Recent advances in interpretable model-based geostatistics for analyzing complex spatial data

Spatial dissimilarity arises from pairwise comparisons of spatially dependent groups (or ensembles). Such pairwise dissimilarities are common in various fields; for example, site-pairwise biological dissimilarities are often used to describe species diversity across a spatial domain. Statistical inference for these outcomes requires a spatial process to obtain valid results, yet considerably less attention has been devoted to constructing spatial processes indexed by pairs of locations. In this talk, I will introduce a generalized chi-squared process, outline its key properties, and embed the GCP in a hierarchical spatial model that enables model-based inference for pairwise dissimilarities. The methodology is illustrated with simulation studies and ecological applications. 

In including random effects to account for dependent observations, the odds ratio interpretation of logistic regression coefficients is changed from population-averaged to subject-specific. This is unappealing in many applications, motivating a rich literature on methods that maintain the marginal logistic regression structure without random effects, such as generalized estimating equations. However, for spatial data, random effect approaches are appealing in providing a full probabilistic characterization of the data that can be used for prediction. We propose a new class of spatial logistic regression models that maintain both population-averaged and subject-specific interpretations through a novel class of bridge processes for spatial random effects. These processes are shown to have appealing computational and theoretical properties, including a scale mixture of normal representation. The new methodology is illustrated with simulations and an analysis of childhood malaria prevalence data in the Gambia. 

A fundamental theoretical limitation undermines current disaster risk models: while real-world natural hazards manifest as complex, interconnected phenomena, existing approaches suffer from two critical constraints. First, conventional damage prediction models remain predominantly deterministic, relying on fixed parameters established through expert judgment rather than learned from data. Second, even recent probabilistic frameworks are fundamentally restricted by their underlying assumption of hazard independence, an assumption that directly contradicts the observed reality of cascading and compound disasters. By relying on fixed expert parameters rather than empirical data and treating hazards as independent phenomena, these models dangerously misrepresent the true risk landscape. This work addresses this critical challenge by developing the Multi-Hazard Bayesian Hierarchical Model (MH-BHM), which reconceptualizes the classical risk equation beyond its deterministic origins. The model's core theoretical contribution lies in reformulating a classical risk formula as a fully probabilistic model that naturally accommodates hazard interactions through its hierarchical structure while preserving the interpretability of the traditional hazard-exposure-vulnerability framework. Using tropical cyclone damage data (1952-2020) from the Philippines as a test case, with out-of-sample validation on recent events (2020-2022), the model demonstrates significant empirical advantages: a reduction in damage prediction error by 61\% compared to a single-hazard model, and 80\% compared to a benchmark deterministic model, corresponding to an improvement in damage estimation accuracy of USD 0.8 billion and USD 2 billion, respectively. This improved accuracy enables more effective disaster risk management across multiple domains, from optimized insurance pricing and national resource allocation to local adaptation strategies, fundamentally improving society's capacity to prepare for and respond to disasters. 

A variety of quantities are collected by spatially distributed sensors with known levels of detection (LOD), beyond which the response variable cannot be measured. When the (transformation of) underlying responses are modelled by a Gaussian process (GP), the measurements follow a (partially) censored GP, posing significant computational challenges for estimation and inference using existing methods. We propose scalable methods for estimating multivariate normal (MVN) probabilities and sampling truncated MVN (TMVN) distributions through tactically constructing conditional independence structures that address the likelihood estimation and posterior inference of censored GPs, respectively. The proposed methods are based on the minimax exponential tilting (MET) method and a comparison with the state-of-the-arts is provided.