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The last decade has seen an explosion in data sources available for the monitoring and prediction of environmental phenomena. While several inferential methods have been developed that make predictions on the underlying process by combining…
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,…
Geostatistical modeling of the reservoir intrinsic properties starts only with sparse data available. These estimates will depend largely on the number of wells and their location. The drilling costs are so high that they do not allow new…
Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem,…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology and cosmology. Despite growing literature, there is little published concerning the comparison of…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…
Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated…
A key challenge in environmental health research is unmeasured spatial confounding, driven by unobserved spatially structured variables that influence both treatment and outcome. A common approach is to fit a spatial regression that models…
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a…
We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) $\hat f_n$ is inconsistent in this…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…
Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators…
Studies investigating the causal effects of spatially varying exposures on outcomes often rely on observational and spatially indexed data. A prevalent challenge is unmeasured spatial confounding, where an unobserved spatially varying…
This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…
Assessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…