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The trade-off in remote sensing instruments that balances the spatial resolution and temporal frequency limits our capacity to monitor spatial and temporal dynamics effectively. The spatiotemporal data fusion technique is considered as a…
Time series in natural sciences, such as hydrology and climatology, and other environmental applications, often consist of continuous observations constrained to the unit interval (0,1). Traditional Gaussian-based models fail to capture…
This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…
Compositional data find broad application across diverse fields due to their efficacy in representing proportions or percentages of various components within a whole. Spatial dependencies often exist in compositional data, particularly when…
Integrated Nested Laplace Approximation provides a fast and effective method for marginal inference on Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R…
Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we…
In recent years, spatial and spatio-temporal modeling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping). In this work we propose different spatial models to study hospital…
Conditional auto-regressive (CAR) distributions are widely used to induce spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships…
This paper proposes a wavelet-based method for analysing periodic autoregressive moving average (PARMA) time series. Even though Fourier analysis provides an effective method for analysing periodic time series, it requires the estimation of…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special…
A class of continuous-time autoregressive moving average (CARMA) process driven by simple semi-Levy measure is defined and its properties are studied. We discuss some new insights on the structure of the semi-Levy measure which is described…
In this paper, we first propose a spatial-temporal coupled risk assessment paradigm by constructing a three-dimensional spatial-temporal risk field (STRF). Specifically, we introduce spatial-temporal distances to quantify the impact of…
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the…
To address the challenge of backpropagating the gradient through categorical variables, we propose the augment-REINFORCE-swap-merge (ARSM) gradient estimator that is unbiased and has low variance. ARSM first uses variable augmentation,…
Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
The stochastic frontier model with heterogeneous technical efficiency explained by exoge-nous variables is augmented with a spatial-temporal component, a generalization relaxing the panel independence assumption in a panel data. The…