factors and spatio-temporal correlations by introducing random fields. Moreover, the implementation of the Integrated Nested Laplace Approximations (INLA) combined with the Stochastic Partial Differential Equation (SPDE) makes it computationally feasible to model large-scale spatio-temporal correlation structures. The model is further applied to two-week data from more than 8000 taxis in Harbin. The empirical results indicate that the proposed approach is capable to capture spatio-temporal variability in destination distribution, and the inclusion of spatial and temporal random effects is of great help to improve the model performance. The case study also examines how the land-use types influence the destination choice. It is believed that the modeling method and the exploratory spatial–temporal analysis of destination distribution in this study can enriches the methodologies for travel demand modeling as well as decision support for transport policy development.

Robust and Gaussian spatial functional regression models for analysis of event-related potentials

Event-related potentials (ERPs) summarize electrophysiological brain response to specific stimuli. They can be considered as correlated functions of time with both spatial correlation across electrodes and nested correlations within subjects. Commonly used analytical methods for ERPs often focus on pre-determined extracted components and/or ignore the correlation among electrodes or subjects, which can miss important insights, and tend to be sensitive to outlying subjects, time points or electrodes. Motivated by ERP data in a smoking cessation study, we introduce a Bayesian spatial functional regression framework that models the entire ERPs as spatially correlated functional responses and the stimulus types as covariates. This novel framework relies on mixed models to characterize the effects of stimuli while simultaneously accounting for the multilevel correlation structure. The spatial correlation among the ERP profiles is captured through basis-space Matérn assumptions that allow either separable or nonseparable spatial correlations over time. We induce both adaptive regularization over time and spatial smoothness across electrodes via a correlated normal-exponential-gamma (CNEG) prior on the fixed effect coefficient functions. Our proposed framework includes both Gaussian models as well as robust models using heavier-tailed distributions to make the regression automatically robust to outliers. We introduce predictive methods to select among Gaussian vs. robust models and models with separable vs. non-separable spatiotemporal correlation structures. Our proposed analysis produces global tests for stimuli effects across entire time (or time-frequency) and electrode domains, plus multiplicity-adjusted pointwise inference based on experiment-wise error rate or false discovery rate to flag spatiotemporal (or spatio-temporal-frequency) regions that characterize stimuli differences, and can also produce inference for any prespecified waveform components. Our analysis of the smoking cessation ERP data set reveals numerous effects across different types of visual stimuli.

Correlation Awareness in Low-Rank Models: Sampling, Algorithms, and Fundamental Limits

The role of correlation awareness in low-rank compressive inverse problems is studied in this article. In such inverse problems, the ultimate goal is to estimate certain physically meaningful parameters from measurements collected across space and time. The spatiotemporal correlation structure of the data can be judiciously exploited to design highly efficient samplers that allow reliable parameter estimation from compressed measurements. For a large class of spectrum estimation problems (including source localization and line spectrum estimation), certain structured samplers, based on the idea of difference sets, will be shown to be optimal and outperform random samplers. Using these samplers, it is even possible to localize more sources than the number of physical sensors. The underlying principles are also extended to sparse estimation problems under the Bayesian framework. Fundamental performance limits in terms of Cramer-Rao bounds (CRBs) are studied in a new underdetermined regime, and certain saturation effects that only occur in this regime are discussed.

Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition

ABSTRACTHigh-dimensional data monitoring and diagnosis has recently attracted increasing attention among researchers as well as practitioners. However, existing process monitoring methods fail to fully use the information of high-dimensional data streams due to their complex characteristics including the large dimensionality, spatio-temporal correlation structure, and nonstationarity. In this article, we propose a novel process monitoring methodology for high-dimensional data streams including profiles and images that can effectively address foregoing challenges. We introduce spatio-temporal smooth sparse decomposition (ST-SSD), which serves as a dimension reduction and denoising technique by decomposing the original tensor into the functional mean, sparse anomalies, and random noises. ST-SSD is followed by a sequential likelihood ratio test on extracted anomalies for process monitoring. To enable real-time implementation of the proposed methodology, recursive estimation procedures for ST-SSD are developed. ST-SSD also provides useful diagnostics information about the location of change in the functional mean. The proposed methodology is validated through various simulations and real case studies. Supplementary materials for this article are available online.