Hamiltonian Monte Carlo Method Research Articles

Reliability analysis of complex systems using subset simulations with Hamiltonian Neural Networks

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with computationally efficient gradient evaluations using Hamiltonian neural networks. This combination is especially advantageous because the neural network architecture conserves the Hamiltonian, which defines the acceptance criteria of the Hamiltonian Monte Carlo sampler. Hence, this strategy achieves high acceptance rates at low computational cost. Our approach estimates small failure probabilities using Subset Simulations. However, in low-probability sample regions, the gradient evaluation is particularly challenging. The remarkable accuracy of the proposed strategy is demonstrated on different reliability problems, and its efficiency is compared to the traditional Hamiltonian Monte Carlo method. We note that this approach can reach its limitations for gradient estimations in low-probability regions of complex and high-dimensional distributions. Thus, we propose techniques to improve gradient prediction in these particular situations and enable accurate estimations of the probability of failure. The highlight of this study is the reliability analysis of a system whose parameter distributions must be inferred with Bayesian inference problems. In such a case, the Hamiltonian Monte Carlo method requires a full model evaluation for each gradient evaluation and, therefore, comes at a very high cost. However, using Hamiltonian neural networks in this framework replaces the expensive model evaluation, resulting in tremendous improvements in computational efficiency.

Assessing the E-bike trends and impact on sustainable mobility: A national-level study in the Netherlands

Over the past decade, e-bikes have become increasingly popular, sparking interest in their potential replacement for car use and benefit for the environment. However, many studies on e-bike development and their substitution effects exhibit limitations. These include a lack of modeling on e-bike trend development, inadequate assessments of their impact on national-level mobility, a predominant focus on commuting, and a lack of foresight into future e-bike substitution effects. Our research introduces an innovative approach to model e-bike development, employing a multilevel Richards growth curve model fitted within a hierarchical Bayesian framework using the Hamiltonian Monte Carlo (HMC) method. Further, we incorporate an intention-based method to delve into the potential of e-bikes in stimulating sustainable mobility in the Netherlands. Our findings highlight an ongoing increase in e-bike distance share, with marked gender and generational differences in growth patterns. Notably, women have higher e-bike usage than men, and this gap is narrowing for older age groups while widening among younger demographics, suggesting that younger people may adopt e-bike usage differently than older generation. E-bike ownership strongly reduces the conventional bicycle use and, to a lesser extent, car and public transport use, especially for commuting. This study provides insight into whether and to what extent e-bikes substitute for car use and other modes of transportation, and how the expected growth in e-bike use in coming years may impact national mobility in the Netherlands.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Hamiltonian Monte Carlo based elastic full-waveform inversion of wide-angle seismic data

SUMMARY Full-waveform inversion (FWI) of seismic data provides quantitative constraints on subsurface structures. Despite its widespread success, FWI of data around the critical angle is challenging because of the abrupt change in amplitude and phase at the critical angle and the complex waveforms, especially in the presence of a sharp velocity contrast, such as at the Moho transition zone (MTZ). Furthermore, the interference of refracted lower crustal (Pg) and upper mantle (Pn) arrivals with the critically reflected Moho (PmP) arrivals in crustal and mantle studies makes the application of conventional FWI based on linearized model updates difficult. To address such a complex relationship between the model and data, one should use an inversion method based on a Bayesian formulation. Here, we propose to use a Hamiltonian Monte Carlo (HMC) method for FWI of wide-angle seismic data. HMC is a non-linear inversion technique where model updates follow the Hamiltonian mechanics while using the gradient information present in the probability distribution, making it similar to iterative gradient techniques like FWI. It also involves procedures for generating distant models for sampling the posterior distribution, making it a Bayesian method. We test the performance and applicability of HMC based elastic FWI by inverting the non-linear part of the synthetic seismic data from a three-layer and a complex velocity model, followed by the inversion of wide-angle seismic data recorded by two ocean bottom seismometers over a 70 Ma old oceanic crustal segment in the equatorial Atlantic Ocean. The inversion results from both synthetic and real data suggest that HMC based FWI is an appropriate method for inverting the non-linear part of seismic data for crustal studies.

A new OSL dose model to account for post-depositional mixing of sediments

In applications of optically stimulated luminescence (OSL) dating to unconsolidated sediments, the burial age of a sample of grains is estimated using statistical models of the distribution of the experimentally determined equivalent doses of the grains, together with estimates of the environmental dose rate. For grains that have been vertically mixed after deposition (e.g., due to bioturbation), existing dose models may fail to appropriately account for the complexity of the mixing process, thus producing inaccurate age estimates of the original time of deposition of the ‘native’ grains in any particular sample (usually the quantity of most interest). Here we introduce a new dose model, the asymmetric Laplacian mixture model (ALMM), developed for vertically mixed samples with single-grain dose distributions. The approach is based on a continuous statistical mixture that models the displacement of grains in both upward and downward directions. The central dose of the native grains in each sediment sample is estimated by the ALMM, as well as the parameters associated with overdispersion of single-grain dose distributions and the (modelled) mixing process. Using Bayesian methodology, we apply the model to two series of vertically contiguous samples collected at the site of Nawarla Gabarnmang in northern Australia. Independent age estimates obtained from radiocarbon dating of charcoal fragments support the OSL ages for the native grains estimated by the ALMM. Moreover, our study includes sensitivity analyses that show the model is robust to variation in the experimental error of the OSL data, as well as a simulation study that demonstrates the model’s good ability to recover the simulated central dose and its excellent coverage properties. The ALMM is introduced in the context of compound Gaussian distributions, a broadly encompassing statistical framework that includes many of the most commonly used dose models. This unifying and accessible perspective on the statistical modelling of dose distributions will support practitioners in selecting an appropriate model for samples affected by post-depositional mixing, and hopefully stimulate further theoretical developments. A new R package rstanosl is provided that fits the ALMM and other commonly used dose models using Hamiltonian Monte Carlo methods via the Stan programming language.

The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach

Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct. Many regression model selection criteria are considered, including the maximum likelihood (ML) point estimation of the parameter and the logarithm of the likelihood of the dataset. This paper demonstrates the information complexity (ICOMP), Bayesian deviance information, or the widely applicable information criterion (WAIC) of the BRMS to hierarchical linear models fitted with repeated measures with a simulation and two real data examples. The Fisher information matrix for the Bayesian hierarchical model considering fixed and random parameters under maximizing a posterior estimation is derived. Using Gibbs sampling and Hybrid Hamiltonian Monte Carlo approaches, six different models were fitted for three distinct application datasets. The best-fitted candidate models were identified under each application dataset with the two MCMC approaches. In this case, the Bayesian hierarchical (mixed effect) linear model with random intercepts and random slopes estimated using the Hamiltonian Monte Carlo method best fits the two application datasets. Information complexity (ICOMP) is a better indicator of the best-fitted models than DIC and WAIC. In addition, the information complexity criterion showed that hierarchical models with gradient-based Hamiltonian Monte Carlo estimation are the best fit and have supper convergence relative to the gradient-free Gibbs sampling methods.

Joint Inversion of UMRS-TEM Data and Its Application for Detection in the Tunnel Using Hamiltonian Monte Carlo Method

Joint Inversion of UMRS-TEM Data and Its Application for Detection in the Tunnel Using Hamiltonian Monte Carlo Method

A Bayesian Analysis of a Cognitive-Behavioral Therapy Intervention for High-Risk People on Probation

This analysis employs a Bayesian framework to estimate the impact of a Cognitive-Behavioral Therapy (CBT) intervention on the recidivism of high-risk people under community supervision. The study relies on the reanalysis of experimental datal using a Bayesian logistic regression model. In doing so, new estimates of programmatic impact were produced using weakly informative Cauchy priors and the Hamiltonian Monte Carlo method. The Bayesian analysis indicated that CBT reduced the prevalence of new charges for total, non-violent, property, and drug crimes. However, the effectiveness of the CBT program varied meaningfully depending on the participant's age. The probability of the successful reduction of drug offenses was high only for younger individuals (<26 years old), while there was an impact on property offenses only for older individuals (>26 years old). In general, the probability of the successful reduction of new charges was higher for the older group of people on probation. Generally, this study demonstrates that Bayesian analysis can complement the more commonplace Null Hypothesis Significance Test (NHST) analysis in experimental research by providing practically useful probability information. Additionally, the specific findings of the reestimation support the principles of risk-needs responsivity and risk-stratified community supervision and align with related findings, though important differences emerge. In this case, the Bayesian estimations suggest that the effect of the intervention may vary for different types of crime depending on the age of the participants. This is informative for the development of evidence-based correctional policy and effective community supervision programming.

Hierarchical Bayesian Inference of Globular Cluster Properties

Abstract We present a hierarchical Bayesian inference approach to estimating the structural properties and the phase space center of a globular cluster (GC) given the spatial and kinematic information of its stars based on lowered isothermal cluster models. As a first step towards more realistic modelling of GCs, we built a differentiable, accurate emulator of the lowered isothermal distribution function using interpolation. The reliable gradient information provided by the emulator allows the use of Hamiltonian Monte Carlo methods to sample large Bayesian models with hundreds of parameters, thereby enabling inference on hierarchical models. We explore the use of hierarchical Bayesian modelling to address several issues encountered in observations of GC including an unknown GC center, incomplete data, and measurement errors. Our approach not only avoids the common technique of radial binning but also incorporates the aforementioned uncertainties in a robust and statistically consistent way. Through demonstrating the reliability of our hierarchical Bayesian model on simulations, our work lays out the foundation for more realistic and complex modelling of real GC data.

Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation.

As an alternative to animal use, computer simulations are useful for predicting pharmacokinetics and cardiovascular activities. For this purpose, we constructed a statistical model to simulate the effects of local anesthetic agents. To train the model, animal experiments were performed on 6-week-old male Hartley guinea pigs. Firstly, the guinea pigs' backs were shaved, then local anesthetic agents were subcutaneously injected, with subsequent stimulation of the anesthetized site with a needle six times at regular intervals. The number of reactions (score value) was counted. In this statistical model, the probability of reacting to needle stimulation was calculated using the elapsed time, type of local anesthetic agent, and presence or absence of adrenaline. Score values were assumed to follow a binomial distribution at the calculated probability. Parameters were estimated using the Bayesian hierarchical model and Hamiltonian Monte Carlo method. The predicted curves using the estimated parameters fitted well the observed animal values. When score values were predicted using randomly generated parameters, the median of duration was similar between animal experiments and simulations (Procaine: 55 min vs. 50 min, Lidocaine: both 60 min, and Mepivacaine: both 85 min). This approach effectively modeled the effects of local anesthetic agents. It is possible to create the simulator using the parameter values estimated in this study.

Evaluation of phase-adjusted interventions for COVID-19 using an improved SEIR model.

A local COVID-19 outbreak with two community clusters occurred in a large industrial city, Shaoxing, China, in December 2021 after serial interventions were imposed. We aimed to understand the reason by analysing the characteristics of the outbreak and evaluating the effects of phase-adjusted interventions. Publicly available data from 7 December 2021 to 25 January 2022 were collected to analyse the epidemiological characteristics of this outbreak. The incubation period was estimated using Hamiltonian Monte Carlo method. A well-fitted extended susceptible-exposed-infectious-recovered model was used to simulate the impact of different interventions under various combination of scenarios. There were 387 SARS-CoV-2-infected cases identified, and 8.3% of them were initially diagnosed as asymptomatic cases. The estimated incubation period was 5.4 (95% CI 5.2-5.7) days for all patients. Strengthened measures of comprehensive quarantine based on tracing led to less infections and a shorter duration of epidemic. With a same period of incubation, comprehensive quarantine was more effective in containing the transmission than other interventions. Our findings reveal an important role of tracing and comprehensive quarantine in blocking community spread when a cluster occurred. Regions with tense resources can adopt home quarantine as a relatively affordable and low-impact intervention measure compared with centralized quarantine.

Creating High-Quality Synthetic Health Data: Framework for Model Development and Validation.

Electronic health records are a valuable source of patient information that must be properly deidentified before being shared with researchers. This process requires expertise and time. In addition, synthetic data have considerably reduced the restrictions on the use and sharing of real data, allowing researchers to access it more rapidly with far fewer privacy constraints. Therefore, there has been a growing interest in establishing a method to generate synthetic data that protects patients' privacy while properly reflecting the data. This study aims to develop and validate a model that generates valuable synthetic longitudinal health data while protecting the privacy of the patients whose data are collected. We investigated the best model for generating synthetic health data, with a focus on longitudinal observations. We developed a generative model that relies on the generalized canonical polyadic (GCP) tensor decomposition. This model also involves sampling from a latent factor matrix of GCP decomposition, which contains patient factors, using sequential decision trees, copula, and Hamiltonian Monte Carlo methods. We applied the proposed model to samples from the MIMIC-III (version 1.4) data set. Numerous analyses and experiments were conducted with different data structures and scenarios. We assessed the similarity between our synthetic data and the real data by conducting utility assessments. These assessments evaluate the structure and general patterns present in the data, such as dependency structure, descriptive statistics, and marginal distributions. Regarding privacy disclosure, our model preserves privacy by preventing the direct sharing of patient information and eliminating the one-to-one link between the observed and model tensor records. This was achieved by simulating and modeling a latent factor matrix of GCP decomposition associated with patients. The findings show that our model is a promising method for generating synthetic longitudinal health data that is similar enough to real data. It can preserve the utility and privacy of the original data while also handling various data structures and scenarios. In certain experiments, all simulation methods used in the model produced the same high level of performance. Our model is also capable of addressing the challenge of sampling patients from electronic health records. This means that we can simulate a variety of patients in the synthetic data set, which may differ in number from the patients in the original data. We have presented a generative model for producing synthetic longitudinal health data. The model is formulated by applying the GCP tensor decomposition. We have provided 3 approaches for the synthesis and simulation of a latent factor matrix following the process of factorization. In brief, we have reduced the challenge of synthesizing massive longitudinal health data to synthesizing a nonlongitudinal and significantly smaller data set.

HMCLab: a framework for solving diverse geophysical inverse problems using the Hamiltonian Monte Carlo method

SUMMARY The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a need for common platforms to solve different geophysical inverse problems and showing potential and pitfalls of the methodology. In this work, we demonstrate a common framework within which it is possible to solve such inverse problems ranging from, for example, earthquake source location to potential field data inversion and seismic tomography. This allows us to fully address nonlinear problems and to derive useful information about the subsurface, including uncertainty estimation. This approach can, in fact, provide probabilities related to certain properties or structures of the subsurface, such as histograms of the value of some physical property, the expected volume of buried geological bodies or the probability of having boundaries defining different layers. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods. This unique combination of HMC and adjoint methods is what makes the solution of tomographic problems ultimately feasible. These results can be obtained with ‘HMCLab’, a numerical laboratory for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers (HMC and others) and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyse the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community.

Bayesian multivariate nonlinear state space copula models

A novel flexible class of multivariate nonlinear non-Gaussian state space models, based on copulas, is proposed. Specifically, it is assumed that the observation equation and the state equation are defined by copula families that are not necessarily equal. Inference is performed within the Bayesian framework, using the Hamiltonian Monte Carlo method. Simulation studies show that the proposed copula-based approach is extremely flexible, since it is able to describe a wide range of dependence structures and, at the same time, allows us to deal with missing data. The application to atmospheric pollutant measurement data shows that the approach is suitable for accurate modeling and prediction of data dynamics in the presence of missing values. Comparison to a Gaussian linear state space model and to Bayesian additive regression trees shows the superior performance of the proposed model with respect to predictive accuracy.

Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems

Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks (PINNs) and deep operator networks (DeepONets) are two such models. The former encodes the physical laws via the automatic differentiation, while the latter learns the hidden physics from data. Generally, the noisy and limited observational data as well as the over-parameterization in neural networks (NNs) result in uncertainty in predictions from deep learning models. In paper “MENG, X., YANG, L., MAO, Z., FERRANDIS, J. D., and KARNIADAKIS, G. E. Learning functional priors and posteriors from data and physics. Journal of Computational Physics, 457, 111073 (2022)”, a Bayesian framework based on the generative adversarial networks (GANs) has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets. Specifically, the proposed approach in “MENG, X., YANG, L., MAO, Z., FERRANDIS, J. D., and KARNIADAKIS, G. E. Learning functional priors and posteriors from data and physics. Journal of Computational Physics, 457, 111073 (2022)” has two stages: (i) prior learning, and (ii) posterior estimation. At the first stage, the GANs are utilized to learn a functional prior either from a prescribed function distribution, e.g., the Gaussian process, or from historical data and available physics. At the second stage, the Hamiltonian Monte Carlo (HMC) method is utilized to estimate the posterior in the latent space of GANs. However, the vanilla HMC does not support the mini-batch training, which limits its applications in problems with big data. In the present work, we propose to use the normalizing flow (NF) models in the context of variational inference (VI), which naturally enables the mini-batch training, as the alternative to HMC for posterior estimation in the latent space of GANs. A series of numerical experiments, including a nonlinear differential equation problem and a 100-dimensional (100D) Darcy problem, are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the “gold rule” HMC. Moreover, the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation (PDE) problems with big data.

Hamiltonian MCMC methods for estimating rare events probabilities in high-dimensional problems

Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, based on an introduced framework termed Approximate Sampling Target with Post-processing Adjustment (ASTPA), which herein is integrated with and supported by gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) methods. The developed techniques in this paper are applicable from low- to high-dimensional stochastic spaces, and the basic idea is to construct a relevant target distribution by weighting the original random variable space through a one-dimensional output likelihood model, using the limit-state function. To sample from this target distribution, we exploit HMCMC algorithms, a family of MCMC methods that adopts physical system dynamics, rather than solely using a proposal probability distribution, to generate distant sequential samples, and we develop a new Quasi-Newton mass preconditioned HMCMC scheme (QNp-HMCMC), which is particularly efficient and suitable for high-dimensional spaces. To eventually compute the rare event probability, an original post-sampling step is devised using an inverse importance sampling procedure based on the already obtained samples. The statistical properties of the estimator are analyzed as well, and the performance of the proposed methodology is examined in detail and compared against Subset Simulation in a series of challenging low- and high-dimensional problems.

Inference on a Multi-Patch Epidemic Model with Partial Mobility, Residency, and Demography: Case of the 2020 COVID-19 Outbreak in Hermosillo, Mexico.

Most studies modeling population mobility and the spread of infectious diseases, particularly those using meta-population multi-patch models, tend to focus on the theoretical properties and numerical simulation of such models. As such, there is relatively scant literature focused on numerical fit, inference, and uncertainty quantification of epidemic models with population mobility. In this research, we use three estimation techniques to solve an inverse problem and quantify its uncertainty for a human-mobility-based multi-patch epidemic model using mobile phone sensing data and confirmed COVID-19-positive cases in Hermosillo, Mexico. First, we utilize a Brownian bridge model using mobile phone GPS data to estimate the residence and mobility parameters of the epidemic model. In the second step, we estimate the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian-inspired evolutionary algorithm (EA)-that is, a genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification in the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results demonstrate that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from the HMC method yield large credible intervals, improving their coverage for the observed and predicted daily incidences. Furthermore, we observe that the use of a multi-patch model with mobility yields improved predictions when compared to a single-patch model.

A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems

A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems

Estimating the differences between inter-operator contrast enhancement in cerebral CT angiography.

Computed tomography (CT) angiography (CTA) is a non-invasive imaging method used to detect arteries and examine various brain diseases. When CTA is performed for follow-up or postoperative evaluation, reproducibility of vessel delineation is required. A reproducible and stable contrast enhancement can be achieved by manipulating the factors affecting it. Previous studies have investigated several factors that alter the contrast enhancement of arteries. However, no reports establishing the effect of different operators on contrast enhancement exist. To assess the differences between inter-operator arterial contrast enhancement in cerebral CTA using Bayesian statistical modeling. Image data were obtained using a multistage sampling method from the cerebral CTA scans of patients who underwent the process between January 2015 and December 2018. Several Bayesian statistical models were developed, and the objective variable was the mean CT number of the bilateral internal carotid arteries after contrast enhancement. The explanatory variables were sex, age, fractional dose (FD), and the operator's information. The posterior distributions of the parameters were computed via Bayesian inference using the Markov chain Monte Carlo (MCMC) method, with the Hamiltonian Monte Carlo method employed as the algorithm. The posterior predictive distributions were computed using the posterior distributions of the parameters. Finally, the differences between inter-operator arterial contrast enhancement on the CT number in cerebral CTA were estimated. The posterior distributions showed that all parameters representing the difference between operators included zero at the 95% credible intervals (CIs). The maximum mean difference between inter-operator CT number in the posterior predictive distribution was only 12.59 Hounsfield units (HUs). The Bayesian statistical modeling results suggest that contrast enhancement of cerebral CTA examination between operator-to-operator differences in postcontrast CT number was small compared to those within-operator differences resulting from factors not considered in the model.

Uncertainty in systemic risks rankings: Bayesian and frequentist analysis

We propose efficient Bayesian Hamiltonian Monte Carlo method for estimation of systemic risk measures, LRMES, SRISK and ΔCoVaR, and apply it for thirty global systemically important banks and for eighteen largest US financial institutions over the period of 2000–2020. The advantage of the Hamiltonian method is an efficient estimation of all parameters jointly in high dimensional models and providing posterior distributions incorporating parameter uncertainty. The systemic risk measures are computed based on the Dynamic Conditional Correlations model with generalized asymmetric volatility. We estimate the systemic risks posterior distributions and two-step maximum likelihood distributions with bootstrap simulations for LRMES. The systemic risk rankings at different quantiles of the distributions vary considerably using bootstrap approach for computation of LRMES and SRISK, and are more stable with Bayesian posterior distributions using a parametric model. A policymaker may choose to rank the firms using some quantile of their systemic risk distributions such as 90, 95, or 99% depending on risk preferences with higher quantiles being more conservative.