Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare--especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.

Extreme events with potential deadly outcomes, such as those organized by terror groups, are highly unpredictable in nature and an imminent threat to society. In particular, quantifying the likelihood of a terror attack occurring in an arbitrary space-time region and its relative societal risk, would facilitate informed measures that would strengthen national security. This paper introduces a novel self-exciting marked spatio-temporal model for attacks whose inhomogeneous baseline intensity is written as a function of covariates. Its triggering intensity is succinctly modeled with a Gaussian Process prior distribution to flexibly capture intricate spatio-temporal dependencies between an arbitrary attack and previous terror events. By inferring the parameters of this model, we highlight specific space-time areas in which attacks are likely to occur. Furthermore, by measuring the outcome of an attack in terms of the number of casualties it produces, we introduce a novel mixture distribution for the number of casualties. This distribution flexibly handles low and high number of casualties and the discrete nature of the data through a {\it Generalized ZipF} distribution. We rely on a customized Markov chain Monte Carlo (MCMC) method to estimate the model parameters. We illustrate the methodology with data from the open source Global Terrorism Database (GTD) that correspond to attacks in Afghanistan from 2013-2018. We show that our model is able to predict the intensity of future attacks for 2019-2021 while considering various covariates of interest such as population density, number of regional languages spoken, and the density of population supporting the opposing government.