Justin A. Krometis

Seismic risk estimates are greatly improved with an increased understanding of historical (and pre‐historical) seismic events. Although Bayesian inference has been shown to provide reasonable estimates of the location and magnitude of historical earthquakes from anecdotal tsunamigenic evidence, the validity and robustness of such an approach has yet to be definitively demonstrated. Thus, in this article we present a careful analysis of the uncertainty inherent to this statistical recreation of historical seismic events. Using a priori estimates on the posterior and numerical approximations of the Hessian, we demonstrate that the 1852 Banda Sea earthquake and tsunami is well‐understood given certain explicit hypotheses. Using the same techniques we also find that the 1820 south Sulawesi event may best be explained by a dual fault rupture, best attributed to the Kalatoa fault potentially conjoining the Flores thrust and Walanae/Selayar fault.

Using deep learning model predictions requires not only understanding the model’s confidence but also its uncertainty, so we know when to trust the prediction or require support from a human. In this study, we used Monte Carlo dropout (MCDO) to characterize the uncertainty of deep learning image classification algorithms, including feature fusion models, on simulated synthetic aperture radar (SAR) images of persistent ship wakes. Comparing to a baseline, we used the distribution of predictions from dropout with simple mean value ensembling and the Kolmogorov—Smirnov (KS) test to classify in-domain and out-of-domain (OOD) test samples, created by rotating images to angles not present in the training data. Our objective was to improve the classification robustness and identify OOD images during the test time. The mean value ensembling did not improve the performance over the baseline, in that there was a –1.05% difference in the Matthews correlation coefficient (MCC) from the baseline model averaged across all SAR bands. The KS test, by contrast, saw an improvement of +12.5% difference in MCC and was able to identify the majority of OOD samples. Leveraging the full distribution of predictions improved the classification robustness and allowed labeling test images as OOD. The feature fusion models, however, did not improve the performance over the single SAR-band models, demonstrating that it is best to rely on the highest quality data source available (in our case, C-band).

We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this ‘uncertainty’ can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov chain Monte Carlo algorithms designed to resolve infinite-dimensional statistical quantities.

We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this "uncertainty" can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov Chain Monte Carlo (MCMC) algorithms designed to resolve infinite dimensional statistical quantities.

Improving understanding of current seismic risk is often dependent on developing a more complete characterization of earthquakes that have occurred in the past, and in particular before the development of modern sensing equipment in the middle of the twentieth century. However, accounts of such events are typically anecdotal in nature, limiting efforts to model them to more heuristic approaches. To address this shortfall, we develop a framework based in Bayesian inference to provide a more rigorous methodology for estimating pre-instrumental earthquakes. By directly modeling accounts of resultant tsunamis via probability distributions, the framework allows practitioners to make principled estimates of key characteristics (e.g., magnitude and location) of historical earthquakes. To illustrate this idea, we apply the methodology to the estimation of an earthquake in Eastern Indonesia in the mid 19th century, the source of which is currently the subject of considerable debate in the geological community. The approach taken here gives evidence that even "small data" that is limited in scope and extremely uncertain can still be used to yield information on past seismic events. Moreover, sensitivity bounds indicate that the results obtained here are robust despite the inherent uncertainty in the observations.

Training deep learning models requires having the right data for the problem and understanding both your data and the models’ performance on that data. Training deep learning models is difficult when data are limited, so in this paper, we seek to answer the following question: how can we train a deep learning model to increase its performance on a targeted area with limited data? We do this by applying rotation data augmentations to a simulated synthetic aperture radar (SAR) image dataset. We use the Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction technique to understand the effects of augmentations on the data in latent space. Using this latent space representation, we can understand the data and choose specific training samples aimed at boosting model performance in targeted under-performing regions without the need to increase training set sizes. Results show that using latent space to choose training data significantly improves model performance in some cases; however, there are other cases where no improvements are made. We show that linking patterns in latent space is a possible predictor of model performance, but results require some experimentation and domain knowledge to determine the best options.

Although the United States Safe Drinking Water Act (SDWA) theoretically ensures drinking water quality, recent studies have questioned the reliability and equity associated with community water system (CWS) service. This study aimed to identify SDWA violation differences (i.e., monitoring and reporting (MR) and health-based (HB)) between Virginia CWSs given associated service demographics, rurality, and system characteristics. A novel geospatial methodology delineated CWS service areas at the zip code scale to connect 2000 US Census demographics with 2006–2016 SDWA violations, with significant associations determined via negative binomial regression. The proportion of Black Americans within a service area was positively associated with the likelihood of HB violations. This effort supports the need for further investigation of racial and socioeconomic disparities in access to safe drinking water within the United States in particular and offers a geospatial strategy to explore demographics in other settings where data on infrastructure extents are limited. Further interdisciplinary efforts at multiple scales are necessary to identify the entwined causes for differential risks in adverse drinking water quality exposures and would be substantially strengthened by the mapping of official CWS service boundaries.

This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based around ideas from Hamiltonian dynamics. Our starting point is an abstract result developed in the generality of measurable state spaces that addresses proposal kernels that possess a certain involution structure. Note that, while this underlying proposal structure suggests a scope which includes Hamiltonian-type kernels, we demonstrate that our abstract result is, in an appropriate sense, equivalent to an earlier general state space setting developed in [Tierney, Annals of Applied Probability, 1998] where the connection to Hamiltonian methods was more obscure. Altogether, the theoretical unity and reach of our main result provides a basis for deriving novel sampling algorithms while laying bare important relationships between existing methods.

We demonstrate the efficacy of a Bayesian statistical inversion framework for reconstructing the likely characteristics of large pre‐instrumentation earthquakes from historical records of tsunami observations. Our framework is designed and implemented for the estimation of the location and magnitude of seismic events from anecdotal accounts of tsunamis including shoreline wave arrival times, heights, and inundation lengths over a variety of spatially separated observation locations. The primary advantage of this approach is that all of the assumptions made in the inversion process are incorporated explicitly into the mathematical framework. As an initial test case we use our framework to reconstruct the great 1852 earthquake and tsunami of eastern Indonesia. Relying on the assumption that these observations were produced by a subducting thrust event, the posterior distribution indicates that the observables were the result of a massive mega‐thrust event with magnitude near 8.8 Mw and a likely rupture zone in the north‐eastern Banda arc. The distribution of predicted epicentral locations overlaps with the largest major seismic gap in the region as indicated by instrumentally recorded seismic events. These results provide a geologic and seismic context for hazard risk assessment in coastal communities experiencing growing population and urbanization in Indonesia. In addition, the methodology demonstrated here highlights the potential for applying a Bayesian approach to enhance understanding of the seismic history of other subduction zones around the world.