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This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The…
A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning…
In modern spatial statistics, the structure of data that is collected has become more heterogeneous. Depending on the type of spatial data, different modeling strategies for spatial data are used. For example, a kriging approach for…
Accurately reconstructing a global spatial field from sparse data has been a longstanding problem in several domains, such as Earth Sciences and Fluid Dynamics. Historically, scientists have approached this problem by employing complex…
In this article, we develop fully Bayesian, copula-based, spatial-statistical models for large, noisy, incomplete, and non-Gaussian spatial data. Our approach includes novel constructions of copulas that accommodate a spatial-random-effects…
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular and unbounded coefficients. Under mild local structural…
Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
In the quantitative analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) compartment models allow to describe the uptake of contrast medium with biological meaningful kinetic parameters. As simple models often fail to…
Air pollution remains a major environmental risk factor that is often associated with adverse health outcomes. However, quantifying and evaluating its effects on human health is challenging due to the complex nature of exposure data. Recent…
Spatial point process (SPP) models are commonly used to analyze point pattern data in many fields, including presence-only data in ecology. Existing exact Bayesian methods for fitting these models are computationally expensive because they…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…