In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function within a Gaussian process framework. This paper introduces a new paradigm for constructing asymmetric space-time covariances, which we refer to as "reflective asymmetric," by leveraging recently-introduced models for multivariate spatial data. We first provide new results for reflective asymmetric multivariate spatial models that extends their applicability. We then propose their asymmetric space-time extension, which come from a substantially different perspective than Lagrangian asymmetric space-time covariances. There are fewer parameters in the new models, one controls both the spatial and temporal marginal covariances, and the standard separable model is a special case. In simulation studies and analysis of the frequently-studied Irish wind data, these new models also improve model fit and prediction performance, and they can be easier to estimate. These features indicate broad applicability for improved analysis in environmental and other
Nonstationarity in spatial and spatio-temporal processes is ubiquitous in environmental datasets, but is not often addressed in practice, due to a scarcity of statistical software packages that implement nonstationary models. In this article, we introduce the R software package deepspat, which allows for modeling, fitting and prediction with nonstationary spatial and spatio-temporal models applied to Gaussian and extremes data. The nonstationary models in our package are constructed using a deep multi-layered deformation of the original spatial or spatio-temporal domain, and are straightforward to implement. Model parameters are estimated using gradient-based optimization of customized loss functions with tensorflow, which implements automatic differentiation. The functionalities of the package are illustrated through simulation studies and an application to Nepal temperature data.
In this work we study Weakly Supervised Spatio-Temporal Video Grounding (WSTVG), a challenging task of localizing subjects spatio-temporally in videos using only textual queries and no bounding box supervision. Inspired by recent advances in vision-language foundation models, we investigate their utility for WSTVG, leveraging their zero-shot grounding capabilities. However, we find that a simple adaptation lacks essential spatio-temporal grounding abilities. To bridge this gap, we introduce Tubelet Referral Grounding (TRG), which connects textual queries to tubelets to enable spatio-temporal predictions. Despite its promise, TRG struggles with compositional action understanding and dense scene scenarios. To address these limitations, we propose STPro, a novel progressive learning framework with two key modules: (1) Sub-Action Temporal Curriculum Learning (SA-TCL), which incrementally builds compositional action understanding, and (2) Congestion-Guided Spatial Curriculum Learning (CG-SCL), which adapts the model to complex scenes by spatially increasing task difficulty. STPro achieves state-of-the-art results on three benchmark datasets, with improvements of 1.0% on VidSTG-Declarati
FRK is an R software package for spatial/spatio-temporal modelling and prediction with large datasets. It facilitates optimal spatial prediction (kriging) on the most commonly used manifolds (in Euclidean space and on the surface of the sphere), for both spatial and spatio-temporal fields. It differs from many of the packages for spatial modelling and prediction by avoiding stationary and isotropic covariance and variogram models, instead constructing a spatial random effects (SRE) model on a fine-resolution discretised spatial domain. The discrete element is known as a basic areal unit (BAU), whose introduction in the software leads to several practical advantages. The software can be used to (i) integrate multiple observations with different supports with relative ease; (ii) obtain exact predictions at millions of prediction locations (without conditional simulation); and (iii) distinguish between measurement error and fine-scale variation at the resolution of the BAU, thereby allowing for reliable uncertainty quantification. The temporal component is included by adding another dimension. A key component of the SRE model is the specification of spatial or spatio-temporal basis fu
Non-Gaussian spatial and spatio-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines. FRK is an R package for spatial/spatio-temporal modelling and prediction with very large data sets that, to date, has only supported linear process models and Gaussian data models. In this paper, we describe a major upgrade to FRK that allows for non-Gaussian data to be analysed in a generalised linear mixed model framework. These vastly more general spatial and spatio-temporal models are fitted using the Laplace approximation via the software TMB. The existing functionality of FRK is retained with this advance into non-Gaussian models; in particular, it allows for automatic basis-function construction, it can handle both point-referenced and areal data simultaneously, and it can predict process values at any spatial support from these data. This new version of FRK also allows for the use of a large number of basis functions when modelling the spatial process, and is thus often able to achieve more accurate predictions than previous versions of the package in a Gaussian setting. We demonstrate innovative features in this new version of FRK, hi
Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.
Pandemics, with their profound societal and economic impacts, pose significant threats to global health, mortality rates, economic stability, and political landscapes. In response to these challenges, numerous studies have employed spatio-temporal models to enhance our understanding and management of these complex phenomena. These spatio-temporal models can be roughly divided into two main spatial categories: norm-based and graph-based. Norm-based models are usually more accurate and easier to model but are more computationally intensive and require more data to fit. On the other hand, graph-based models are less accurate and harder to model but are less computationally intensive and require fewer data to fit. As such, ideally, one would like to use a graph-based model while preserving the representation accuracy obtained by the norm-based model. In this study, we explore the ability to transform from norm-based to graph-based spatial representation for these models. We first show no analytical mapping between the two exists, requiring one to use approximation numerical methods instead. We introduce a novel framework for this task together with twelve possible implementations using
Due to the surge of spatio-temporal data volume, the popularity of location-based services and applications, and the importance of extracted knowledge from spatio-temporal data to solve a wide range of real-world problems, a plethora of research and development work has been done in the area of spatial and spatio-temporal data analytics in the past decade. The main goal of existing works was to develop algorithms and technologies to capture, store, manage, analyze, and visualize spatial or spatio-temporal data. The researchers have contributed either by adding spatio-temporal support with existing systems, by developing a new system from scratch for processing spatio-temporal data, or by implementing algorithms for mining spatio-temporal data. The existing ecosystem of spatial and spatio-temporal data analytics can be categorized into three groups, (1) spatial databases (SQL and NoSQL), (2) big spatio-temporal data processing infrastructures, and (3) programming languages and software tools for processing spatio-temporal data. Since existing surveys mostly investigated big data infrastructures for processing spatial data, this survey has explored the whole ecosystem of spatial and
Understanding the spread of any disease is a highly complex and interdisciplinary exercise as biological, social, geographic, economic, and medical factors may shape the way a disease moves through a population and options for its eventual control or eradication. Disease spread poses a serious threat in animal and plant health and has implications for ecosystem functioning and species extinctions as well as implications in society through food security and potential disease spread in humans. Space-time epidemiology is based on the concept that various characteristics of the pathogenic agents and the environment interact in order to alter the probability of disease occurrence and form temporal or spatial patterns. Epidemiology aims to identify these patterns and factors, to assess the relevant uncertainty sources, and to describe disease in the population. Thus disease spread at the population level differs from the approach traditionally taken by veterinary practitioners that are principally concerned with the health status of the individual. Patterns of disease occurrence provide insights into which factors may be affecting the health of the population, through investigating which
This paper presents a novel spatio-temporal LSTM (SPATIAL) architecture for time series forecasting applied to environmental datasets. The framework was evaluated across multiple sensors and for three different oceanic variables: current speed, temperature, and dissolved oxygen. Network implementation proceeded in two directions that are nominally separated but connected as part of a natural environmental system -- across the spatial (between individual sensors) and temporal components of the sensor data. Data from four sensors sampling current speed, and eight measuring both temperature and dissolved oxygen evaluated the framework. Results were compared against RF and XGB baseline models that learned on the temporal signal of each sensor independently by extracting the date-time features together with the past history of data using sliding window matrix. Results demonstrated ability to accurately replicate complex signals and provide comparable performance to state-of-the-art benchmarks. Notably, the novel framework provided a simpler pre-processing and training pipeline that handles missing values via a simple masking layer. Enabling learning across the spatial and temporal direc
CircSpaceTime is the only R package currently available that implements Bayesian models for spatial and spatio-temporal interpolation of circular data. Such data are often found in applications where, among the many, wind directions, animal movement directions, and wave directions are involved. To analyze such data we need models for observations at locations s and times t, as the so-called geostatistical models, providing structured dependence assumed to decay in distance and time. The approach we take begins with Gaussian processes defined for linear variables over space and time. Then, we use either wrapping or projection to obtain processes for circular data. The models are cast as hierarchical, with fitting and inference within a Bayesian framework. Altogether, this package implements work developed by a series of papers; the most relevant being Jona Lasinio, Gelfand, and Jona Lasinio (2012); Wang and Gelfand (2014); Mastrantonio, Jona Lasinio, and Gelfand (2016). All procedures are written using Rcpp. Estimates are obtained by MCMC allowing parallelized multiple chains run. The implementation of the proposed models is considerably improved on the simple routines adopted in th
Understanding the movement patterns of objects (e.g., humans and vehicles) in a city is essential for many applications, including city planning and management. This paper proposes a method for predicting future city-wide crowd flows by modeling the spatio-temporal patterns of historical crowd flows in fine-grained city-wide maps. We introduce a novel neural network named PArallel Spatio-Temporal Attention with spatial auto-correlation gating (PASTA) that effectively captures the irregular spatio-temporal patterns of fine-grained maps. The novel components in our approach include spatial auto-correlation gating, multi-scale residual block, and temporal attention gating module. The spatial auto-correlation gating employs the concept of spatial statistics to identify irregular spatial regions. The multi-scale residual block is responsible for handling multiple range spatial dependencies in the fine-grained map, and the temporal attention gating filters out irrelevant temporal information for the prediction. The experimental results demonstrate that our model outperforms other competing baselines, especially under challenging conditions that contain irregular spatial regions. We also
Recent advances in multimodal large language models (MLLMs) have shown remarkable capabilities in integrating vision and language for complex reasoning. While most existing benchmarks evaluate models under offline settings with a fixed set of pre-recorded inputs, we introduce OST-Bench, a benchmark designed to evaluate Online Spatio-Temporal understanding from the perspective of an agent actively exploring a scene. The Online aspect emphasizes the need to process and reason over incrementally acquired observations, while the Spatio-Temporal component requires integrating current visual inputs with historical memory to support dynamic spatial reasoning. OST-Bench better reflects the challenges of real-world embodied perception. Built on an efficient data collection pipeline, OST-Bench consists of 1.4k scenes and 10k question-answer pairs collected from ScanNet, Matterport3D, and ARKitScenes. We evaluate several leading MLLMs on OST-Bench and observe that they fall short on tasks requiring complex spatio-temporal reasoning. Under the online setting, their accuracy declines as the exploration horizon extends and the memory grows. Through further experimental analysis, we identify comm
Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that are collectively called linear dynamic spatio-temporal models (LDSTMs). However, real world environmental processes are highly complex and are seldom representable by models with such simple linear structure. Hence, nonlinear dynamic spatio-temporal models (NLDSTMs) based on the idea of nonlinear observational and evolutionary equation have been proposed as an alternative. However, in that case, the caveat lies in selecting the specific form of nonlinearity from a large class of potentially appropriate nonlinear functions. Moreover, modeling by NLDSTMs requires precise knowledge about the dynamics underlying the data. In this article, we address this problem by introducing the Gaussian random functional dynamic spatio-temporal model (GRFDSTM). Unlike the LDSTMs or NLDSTMs, in GRFDSTM both the functions governing the observational and evolutionary equations are composed of Gaussian random functions. We exhibit many interesting theoretical properti
Spatial coherence quantifies spatial field correlations over time, and is one of the fundamental properties of light. Here we investigate the spatial coherence of highly multimode lasers in the regime of short time scales. Counter intuitively, we show that in this regime, the temporal (longitudinal) modes play a crucial role in spatial coherence reduction. To evaluate the spatial coherence we measured the temporal dynamics of speckle fields generated by a highly multimode laser with over $10^5$ lasing spatial (transverse) modes, and examined the dependence of speckle contrast on the exposure time of the detecting device. We show that in the regime of short time scale, the spatial and temporal modes interact to form spatio-temporal supermodes, such that the spatial degrees of freedom are encoded onto the temporal modes. As a result, the speckle contrast depends on the number of temporal modes, and the degree of spatial coherence is reduced and the speckle contrast is suppressed. In the regime of long times scale, the supermodes are no longer a valid representation of the laser modal structure. Consequently, the spatial coherence is independent of the temporal modes, and the classica
The epidemiology has recently witnessed great advances based on computational models. Its scope and impact are getting wider thanks to the new data sources feeding analytical frameworks and models. Besides traditional variables considered in epidemiology, large-scale social patterns can be now integrated in real time with multi-source data bridging the gap between different scales. In a hyper-connected world, models and analysis of interactions and social behaviors are key to understand and stop outbreaks. Big Data along with apps are enabling for validating and refining models with real world data at scale, as well as new applications and frameworks to map and track diseases in real time or optimize the necessary resources and interventions such as testing and vaccination strategies. Digital epidemiology is positioning as a discipline necessary to control epidemics and implement actionable protocols and policies. In this review we address the research areas configuring current digital epidemiology: transmission and propagation models and descriptions based on human networks and contact tracing, mobility analysis and spatio-temporal propagation of infectious diseases and infodemics
Spatio-temporal knowledge graphs (STKGs) enhance traditional KGs by integrating temporal and spatial annotations, enabling precise reasoning over questions with spatio-temporal dependencies. Despite their potential, research on spatio-temporal knowledge graph question answering (STKGQA) remains limited. This is primarily due to the lack of datasets that simultaneously contain spatio-temporal information, as well as methods capable of handling implicit spatio-temporal reasoning. To bridge this gap, we introduce the spatio-temporal question answering dataset (STQAD), the first comprehensive benchmark comprising 10,000 natural language questions that require both temporal and spatial reasoning. STQAD is constructed with real-world facts containing spatio-temporal information, ensuring that the dataset reflects practical scenarios. Furthermore, our experiments reveal that existing KGQA methods underperform on STQAD, primarily due to their inability to model spatio-temporal interactions. To address this, we propose the spatio-temporal complex question answering (STCQA) method, which jointly embeds temporal and spatial features into KG representations and dynamically filters answers thro
Spatial and spatio-temporal single-structure point process models are widely used in epidemiology, biology, ecology, seismology... . However, most natural phenomena present multiple interaction structure or exhibit dependence at multiple scales in space and/or time, leading to define new spatial and spatio-temporal multi-structure point process models. In this paper, we investigate and review such multi-structure point process models mainly based on Gibbs and Cox processes.
Cancer data, particularly cancer incidence and mortality, are fundamental to understand the cancer burden, to set targets for cancer control and to evaluate the evolution of the implementation of a cancer control policy. However, the complexity of data collection, classification, validation and processing result in cancer incidence figures often lagging two to three years behind the calendar year. In response, national or regional population-based cancer registries (PBCRs) are increasingly interested in methods for forecasting cancer incidence. However, in many countries there is an additional difficulty in projecting cancer incidence as regional registries are usually not established in the same year and therefore cancer incidence data series between different regions of a country are not harmonised over time. This study addresses the challenge of forecasting cancer incidence with incomplete data at both regional and national levels. To achieve this, we propose the use of multivariate spatio-temporal shared component models that jointly model mortality data and available cancer incidence data. We evaluate the performance of these multivariate models using lung cancer incidence dat
This paper proposes tds mgtwr, a multiscale geographically and temporally weighted regression (MGTWR) model with covariate-specific spatial and temporal scales. The approach combines a separable spatio-temporal kernel with a Top-Down Scale (TDS) calibration scheme, where spatial and temporal bandwidths are selected for each covariate through a coordinate-wise search over ordered grids guided by the corrected Akaike Information Criterion (AICc). By avoiding unconstrained multidimensional optimization, this strategy extends to the spatio-temporal setting the stabilizing properties of TDS calibration scheme Geniaux (2026). The multiscale backfitting procedure combines the Top-Down Scale calibration scheme with an adaptive, importance-driven update schedule that prioritizes covariates according to their current scale-normalized contribution to the fitted signal, thereby limiting the number of local recalibrations required and accelerating convergence while maintaining estimator fidelity. We also introduce a generic prediction method for MGWR and MGTWR based on kernel sharpening. Monte Carlo experiments show that modeling both space and time improves coefficient recovery and predictive