Related papers: Stochastic Boundaries in Spatial General Equilibri…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
Environmental epidemiologists are increasingly interested in establishing causality between exposures and health outcomes. A popular model for causal inference is the Rubin Causal Model (RCM), which typically seeks to estimate the average…
Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem…
We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in…
Causal reasoning is often challenging with spatial data, particularly when handling high-dimensional inputs. To address this, we propose a neural network (NN) based framework integrated with an approximate Gaussian process to manage spatial…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusions with polynomial drift vector and diffusion…
I develop a continuous functional framework for spatial treatment effects grounded in Navier-Stokes partial differential equations. Rather than discrete treatment parameters, the framework characterizes treatment intensity as continuous…
Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…
We study the drivers and spatial diffusion of U.S. state population growth using a dynamic spatial model for 49 states, 1965-2017. Methodologically, we recover the spatial network structure from the data, rather than imposing it a priori…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
The Diffusion Probabilistic Model (DPM) has demonstrated remarkable performance across a variety of generative tasks. The inherent randomness in diffusion models helps address issues such as blurring at the edges of medical images and…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
Spatiotemporal prediction over graphs (STPG) is challenging, because real-world data suffers from the Out-of-Distribution (OOD) generalization problem, where test data follow different distributions from training ones. To address this…
I develop a comprehensive theoretical framework for dynamic spatial treatment effect boundaries using continuous functional definitions grounded in Navier-Stokes partial differential equations. Rather than discrete treatment effect…
Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…
A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
Over the past few decades, addressing "spatial confounding" has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed solutions are tied to specific analysis models and…