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Air pollution is a great concern because of its impact on human health and on the environment. Statistical models play an important role in improving knowledge of this complex spatio-temporal phenomenon and in supporting public agencies and…

Foundation models for time series are emerging as powerful general-purpose backbones, yet their potential for domain-specific biomedical signals such as electroencephalography (EEG) remains rather unexplored. In this work, we investigate…

We introduce and analyze a variant of multivariate singular spectrum analysis (mSSA), a popular time series method to impute and forecast a multivariate time series. Under a spatio-temporal factor model we introduce, given $N$ time series…

Electrophysiological brain signals, such as electroencephalography (EEG), exhibit both periodic and aperiodic components, with the latter often modeled as 1/f noise and considered critical to cognitive and neurological processes. Although…

Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent…

Abstract Covariance matrix estimation is a challenging problem in cosmology. Recent work has shown that model covariance matrices can be precise, and that at relatively large scales they can also be accurate. We introduce a data-driven…

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…

In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…

We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…

Predictive learning uses a known state to generate a future state over a period of time. It is a challenging task to predict spatiotemporal sequence because the spatiotemporal sequence varies both in time and space. The mainstream method is…

The Electro-Encephalo-Graphy (EEG) technique consists of estimating the cortical distribution of signals over time of electrical activity and also of locating the zones of primary sensory projection. Moreover, it is able to record…

Detecting oscillations in solar and stellar time series is complicated by non-stationary red noise and evolving background emission. Methods based on detrending and AR(1)-based wavelet analysis can introduce spurious periodicities and do…

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and…

The analysis of spatio-temporal data has been the object of research in several areas of knowledge. One of the main objectives of such research is the need to evaluate the behavior of climate effects in certain regions across a period of…

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high…

Accurate decoding of EEG signals requires comprehensive modeling of both temporal dynamics within individual channels and spatial dependencies across channels. While Transformer-based models utilizing channel-independence (CI) strategies…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

This article introduces a dynamic spatiotemporal stochastic volatility (SV) model with explicit terms for the spatial, temporal, and spatiotemporal spillover effects. Moreover, the model includes time-invariant site-specific constant…

An important field of research in functional neuroimaging is the discovery of integrated, distributed brain systems and networks, whose different regions need to work in unison for normal functioning. The EEG is a non-invasive technique…

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…