publications

2026

1. Mad Props: Parallelism in Markov Chain Monte Carlo Through the Lens of the Infinite Proposal Limit

   Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis, and 1 more author

   2026

   Abs DOI

   Multiproposal MCMC (MP-MCMC) algorithms use clouds of proposals to efficiently traverse state spaces and overcome complex target geometries. While MCMC methods are embarrassingly parallel by nature, the non-trivial forms of parallelism provided by the MP-MCMC formalism sometimes leads to significant improvements over a naive approach. Here, one important tuning parameter is the number of proposals p used by a single MP-MCMC iteration. While a number of computational strategies have been proposed to efficiently leverage large numbers of proposals within the MP-MCMC paradigm, much remains unknown about these algorithms, particularly in the large p-regime. In this contribution, we discover surprising results by identifying and studying several promising new methods (Algorithm 1.1, Algorithm 3.3, Algorithm 3.4), ruling out other extant approaches and discovering new relationships between different MP-MCMC methodologies. Our analysis is centered on a general state space multiproposal involutive theory recently constructed by the authors combined with the consideration of the large p-limit kernels for MP-MCMC algorithms within a variety of different classes of proposal and acceptance structures.

2. Machine Learning Prediction of Vaginal Tissue Tears Using Finite Element Simulations Informed by Planar Biaxial Testing

   Mostafa Zakeri, Justin Krometis, Traian Iliescu, and 1 more author

   2026

   Abs DOI

   Vaginal tissue tearing during childbirth is a prevalent injury with potential long-term consequences, yet the mechanical factors influencing tear behavior remain poorly understood due to the difficulty of conducting in vivo studies. This study aims to investigate how tear geometry and fiber orientation influence local stress and strain patterns, and whether machine learning (ML) can accurately predict tissue responses from finite element (FE) simulation data.

2025

1. Gaussian Process Assisted Meta-learning for Image Classification and Object Detection Models

   Anna R. Flowers, Christopher T. Franck, Robert B. Gramacy, and 1 more author

   2025

   Abs DOI

   Collecting operationally realistic data to inform machine learning models can be costly. Before collecting new data, it is helpful to understand where a model is deficient. For example, object detectors trained on images of rare objects may not be good at identification in poorly represented conditions. We offer a way of informing subsequent data acquisition to maximize model performance by leveraging the toolkit of computer experiments and metadata describing the circumstances under which the training data was collected (e.g., season, time of day, location). We do this by evaluating the learner as the training data is varied according to its metadata. A Gaussian process (GP) surrogate fit to that response surface can inform new data acquisitions. This meta-learning approach offers improvements to learner performance as compared to data with randomly selected metadata, which we illustrate on both classic learning examples, and on a motivating application involving the collection of aerial images in search of airplanes.

2. Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes From Historical Anecdotes

   N. E. Glatt-Holtz, R. A. Harris, A. J. Holbrook, and 4 more authors

   2025

   Abs DOI arXiv

   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.

3. A Comparison of Bayesian Methods for Integrated Test and Evaluation

   Justin Krometis, Kyle Provost, Corinne Stafford, and 2 more authors

   2025

   DOI
4. JMBBM

   Deep learning reduced order models of vaginal tear propagation

   William Snyder, Mostafa Zakeri, Justin Krometis, and 3 more authors

   Journal of the Mechanical Behavior of Biomedical Materials, Jun 2025

   Abs DOI HTML

   Childbirth often has traumatic consequences that profoundly affect the mother’s health. The passage of a baby through the vagina causes tissue lacerations, such as vaginal tears, which lead to pelvic floor disorders later in life. Despite advances in obstetrics, accurately predicting the possible complications of vaginal delivery remains challenging with current clinical methods. This paper introduces new computational methods that integrate finite element (FE) analysis, proper orthogonal decomposition (POD), and machine learning (ML) to predict vaginal deformations and tearing. Based on ex vivo micro-mechanical data collected from rodents, FE models of the vaginal canal subjected to increasing pressure with propagating tears are created. Snapshots of the FE displacement fields at increasing pressures and with different collagen fiber organization in the proximal, mid, and distal regions of the vagina are then used to develop (a) full-order ML models and (b) POD-based reduced order models with coefficients computed using ML. Both the full-order ML models and POD-ML models with POD bases of dimension l≥2 approximated the FE results with root squared mean errors of O(10−2). Training (offline) times for the ML and POD-ML models were O(102) and O(10) seconds, respectively, whereas prediction (online) times for both ML and POD-ML models were O(10−3) seconds. Thus, the POD-ML models outperformed the ML models in terms of training efficiency while achieving similar prediction accuracy. Our findings demonstrate that the integration of these techniques can lead to faster computations of vaginal delivery outcomes. POD-based reduced order models and ML-based computational tools emerge as non-invasive methods for quantifying vaginal tissue deformations and tears.

2024

1. Sacred and Profane: from the Involutive Theory of MCMC to Helpful Hamiltonian Hacks

   Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis, and 2 more authors

   Oct 2024

   arXiv:2410.17398

   Abs DOI arXiv

   In the first edition of this Handbook, two remarkable chapters consider seemingly distinct yet deeply connected subjects ...

2. MORJ

   A Framework for Using Priors in a Continuum of Testing

   Victoria R.C. Sieck, Justin A. Krometis, and Steven Thorsen

   Military Operations Research, 2024

   Abs DOI HTML

   A strength of the Bayesian paradigm is that it can leverage all available information—to include subject matter expert opinion and previous (possibly dissimilar) data—through prior probabilities (priors). This article develops a framework for thinking about how differently characterized priors can be appropriately used throughout the continuum of testing. In addition to the application of various priors, the application of the evolution of priors contributes greatly to analytical understanding and will be addressed, considering cases such as when a system’s state significantly changes (e.g., is modified) during phases of testing. The evolution of priors can start with priors attempting to provide no information and evolve toward priors that capture the (newly) available information. This article further discusses priors based on institutional knowledge, as well as those based on previous testing data; the focus will be on previous, in some ways dissimilar, data, relative to a current test event. A discussion on which priorsmightbemorecommonin various phases of testing, types of information that can be used in priors, and how priors evolve as information accumulates is also included. Finally, a real-world example using the Stryker family of vehicles demonstrates how priors can be employed in a continuum-of-testing construct.

3. TMA

   Parallel MCMC algorithms: theoretical foundations, algorithm design, case studies

   Nathan E Glatt-Holtz, Andrew J Holbrook, Justin A Krometis, and 1 more author

   Transactions of Mathematics and Its Applications, Dec 2024

   Abs DOI arXiv HTML

   Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution {}mu \. We build a rigorous foundational framework for pMCMC algorithms that situates these methods within a unified ‘extended phase space’ measure-theoretic formalism. Drawing on our recent work that provides a comprehensive theory for reversible single-proposal methods, we herein derive general criteria for multiproposal acceptance mechanisms that yield ergodic chains on general state spaces. Our formulation encompasses a variety of methodologies, including proposal cloud resampling and Hamiltonian methods, while providing a basis for the derivation of novel algorithms. In particular, we obtain a top-down picture for a class of methods arising from ‘conditionally independent’ proposal structures. As an immediate application of this formalism, we identify several new algorithms including a multiproposal version of the popular preconditioned Crank–Nicolson (pCN) sampler suitable for high- and infinite-dimensional target measures that are absolutely continuous with respect to a Gaussian base measure. To supplement the aforementioned theoretical results, we carry out a selection of numerical case studies that evaluate the efficacy of these novel algorithms. First, noting that the true potential of pMCMC algorithms arises from their natural parallelizability and the ease with which they map to modern high-performance computing architectures, we provide a limited parallelization study using TensorFlow and a graphics processing unit to scale pMCMC algorithms that leverage as many as 100k proposals at each step. Second, we use our multiproposal pCN algorithm (mpCN) to resolve a selection of problems in Bayesian statistical inversion for partial differential equations motivated by fluid measurement. These examples provide preliminary evidence of the efficacy of mpCN for high-dimensional target distributions featuring complex geometries and multimodal structures.

4. RS

   Uncertainty Quantification in Data Fusion Classifier for Ship-Wake Detection

   Maice Costa, Daniel Sobien, Ria Garg, and 3 more authors

   Remote Sensing, Jan 2024

   Number: 24 Publisher: Multidisciplinary Digital Publishing Institute

   Abs DOI HTML

   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).

5. ITEA

   Dodging Pitfalls in Packages for Artificial Intelligence and Machine Learning

   Justin Krometis and William Snyder

   The ITEA Journal of Test and Evaluation, Jun 2024

   Abs DOI HTML

   Recent years have seen an explosion in the application of artificial intelligence and machine learning (AI/ML) to practical problems from computer vision to game playing to algorithm design. This growth has been mirrored and, in many ways, been enabled by the development and maturity of publicly-available software packages that make model building, training, and testing easier than ever. While these packages provide tremendous power and flexibility to users, and greatly facilitate learning and deploying AI/ML techniques, they and the models they provide are extremely complicated and as a result can present a number of subtle but serious pitfalls. This paper presents three examples where obscure settings or bugs in these packages dramatically changed model behavior or performance – one from a deep learning regression application, one from reinforcement learning, and one from computer vision classification. These examples illustrate the importance of thinking carefully about the results that a model is producing and carefully checking each step in its development before trusting its output.

6. NEJ

   Maximizing the Use of Data to Make Winning Decisions in the Face of Finite Resources

   Kyle Risher, Daniel Wolodkin, Justin Krometis, and 4 more authors

   Naval Engineers Journal, 2024

   Abs HTML

   Data collected across the acquisition life cycle, under different conditions, are not always used to maximize the knowledge about the operational performance of Department of Defense (DoD) systems. In the case of an acquisition process intended to deliver warfighting capabilities to address critical operational gaps, all data can and should improve knowledge about the system and must be leveraged to help authorities make the most informed decisions. Care must be given to how such data are used though to avoid their misuse potentially leading to incorrect conclusions and misinformed decisions. This article describes such challenges and introduces key analytical concepts based on math, science, statistics, and software engineering intended to maximize the information extracted from all data collected throughout the acquisition process. This article demonstrates the utility of those concepts on an example focused on the test and evaluation of the operational availability of a notional torpedo.

7. GJI

   A tale of two faults: Statistical reconstruction of the 1820 Flores Sea earthquake using tsunami observations alone

   T Paskett, J P Whitehead, R A Harris, and 4 more authors

   Geophysical Journal International, Feb 2024

   Abs DOI arXiv HTML

   Using a Bayesian approach we compare anecdotal tsunami runup observations from the 29 December 1820 Flores Sea earthquake with close to 200,000 tsunami simulations to determine the most probable earthquake parameters causing the tsunami. Using a dual hypothesis of the source earthquake either originating from the Flores Thrust or the Walanae/Selayar Fault, we found that neither source perfectly matches the observational data, particularly while satisfying seismic constraints of the region. Instead both posteriors have shifted to the edge of the prior indicating that the actual earthquake may have run along both faults.

2023

1. AAP

   On the accept–reject mechanism for Metropolis–Hastings algorithms

   Nathan Glatt-Holtz, Justin Krometis, and Cecilia Mondaini

   The Annals of Applied Probability, Dec 2023

   Publisher: Institute of Mathematical Statistics

   Abs DOI arXiv HTML

   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 (Ann. Appl. Probab. 8 (1998) 1–9) where the connection to Hamiltonian methods was more obscure. On the basis of our abstract results we develop several new classes of extended phase space, HMC-like algorithms. First we tackle the classical finite-dimensional setting of a continuously distributed target measure. We then consider an infinite-dimensional framework for targets which are absolutely continuous with respect to a Gaussian measure with a trace-class covariance. Each of these algorithm classes can be viewed as “surrogate-trajectory” methods, providing a versatile methodology to bypass expensive gradient computations through skillful reduced order modeling and/or data driven approaches as we begin to explore in a forthcoming companion work (Glatt-Holtz et al. (2023)). On the other hand, along with the connection of our main abstract result to the framework in (Ann. Appl. Probab. 8 (1998) 1–9), these algorithm classes provide a unifying picture connecting together a number of popular existing algorithms which arise as special cases of our general frameworks under suitable parameter choices. In particular we show that, in the finite-dimensional setting, we can produce an algorithm class which includes the Metropolis adjusted Langevin algorithm (MALA) and random walk Metropolis method (RWMC) alongside a number of variants of the HMC algorithm including the geometric approach introduced in (J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 (2011) 123–214). In the infinite-dimensional situation, we show that the algorithm class we derive includes the preconditioned Crank–Nicolson (pCN), ∞MALA and ∞HMC methods considered in (Stoch. Dyn. 8 (2008) 319–350; Stochastic Process. Appl. 121 (2011) 2201–2230; Statist. Sci. 28 (2013) 424–446) as special cases.

2. IP

   A statistical framework for domain shape estimation in Stokes flows

   Jeff Borggaard, Nathan E. Glatt-Holtz, and Justin Krometis

   Inverse Problems, Jun 2023

   Publisher: IOP Publishing

   Abs DOI arXiv HTML

   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.

3. CAMWA

   A numerical comparison of simplified Galerkin and machine learning reduced order models for vaginal deformations

   William Snyder, Alex Santiago Anaya, Justin Krometis, and 2 more authors

   Computers & Mathematics with Applications, Dec 2023

   Abs DOI HTML

   High-fidelity computer simulations of childbirth remain prohibitively expensive and time consuming, making them impractical for guiding decision-making during obstetric emergencies. Cheap computer simulations that preserve the accuracy of high-fidelity models can be developed using surrogate modeling. Two common approaches to surrogate modeling are physics-based reduced order modeling (ROM) and machine learning (ML), with the latter gaining popularity as the scientific computing community seeks to leverage advances from other, mostly non-physics-based, computational strategies. Although ROM and ML have been compared for various problems, to our knowledge, such a comparison for simulations of vaginal deformations is currently missing. This study provides a baseline numerical comparison between methods from these two fundamentally different approaches. Since there are many methods falling into each modeling approach, to provide a fair and natural comparison, we select a basic model from each category, with each allowing (i) a straightforward implementation in commercial software packages, and (ii) use by practitioners with limited experience in the field. As a benchmark for the numerical comparison of the ROM and ML approaches, we use the finite element (FE) modeling of the ex vivo deformations of rat vaginal tissue subjected to inflation testing to study the effect of a pre-imposed tear. From the ROM strategies, we consider a simplified Galerkin ROM (G-ROM) that is based on the linearization of the underlying nonlinear equations. From the ML strategies, we select a feed-forward neural network to create mappings from constitutive model parameters and luminal pressure values to either the FE displacement history (in which case we denote the resulting model ML) or the proper orthogonal decomposition (POD) coefficients of the displacement history (in which case we denote the resulting model POD-ML). The numerical investigation of G-ROM, ML, and POD-ML takes place in the reconstructive regime. The numerical results show that the G-ROM outperforms the ML model in terms of offline central processing unit (CPU) time for model training, online CPU time required to generate approximations, and relative error with respect to the FE models. The G-ROM achieves superior error performance to the best ML model with 11 POD basis functions. With higher-dimensional POD bases, the G-ROM achieves a relative error 3 orders of magnitude lower than that of the best ML model with an online CPU time still on the same order of magnitude as the best ML model. The POD-ML model improves on the speed performance of the ML, having online CPU times comparable to those of the G-ROM given the same size of POD bases. However, the POD-ML model does not improve on the error performance of the ML and is still outperformed by the G-ROM for POD bases of size greater than 11. This baseline numerical investigation serves as a starting point for future computer simulations that consider state-of-the-art G-ROM and ML strategies, and the in vivo geometry, boundary conditions, and material properties of the human vagina, as well as their changes during labor.

2022

1. MAKE

   Improving Deep Learning for Maritime Remote Sensing through Data Augmentation and Latent Space

   Daniel Sobien, Erik Higgins, Justin Krometis, and 2 more authors

   Machine Learning and Knowledge Extraction, Sep 2022

   Abs DOI HTML

   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.

2021

1. JGR

   Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis: a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami

   Hayden Ringer, Jared P Whitehead, Justin Krometis, and 8 more authors

   Journal of Geophysical Research, 2021

   DOI arXiv HTML
2. Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes from Historical Anecdotes

   Justin A Krometis, Hayden J Ringer, Jared P Whitehead, and 2 more authors

   arXiv preprint arXiv:2106.07797, 2021

   arXiv
3. IJERPH

   The demographics of SDWA compliance in Virginia community water systems

   Cristina Marcillo, Leigh-Anne Krometis, and Justin Krometis

   International Journal of Environmental Research and Public Health, 2021

   DOI HTML

2020

1. AAP

   On Bayesian Consistency for Flows Observed Through a Passive Scalar

   Jeff Borggaard, Nathan Glatt-Holtz, and Justin Krometis

   Annals of Applied Probability, 2020

   DOI arXiv HTML
2. JUQ

   A Bayesian Approach to Estimating Background Flows from a Passive Scalar

   Jeff Borggaard, Nathan Glatt-Holtz, and Justin Krometis

   SIAM/ASA Journal on Uncertainty Quantification, 2020

   DOI arXiv HTML

2019

1. JCP

   GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for Inverse Problems Constrained by Diffusion PDEs

   Jeff Borggaard, Nathan Glatt-Holtz, and Justin Krometis

   Journal of Computational Physics, 2019

   DOI arXiv HTML

2018

1. Thesis

   A Bayesian Approach to Estimating Background Flows from a Passive Scalar

   Justin Krometis

   Virginia Polytechnic Institute and State University, 2018

   HTML

2011

1. TRB

   Site considerations for points of dispensing after biological terrorist attack: integrated role of transportation planning and medical services

   Yongchang Ma, David Willauer, Justin Krometis, and 2 more authors

   Transportation Research Record: Journal of the Transportation Research Board, 2011

   DOI HTML

2005

1. EPL

   Will jams get worse when slow cars move over?

   Beate Schmittmann, Justin Krometis, and Royce KP Zia

   Europhysics Letters, 2005

   DOI arXiv HTML

2004

1. Thesis

   Lane preference in a simple traffic model

   Justin Krometis

   2004

   HTML