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Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…
This paper introduces area-level Poisson mixed models with temporal and SAR(1) spatially correlated random effects. Small area predictors of the proportions and counts of a dichotomic variable are derived from the new models and the…
We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. We model aggregate count data as arising from…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…
Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region. In contrast, relationships between response and…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
A common problem faced by statistical institutes is that data may be missing from collected data sets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact…
In the realm of large-scale spatiotemporal data, abrupt changes are commonly occurring across both spatial and temporal domains. This study aims to address the concurrent challenges of detecting change points and identifying spatial…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events…
Data quality is an important consideration in many engineering applications and projects. Data collection procedures do not always involve careful utilization of the most precise instruments and strictest protocols. As a consequence, data…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
The spatial scan statistic is widely used in epidemiology and medical studies as a tool to identify hotspots of diseases. The classical spatial scan statistic assumes the number of disease cases in different locations have independent…
A problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing. Linear interpolation methods rely on the Gaussian assumption, which is often unrealistic in practice, or…
This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. Subspace clustering becomes challenging when the dimension of intersection between…
The application of geostatistical and machine learning methods based on Gaussian processes to big space-time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally…