Related papers: Stochastic Boundaries in Spatial General Equilibri…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

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…

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

Medical image segmentation is a challenging task, made more difficult by many datasets' limited size and annotations. Denoising diffusion probabilistic models (DDPM) have recently shown promise in modelling the distribution of natural…

We propose a novel Bayesian framework for changepoint detection in large-scale spherical spatiotemporal data, with broad applicability in environmental and climate sciences. Our approach models changepoints as spatially dependent…

Time-to-event models are commonly used to study associations between risk factors and disease outcomes in the setting of electronic health records (EHR). In recent years, focus has intensified on social determinants of health, highlighting…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…

Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control…

Predicting future frames of a video is challenging because it is difficult to learn the uncertainty of the underlying factors influencing their contents. In this paper, we propose a novel video prediction model, which has…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…

Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject…

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…