Related papers: Dynamic Spatial Treatment Effects as Continuous Fu…
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…
This paper develops a unified framework for identifying spatial and temporal boundaries of treatment effects in difference-in-differences designs. Starting from fundamental fluid dynamics equations (Navier-Stokes), we derive conditions…
Emergency medical services (EMS) response times are critical determinants of patient survival, yet existing approaches to spatial coverage analysis rely on discrete distance buffers or ad-hoc geographic information system (GIS) isochrones…
This paper develops a unified theoretical framework for detecting and estimating boundaries in treatment effects across both spatial and temporal dimensions. We formalize the concept of treatment effect boundaries as structural parameters…
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-similar initial data and are known to be regular outside of a…
This paper develops a continuous functional framework for treatment effects propagating through geographic space and economic networks. We derive a master equation from three independent economic foundations -- heterogeneous agent…
Sustained treatment strategies are common in many domains, particularly in medicine, where many treatment are delivered repeatedly over time. The effects of adherence to a treatment strategy throughout follow-up are often more relevant to…
This paper develops a nonparametric framework for identifying and estimating spatial boundaries of treatment effects in settings with geographic spillovers. While atmospheric dispersion theory predicts exponential decay of pollution under…
Establishing causality is a fundamental goal in fields like medicine and social sciences. While randomized controlled trials are the gold standard for causal inference, they are not always feasible or ethical. Observational studies can…
Causal inference methods are widely applied in the fields of medicine, policy, and economics. Central to these applications is the estimation of treatment effects to make decisions. Current methods make binary yes-or-no decisions based on…
This paper introduces a novel framework for causal inference in spatial economics that explicitly models the stochastic transition from partial to general equilibrium effects. We develop a Denoising Diffusion Probabilistic Model (DDPM)…
In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be…
We study the long-time dynamics of the Navier-Stokes equations in the three-dimensional periodic domains with a body force decaying in time. We introduce appropriate systems of decaying functions and corresponding asymptotic expansions in…
The potential outcomes framework serves as a fundamental tool for quantifying causal effects. The average dose-response function (also called the effect curve), denoted as (\mu(t)), is typically of interest when dealing with a continuous…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Spatially distributed functional data are prevalent in many statistical applications such as meteorology, energy forecasting, census data, disease mapping, and neurological studies. Given their complex and high-dimensional nature,…
Understanding causal relationships in the presence of complex, structured data remains a central challenge in modern statistics and science in general. While traditional causal inference methods are well-suited for scalar outcomes, many…
Segmentation of Multiple Sclerosis (MS) lesions in longitudinal brain MR scans is performed for monitoring the progression of MS lesions. We hypothesize that the spatio-temporal cues in longitudinal data can aid the segmentation algorithm.…
In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…