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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Elastic Bayesian Model Calibration

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 computer 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: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate 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, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples 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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Differentially Private Synthesis and Sharing of Network Data Via Bayesian Exponential Random Graph Models

Abstract Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

graph synthesis↗
DOE OSTI2014

Development of a reduced model of formation reactions in Zr-Al nanolaminates

A computational model of anaerobic reactions in metallic multilayered systems with an equimolar composition of zirconium and aluminum is developed. The reduced reaction formalism of M. Salloum and O. M. Knio, Combust. Flame 157(2): 288–295 (2010) is adopted. Attention is focused on quantifying intermixing rates based on experimental measurements of uniform ignition as well as measurements of self-propagating front velocities. Estimates of atomic diffusivity are first obtained based on a regression analysis. A more elaborate Bayesian inference formalism is then applied in order to assess the impact of uncertainties in the measurements, potential discrepancies between predictions and observations, as well as the sensitivity of predictions to inferred parameters. Intermixing rates are correlated in terms of a composite Arrhenius law, which exhibits a discontinuity around the Al melting temperature. Analysis of the predictions indicates that Arrhenius parameters inferred for the low-temperature branch lie within a tight range, whereas the parameters of the high-temperature branch are characterized by higher uncertainty. The latter is affected by scatter in the experimental measurements, and the limited range of bilayers where observations are available. For both branches, the predictions exhibit higher sensitivity to the activation energy than the pre-exponent, whose posteriors are highly correlated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Constraints on the tensor-to-scalar ratio for non-power-law models

Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r{sub LD} = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Uncertainty quantification of material parameters in modeling coupled metal and high explosive experiments

Experiments involving the coupling of metal and high explosives (HE) are of notable defense-related interest, and we seek to refine the uncertainty quantification associated with models of such experiments. In particular, our focus is on how uncertainty related to the metal constitutive model challenges our ability to infer high explosive model parameters when analyzing focused science experiments. We consider three focused experiments involving an HE accelerating metal: small plate tests with tantalum/LX-14 and tantalum/LX-17 pairings as well as a tantalum/LX-17 cylinder test. For all three models, we perform sensitivity analysis to ascertain the influence of metal strength on the coupled experimental response. Moreover, we calibrate each model in a Bayesian setting and study the quantification of metal strength on the inference of the HE parameters. Based on our results, we offer guidance for future metal/HE experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Quantifying uncertainty in Pareto estimates of global lake area

Abstract Size is a critical factor determining the rate and occurrence of specific lake processes such as carbon sequestration and greenhouse gas emissions and emerging evidence suggests that small lakes in particular have particularly large CO 2 flux rates. Because we do not have a complete census of all lakes, upscaling estimates of such processes to small lakes at broad spatial scales requires the use of lake size‐abundance distributions rather than empirical measurements of area. Existing lake census efforts are incomplete such that as lakes become smaller, they are more likely to be omitted either because they are too small to be resolved from remote sensing products or because of limited ground surveying effort (i.e., “censoring” of small lakes relative to large lakes). The present study explores one potential shortcoming of prior approaches estimating global lake area using lake size‐abundance distributions. Namely, that these prior approaches rely on frequentist curve fitting techniques combined with an ad‐hoc cutoff determination strategy (visual inspection to determine a likely censoring point). This yields an over‐exact lake area estimate that is typically reported with no uncertainty bounds. I show how these shortcomings can be addressed with a Bayesian model that produces larger estimates of lake area uncertainty relative to the typical approach. When used as part of a sensitivity analysis, such an approach has the potential to enable more robust intercomparisons among studies of aquatic processes upscaling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

Data-model integration plays a critical role in assessing and improving our capacity to predict ecosystem dynamics. Similarly, the ability to attach quantitative statements of uncertainty around model forecasts is crucial for model assessment and interpretation and for setting field research priorities. Bayesian methods provide a rigorous data assimilation framework for these applications, especially for problems with multiple data constraints. However, the Markov chain Monte Carlo (MCMC) techniques underlying most Bayesian calibration can be prohibitive for computationally demanding models and large datasets. We employ an alternative method, Bayesian model emulation of sufficient statistics, that can approximate the full joint posterior density, is more amenable to parallelization, and provides an estimate of parameter sensitivity. Analysis involved informative priors constructed from a meta-analysis of the primary literature and specification of both model and data uncertainties, and it introduced novel approaches to autocorrelation corrections on multiple data streams and emulating the sufficient statistics surface. We report the integration of this method within an ecological workflow management software, Predictive Ecosystem Analyzer (PEcAn), and its application and validation with two process-based terrestrial ecosystem models: SIPNET and ED2. In a test against a synthetic dataset, the emulator was able to retrieve the true parameter values. A comparison of the emulator approach to standard brute-force MCMC involving multiple data constraints showed that the emulator method was able to constrain the faster and simpler SIPNET model's parameters with comparable performance to the brute-force approach but reduced computation time by more than 2 orders of magnitude. The emulator was then applied to calibration of the ED2 model, whose complexity precludes standard (brute-force) Bayesian data assimilation techniques. Both models are constrained after assimilation of the observational data with the emulator method, reducing the uncertainty around their predictions. Performance metrics showed increased agreement between model predictions and data. Our study furthers efforts toward reducing model uncertainties, showing that the emulator method makes it possible to efficiently calibrate complex models.

58 GEOSCIENCES↗
DOE OSTI2021

High-energy-density-physics measurements in implosions using Bayesian inference

Convergent high-energy-density (HED) experimental platforms are used to study matter under some of the most extreme conditions that can be produced on Earth, comparable to the interior of stars. There are many challenges in using these systems for fundamental measurements currently being addressed by new analysis methods, such as the combination of a reduced physics model and Bayesian inference, allowing a self-consistent inference of physical quantities with a robust error analysis. These methods in combination with simple (as compared to inertial confinement fusion implosions) implosion platforms, which can be modified to show sensitivity to different physical mechanisms of interest, are used to study the physical properties of matter under extreme conditions. This work discusses a subset of implosion targets for studying opacity effects, electron-ion equilibration, and thermal conductivity and, as an example, a system consisting of a thick-shelled, gas-filled laser-direct-drive implosion is used to show how a reduced model and Bayesian inference can help inform experimental design decisions such as diagnostic choice. It is shown that for this system that a combination of neutron and x-ray self-emission diagnostics is critical for constraining the details of the thermodynamic states in the system and that the conductivity exponent in a Spitzer like framework can be constrained to the 30% level in deuterium at gigabar conditions. Furthermore, this process can be applied to many HED systems to make underlying model assumptions explicit and facilitate experimental design and analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Computational Bayesian Framework for Quantification and Reduction of Predictive Uncertainty in Subsurface Environmental Modeling

Subsurface environmental systems are open and complex, in which intricate hydrologic, microbiologic, and geochemical processes occur and interact at multiple scales. Understanding and predicting system responses to natural forces (e.g., climate changes) and human activities (e.g., contaminant remediation and CO 2 sequestration) is indispensable for managing water resources, cleaning subsurface contamination at many sites of the Department of Energy (DOE), and providing expert analysis to inform policy-making on long-term stewardship of nuclear waste disposal and CO 2 storage sites. Groundwater reactive transport modeling is necessary for understanding and predicting the complex subsurface environmental system. However, as complex systems are never completely predictable, model predictions of the subsurface system are inherently uncertain, and uncertainty is one of the greatest obstacles in simulating the subsurface environment. Quantifying predictive uncertainty of the complex system is critical to test model predictive power, support decision-making, and guide experimental design and data collection for uncertainty reduction. This project tackled two major obstacles to efficient and effective quantification and reduction of predictive uncertainty in simulating the complex subsurface environment. One obstacle is that existing methods of uncertainty quantification are too fragmented and incomplete for understanding and predicting the complex subsurface environment as a whole. The other obstacle is that existing methods of uncertainty quantification are computationally demanding and may not be applicable to groundwater reactive transport modeling that is always computationally expensive. The above two obstacles to uncertainty quantification directly affect the design of data collection schemes for uncertainty reduction. In this project, we developed a comprehensive Bayesian framework to remove the first obstacle. The second obstacle was tackled by using the sparse grid methods, which were originally developed and analyzed for numerical integration in the field of applied mathematics. We integrated the sparse grid methods into the Bayesian framework seamlessly, which led to a sparse-grid-based method of Bayesian uncertainty analysis. The developed computational Bayesian framework has been applied to a number of subsurface environmental problems through collaborating with scientists at the Pacific Northwest National Laboratory and Oak Ridge National Laboratory. The applications demonstrated that the computational Bayesian framework is general and compatible with any models and numerical codes of subsurface modeling. It is thus can be applied to gain insights for subsurface environmental modeling. This project helped the PI achieve his career goal to advance the state-of-the-art computational methods in uncertainty quantification for subsurface environmental modeling. This project supported two doctoral students, two master students, and one post-doc. The two doctoral students, after their graduation, worked as post-docs at the Pacific Northwest National Laboratory and the Oak Ridge National Laboratory. The project produced a total of 29 journal articles (four under review), one book chapter, and a number of conference proceedings and abstracts.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1996

Detection of obstacles on runway using Ego-Motion compensation and tracking of significant features

This report describes a method for obstacle detection on a runway for autonomous navigation and landing of an aircraft. Detection is done in the presence of extraneous features such as tiremarks. Suitable features are extracted from the image and warping using approximately known camera and plane parameters is performed in order to compensate ego-motion as far as possible. Residual disparity after warping is estimated using an optical flow algorithm. Features are tracked from frame to frame so as to obtain more reliable estimates of their motion. Corrections are made to motion parameters with the residual disparities using a robust method, and features having large residual disparities are signaled as obstacles. Sensitivity analysis of the procedure is also studied. Nelson's optical flow constraint is proposed to separate moving obstacles from stationary ones. A Bayesian framework is used at every stage so that the confidence in the estimates can be determined.

Kasturi, Rangachar↗
DOE OSTI2013

Physics-based dimension reduction in uncertainty quantification for radiative transfer

We present a physics-based methodology for quantifying the uncertainty in a given quantity of interest (QOI) that is contributed by uncertainties in opacities in radiation transport problems. Typically, opacities are tabulated as a function of density, temperature, and photon energy group. The size of this table makes a study of uncertainties at this level challenging because of the well-known 'curse of dimensionality.' We address this by studying uncertain parameters in the underlying physical model that generates the opacity tables. At this level, there are fewer uncertain parameters but still too many to analyze directly through computationally expensive radiation transport simulations. In order to explore this large uncertain parameter space, we develop two simplified radiation transport problems that are much less computationally demanding than the target problem of interest. An emulator is created for each QOI for each simplified problem using Bayesian Multivariate Adaptive Regression Splines (BMARS). This emulator is used to create a functional relationship between the QOIs and the uncertain parameters. Sensitivity analysis is performed using the emulator to determine which parameters contribute significantly to the uncertainty. This physics-based screening process reduces the dimension of the parameter space that is then studied via the computationally expensive radiation transport calculation to generate distributions of quantities of interest. Results of this research demonstrate that the QOIs for the target problem agree for varying screening criteria determined by the sensitivity analysis, and the QOIs agree well for varying Latin Hypercube Design (LHD) sample sizes for the uncertain space. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Using a surrogate-assisted Bayesian framework to calibrate the runoff-generation scheme in the Energy Exascale Earth System Model (E3SM) v1

Abstract. Runoff is a critical component of the terrestrial water cycle, and Earth system models (ESMs) are essential tools to study its spatiotemporal variability. Runoff schemes in ESMs typically include many parameters so that model calibration is necessary to improve the accuracy of simulated runoff. However, runoff calibration at a global scale is challenging because of the high computational cost and the lack of reliable observational datasets. In this study, we calibrated 11 runoff relevant parameters in the Energy Exascale Earth System Model (E3SM) Land Model (ELM) using a surrogate-assisted Bayesian framework. First, the polynomial chaos expansion machinery with Bayesian compressed sensing is used to construct computationally inexpensive surrogate models for ELM-simulated runoff at 0.5∘ × 0.5∘ for 1991–2010. The error metric between the ELM simulations and the benchmark data is selected to construct the surrogates, which facilitates efficient calibration and avoids the more conventional, but challenging, construction of high-dimensional surrogates for the ELM simulated runoff. Second, the Sobol' index sensitivity analysis is performed using the surrogate models to identify the most sensitive parameters, and our results show that, in most regions, ELM-simulated runoff is strongly sensitive to 3 of the 11 uncertain parameters. Third, a Bayesian method is used to infer the optimal values of the most sensitive parameters using an observation-based global runoff dataset as the benchmark. Our results show that model performance is significantly improved with the inferred parameter values. Although the parametric uncertainty of simulated runoff is reduced after the parameter inference, it remains comparable to the multimodel ensemble uncertainty represented by the global hydrological models in ISMIP2a. Additionally, the annual global runoff trend during the simulation period is not well constrained by the inferred parameter values, suggesting the importance of including parametric uncertainty in future runoff projections.

58 GEOSCIENCES↗
DOE OSTI2020

Application of Neutron Multiplicity Counting Experiments to Optimal Cross-Section Adjustments

This paper presents the first application of model calibration to neutron multiplicity counting (NMC) experiments for cross-section optimization that is informed by adjoint-based sensitivity analysis (SA) and first-order uncertainty quantification (UQ). We summarize previous work on SA applied to NMC and describe notable modifications and additions. We give the procedure for first-order UQ and Bayesian-inference-based parameter estimation (PE). We then discuss model calibration applied to NMC of a 4.5-kg sphere of weapons-grade, alpha-phase plutonium metal (the BeRP ball) with the nPod neutron multiplicity counter. For the BeRP ball in bare and polyethylene-reflected configurations, we discuss the sensitivity of the first- and second-moment detector responses (i.e., first and second moments of the NMC distribution, respectively) to the cross sections. We describe the sources of uncertainty in the measured and simulated responses. Specifically, uncertainty in the measured responses is due to both random and systematic sources. Uncertainty in the simulated responses is due to the cross-section covariances. We describe in detail the adjustment to the cross sections and cross-section covariances due to the optimization. Due to the contribution of systematic uncertainties to the measured response uncertainties, the adjustment to the cross sections is similar in trend but larger in magnitude compared to that recommended by previous work. We compare the measured responses to responses simulated with nominal and optimized cross sections, demonstrating that the best-estimate cross sections produce simulations of NMC experiments that are more accurate with reduced uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Quantifying uncertainty in Pareto estimates of global lake area

This software contains the code for Bayesian uncertainty analysis of global lake area. Computed uncertainties are compared against more conventional estimation using lake size-abundance distributions. Routines are included to explore sensitivity to observational errors and ad-hoc "censoring" strategies.

Stachelek, Jemma↗
DOE OSTI2025

Pervaporative Dehydration of 2,3-Butanediol by Dense Poly(vinylidene fluoride) Hollow Fiber Membranes: Parameter Estimation, Process Design, and Technoeconomic Evaluation under Uncertainty

Pervaporation, combined with other separation processes, can effectively remove water from fermentation product streams, making it highly suitable for purifying alcohols like 2,3-butanediol (BDO). In this study, a dense poly(vinylidene fluoride) (PVDF) hollow fiber membrane module prototype was fabricated for BDO dehydration, achieving >0.2 LMH total flux and >95% BDO rejection. With a Markov chain Monte Carlo (MCMC) approach, Bayesian inference was used to quantify the uncertainty of the permeance parameters. A membrane cascade model was developed to scale up a process that purifies a preconcentrated BDO feed (70 wt %) to high purity (90 wt %). Through propagation of the uncertainty of the parameters and sensitivity analyses of the process variables, a cascade design was recommended. Despite data and model limitations, the framework enabled a reliable system analysis and economic evaluation, validated through tight confidence intervals in key process metrics, establishing the foundation for future applications of Bayesian methods in membrane-based processes.

Animal feed↗
DOE OSTI2018

Effective Field Theory Analysis and Active Neutron Veto Design for the Cryogenic Dark Matter Search

Astrophysical measurements and cosmological predictions suggest the exists of a large amount of matter in the universe that does not interact via electromagnetic forces. This non-luminescent matter, known dark matter, exists in halos that encompass and are within galaxies, including the Milky Way. Therefore, dark matter particles should should be directly detectable by experiments on Earth, such as the Super Cryogenic Dark Matter Search (SuperCDMS). Dark matter is assumed to be low mass (< 100 GeV/c2) and interact via the weak force using either a spin-independent or spin-dependent coupling. However, making incorrect assumptions about dark matter interactions can lead to misleading results. Because interactions with dark matter particles are rare, direct detection experiments must be able to shield for or reject backgrounds to very low levels. Low energy neutron backgrounds that make it to the detectors are especially dangerous, because they cannot be easily distinguished from the expected dark matter signal. Scintillator doped with a high neutron-capture cross-section material can be used to detect neutrons via their resulting gamma rays. Examples of such detectors using liquid scintillator have been successfully used in past high-energy physics (HEP) experiments. However, a liquid scintillator can leak and is not as amenable to modular or complex shapes as a solid scintillator. The light outputs and efficiencies of gadolinium-loaded polystyrene-based scintillators have been explored using a wide variety of gadolinium compounds with varying concentrations. Collection strategies using a wavelength shift- ing (WLS) fiber and silicon photomultipliers (SiPMs) were also evaluated as a possible neutron veto for an upgrade to SuperCDMS SNOLAB. The scattering of dark matter particles off nuclei in direct detection experiments can be described in terms of a multidimensional effective field theory (EFT). A new systematic analysis technique is developed using the EFT approach and Bayesian inference methods to exploit, when possible, the energy-dependent information of the detected events, experimental efficiencies, and backgrounds. Highly dimensional likelihoods are calculated over the mass of the weakly interacting massive particle (WIMP) and multiple EFT coupling coefficients, which can then be used to set limits on these parameters and choose models (EFT operators) that best fit the direct detection data. Expanding the parameter space beyond the standard spin-independent isoscalar cross section and WIMP mass reduces tensions between previously published experiments. Combining these experiments to form a single joint likelihood leads to stronger limits than when each experiment is considered on its own. Simulations using two nonstandard operators (O3 and O8) are used to test the proposed analysis technique in up to five dimensions and demonstrate the importance of using multiple likelihood projections when determining constraints on WIMP mass and EFT coupling coefficients. In particular, this shows that an explicit momentum dependence in dark matter scattering can be identified. CDMSlite Run 2 was a search for Weakly Interacting Massive Particles (WIMPs) with a cryogenic 600 g Germanium detector operated deep underground. It was operated in a mode optimizing sensitivity to WIMPs of relatively low mass, 2 - 20 GeV, while sacrificing background rejection. An EFT analysis of CDMSlite Run 2 data from SuperCDMS Soudan is presented here. A binned likelihood Bayesian analysis was performed on the data, optimizing over the parameters of EFT interactions and the recoil energy spectra due to the dominant Compton scattering and tritium backgrounds. Recoil energy regions within 5σ of known activation peaks were removed from the analysis. The Bayesian evidences of the resulting likelihoods show that CDMSlite Run 2 data is entirely consistent with the background models with no EFT interaction necessary. Upper limits on the WIMP mass and coupling coefficients amplitudes and phases are presented for each EFT operator.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Bayesian Calibration of Stochastic Agent Based Model via Random Forest

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high-dimensional calibration can be computationally prohibitive. This paper presents a random forest-based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented, and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. Further, these results are compared with previous approximate Bayesian calibration (IMABC) results, and their predictive performance is analyzed, showing improved performance with a reduction in computation.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1974

On the robustness of a Bayes estimate

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Canavos, G. C.↗