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.
Fine particulate matter (PM$_{2.5}$) has become a great concern worldwide due to its adverse health effects. PM$_{2.5}$ concentrations typically exhibit complex spatio-temporal variations. Both the mean and the spatio-temporal dependence evolve with time due to seasonality, which makes the statistical analysis of PM$_{2.5}$ challenging. In geostatistics, Gaussian process is a powerful tool for characterizing and predicting such spatio-temporal dynamics, for which the specification of a spatio-temporal covariance function is the key. While the extant literature offers a wide range of choices fo…
We consider modeling and prediction of Capelin distribution in the Barents sea based on zero-inflated count observation data that vary continuously over a specified survey region. The model is a mixture of two components; a one-point distribution at the origin and a Poisson distribution with spatio-temporal intensity, where both intensity and mixing proportions are modeled by some auxiliary variables and unobserved spatio-temporal effects. The spatio-temporal effects are modeled by a dynamic linear model combined with the predictive Gaussian process. We develop an efficient posterior computati…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out non-parametrically through kernel functions, where one of the most frequent handicaps is the selection of kernel bandwidths prior to estimation. This work presents an intensity estimation mechanism in which the spatial and temporal bandwidths change at each data point in a spatio-temporal point pattern. This class of estimators is called adaptive estimators, an…
Spatio-temporal models are widely used in many research areas including ecology. The recent proliferation of the use of in-situ sensors in streams and rivers supports space-time water quality modelling and monitoring in near real-time. A new family of spatio-temporal models is introduced. These models incorporate spatial dependence using stream distance while temporal autocorrelation is captured using vector autoregression approaches. Several variations of these novel models are proposed using a Bayesian framework. The results show that our proposed models perform well using spatio-temporal da…
We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it requires inverting covariance matrices which have the size of the latent state vector. The computational burden associated with this operation effectively prohibits its applications in high-dimensional settings. We propose a scalable spatio-temporal FFBS approach based on the hierarchical Vecchia approximation of Gaussian processes, which has been previously succes…
The stopp R package deals with spatio-temporal point processes which might have occurred on the Euclidean space or on some specific linear networks such as roads of a city. The package contains functions to summarize, plot, and perform different kinds of analyses on point processes, mainly following the methods proposed in some recent papers in the stream of scientific literature. The main topics of such works, and of the package in turn, include modeling, statistical inference, and simulation issues on spatio-temporal point processes on Euclidean space and linear networks, with a focus on the…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance stationarity, which is unrealistic in many geophysical applications. In this article, we introduce a deep-learning-inspired approach to construct descriptive nonstationary spatio-temporal models by modeling stationary processes on warped spatio-temporal domains. The warping functions we use are constructed using several simple injective warping units which, when co…
A class of physics-informed spatio-temporal models has recently been proposed for modeling spatio-temporal processes governed by advection-diffusion equations. The central idea is to approximate the process by a truncated Fourier series and let the governing physics determine the dynamics of the spectral coefficients. However, because many spatio-temporal processes in real applications are non-periodic with boundary discontinuities, the well-known Gibbs phenomenon and ripple artifact almost always exist in the outputs generated by such models due to truncation of the Fourier series. Hence, the…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance functions which are separable and non-separable in space and time.
As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle the climate crisis. Indeed, being universal nonlinear function approximation tools, Machine Learning algorithms are efficient in analysing and modelling spatially and temporally variable environmental data. While Deep Learning models have proved to be able to capture spatial, temporal, and spatio-temporal dependencies through their automatic feature representa…
In the absence of Gaussianity assumptions without disturbing spatial continuity interpolating along the whole spatial surface for different time lags is challenging. The past researchers pay enough attention to Spatio-temporal interpolation ignoring the dynamic behavior of a spatial mean function, threshold distance, and direction of maintaining spatial continuity. Therefore, we employ hierarchical spatial clustering (HSC) to preserve local spatial stationarity. This research work introduces a hybrid extreme valued copula-based Spatio-temporal interpolation algorithm. Spatial dependence is cap…
Peking University（北京大学）；Beijing Institute of Big Data Research（北京大数据研究院）
The spatio-temporal graph learning is becoming an increasingly important object of graph study. Many application domains involve highly dynamic graphs where temporal information is crucial, e.g. traffic networks and financial transaction graphs. Despite the constant progress made on learning structured data, there is still a lack of effective means to extract dynamic complex features from spatio-temporal structures. Particularly, conventional models such as convolutional networks or recurrent neural networks are incapable of revealing the temporal patterns in short or long terms and exploring …
Penn State University（宾夕法尼亚州立大学）；Hitachi America, Ltd.（日立美国有限公司）
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance from both the methodology development and real-world application perspectives. Given the observed spatially encoded time series covariates and real-valued response data samples, the goal of spatio-temporal regression is to leverage the temporal and spatial dependencies to build a mapping from covariates to response with minimized prediction error. Prior art…
Modeling and predicting solar events, particularly the solar ramping event, is critical for improving situational awareness for solar power generation systems. It has been acknowledged that weather conditions such as temperature, humidity, and cloud density can significantly impact the emergence and position of solar ramping events. As a result, modeling these events with complex spatio-temporal correlations is highly challenging. To tackle the question, we adopt a novel spatio-temporal categorical point process model, which intuitively and effectively addresses correlation and interaction amo…
We introduce WECS (Wavelet Energies Correlation Sreening), an unsupervised sparse procedure to detect spatio-temporal change points on multi-temporal SAR (POLSAR) images or even on sequences of very high resolution images. The procedure is based on wavelet approximation for the multi-temporal images, wavelet energy apportionment, and ultra-high dimensional correlation screening for the wavelet coefficients. We present two complimentary wavelet measures in order to detect sudden and/or cumulative changes, as well as for the case of stationary or non-stationary multi-temporal images. We show WEC…
