Search

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the model's parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: one that isolates the amplitude variation and one that isolates the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise especially when modeling phase variation, but also in a way that it can be done with readily available calibration software. We demonstrate the techniques on a simulated data example and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories' Z-machine., Comment: 45 pages, 21 figures

Detecting changepoints in functional data has become an important problem as interest in monitory of climatologies and other various processing monitoring situations has increased, where the data is functional in nature. The observed data often contains variability in amplitude ($y$-axis) and phase ($x$-axis). If not accounted for properly, incorrect changepoints can be detected, as well as underlying mean functions at those changes will be incorrect. In this paper, an elastic functional changepoint method is developed which properly accounts for these types of variability. Additionally, the method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly, or to ease the computational burden can be computed using functional principal component analysis. We apply the method to both simulated data and real data sets to show its efficiency in handling data with phase variation with both amplitude and phase changepoints.

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.

We introduce HITMIX, a new technique for network seed-set expansion, i.e., the problem of identifying a set of graph vertices related to a given seed-set of vertices. We use the moments of the graph's hitting-time distribution to quantify the relationship of each non-seed vertex to the seed-set. This involves a deterministic calculation for the hitting-time moments that is scalable in the number of graph edges and so avoids directly sampling a Markov chain over the graph. The moments are used to fit a mixture model to estimate the probability that each non-seed vertex should be grouped with the seed set. This membership probability enables us to sort the non-seeds and threshold in a statistically-justified way. To the best of our knowledge, HITMIX is the first full statistical model for seed-set expansion that can give vertex-level membership probabilities. While HITMIX is a global method, its linear computation complexity in practice enables computations on large graphs. We have a high-performance implementation, and we present computational results on stochastic blockmodels and a small-world network from the SNAP repository. The state of the art in this problem is a collection of recently developed local methods, and we show that distinct advantages in solution quality are available if our global method can be used. In practice, we expect to be able to run HITMIX if the graph can be stored in memory., 21 pages, 5 figures

Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More recent models also attempt to capture features such as fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data, whether due to numerical approximation or incomplete physics. In order to make realistic forecasts and improve understanding of the underlying processes, it is necessary to calibrate the numerical model to field data. Traditional calibration methods based on generalized least-square metrics are flawed for linear features such as sea ice cracks. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness, which involves optimally aligning model output with observed features using cutting edge image registration techniques. This work can also have application to other physical models which produce coherent structures.