Uncertainty Analysis by Bayesian Inference

A Bayesian model calibration framework to evaluate brain tissue characterization experiments

Recent literature on building energy performance simulation leans toward implementing uncertainty analysis (UA), instead of deterministic solutions, to handle ever-existing and pivotal uncertainties in building design decision-making process. Variations in weather temperature, degradation of building envelope material properties over time, and random behavior of occupants, among all, are the key sources of uncertainty in building energy consumption predictions. The UA couples to the sensitivity analysis (SA) to identify the most influential inputs on the uncertainties of the building energy consumption. This paper describes a newly-developed UA and SA predictive tool for building energy performance simulations. Energy performance simulations are based on a resistance-capacitance thermal model for the building. For a hypothetical residential building in College Station, Texas, USA, the present work describes and compares predicted probability distribution and sensitivity indexes produced by the UA-SA tool using a transient (dynamic) response analysis (TRA) and static response analysis (SRA). For brevity, the analysis considers uncertainty only for the exterior walls’ parameters including thickness, thermal conductivity, heat transfer coefficient, density, and heat capacity; i.e., a five-dimensional problem is solved. Compared to the TRA, predictions from the SRA underestimate the annual energy consumption up to 30%; however, SRA is significantly faster. Nonetheless, sensitivity indexes from the SRA and TRA closely match.

Bayesian calibration and sensitivity analysis of heat transfer models for fire insulation panels

Brown bullheads (Ameiurus nebulosus) from three contaminated sites (Detroit River, Hamilton Harbour, and Black River) and two relatively clean reference sites (Old Woman Creek and Bay of Quinte) in the lower Great Lakes were monitored for several biomarkers of exposure to chemical contaminants. Bullheads from the contaminated sites had elevated hepatosomatic indices, increased ethoxyresorufin-O-deethylase (EROD) activity, decreased hepatic retinoid stores, and a greater incidence of hepatic neoplasms. Fluorescent aromatic compounds (FACs) in the bile were also elevated in bullheads from the Black River and Hamilton Harbour in comparison to fish from reference sites. A correlation was found between reduction of hepatic retinoid stores and induction of hepatic EROD activity in bullheads. Principal component analysis of biomarker data demonstrated that biomarker patterns in Detroit River bullheads were different from those of Black River and Hamilton Harbour bullheads. Biomarkers in fish are useful monitoring tools for detecting contamination of the aquatic environment, but interpretation of results is limited by within-and between-site variability in the responses, some of which may be explained by mobility of the fish. In contaminated areas, bile fluorescent aromatic compounds appear to be the best indicator of recent exposure to polynuclear aromatic hydrocarbons, whereas responses to other biochemical biomarkers (e.g., EROD and retinoids) appear to be over a longer time period.

Non-linear numerical models of the injection phase of a carbon sequestration (CS) project are computationally demanding. Thus, the computational cost of the calibration of these models using sampling-based solutions can be formidable. The Bayesian adaptive response surface method (BARSM)—an adaptive response surface method (RSM)—is developed to mitigate the cost of sampling-based, continuous calibration of CS models. It is demonstrated that the adaptive scheme has a negligible effect on accuracy, while providing a significant increase in efficiency. In the BARSM, a meta-model replaces the computationally costly full model during the majority of the calibration cycles. In the remaining cycles, the full model is used and samples of these cycles are utilized for adaptively updating the meta-model. The idea behind the BARSM is to take advantage of the fact that sampling-based calibration algorithms typically tend to sample more frequently from areas with a larger posterior density than from areas with a smaller posterior density. This behavior of the sampling-based calibration algorithms is used to adaptively update the meta-model and to make it more accurate where it is most likely to be evaluated. The BARSM is integrated with Unscented Importance Sampling (UIS) (Sarkarfarshi and Gracie, Stoch Env Res Risk Assess 29: 975–993, 2015), which is an efficient Bayesian calibration algorithm. A synthesized case of supercritical CO2 injection in a heterogeneous saline aquifer is used to assess the performance of the BARSM and to compare it with a classical non-adaptive RSM approach and Bayesian calibration method UIS without using RSM. The BARSM is shown to reduce the computational cost compared to non-adaptive Bayesian calibration by 87 %, with negligible effect on accuracy. It is demonstrated that the error of the meta-model fitted using the BARSM, when samples are drawn from the posterior parameter distribution, is negligible and smaller than the monitoring error.

SummaryDynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

Introduction| December 09 2008 Preface Aquatic Ecosystem Health & Management (2008) 11 (4): 353–354. https://doi.org/10.1080/14634980802565901 Cite Icon Cite Share Icon Share Twitter Permissions Search Site Citation Preface. Aquatic Ecosystem Health & Management 9 December 2008; 11 (4): 353–354. doi: https://doi.org/10.1080/14634980802565901 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All Scholarly Publishing CollectiveMichigan State University PressAquatic Ecosystem Health & Management Search Advanced Search The Aquatic Ecosystem Health & Management Society (AEHMS) has been organizing a series of “State of the Lake” conferences around the world, including Lakes Baikal, Erie, Michigan, Winnipeg, Superior, Victoria and Tanganyika. The AEHMS has always followed up conferences with peer – reviewed publications which include integration and synthesis of state of the art information about these lakes. The papers resulting from these conferences have been published either as a peer-reviewed book, or as a special issue of AEHM (see www.aehms.org). This issue, titled Checking the Pulse of Lake Ontario (POLO), is part of this series.The Lake Ontario ecosystem is experiencing significant ecological change. Phosphorus abatement implemented in the 1970s under the auspices of the Great Lakes Water Quality Agreement (GLWQA) has resulted in low spring total phosphorus levels in offshore waters, while nutrients like silicon and nitrate have increased over this period. Consistent with declines in phosphorus... You do not currently have access to this content.

Development and calibration of digital twins for human skin growth in tissue expansion.

An interactive graphical interface tool for parameter calibration, sensitivity analysis, uncertainty analysis, and visualization for the Soil and Water Assessment Tool

In experiments conducted on the Z-machine at Sandia National Laboratories, dynamic material properties cannot be analyzed using traditional analytic methods, necessitating solving an inverse problem. Bayesian model calibration is a statistical framework for solving an inverse problem to estimate parameters input into a computational model in the presence of multiple uncertainties. Disentangling input parameter uncertainty and model misspecification is often poorly identified problem. When using computational models for physical parameter estimation, the issue of parameter identifiability must be carefully considered to obtain accurate and precise estimates of physical parameters. Additionally, in dynamic material properties applications, the experimental output is a function, velocity over time. While we can sample an arbitrarily large number of points from the measured velocity, these curves only contain a finite amount of information about the calibration parameters. In this report, we propose modifications to the Bayesian model calibration framework to simplify and improve the estimation of physical parameters with functional outputs. Specifically, we propose scaling the likelihood function by an effective sample size rather than modeling the discrepancy function; and modularizing input nuisance parameters with weakly identified parameters. We evaluate the performance of these proposed methods using a statistical simulation study and then apply these methods to estimate parameters of the tantalum equation of state. We conclude that these proposed methods can provide simple, fast, and statistically valid alternatives to the full Bayesian model calibration procedure; and that these methods can be used to estimate parameters of the equation of state for tantalum.

<p>The open source Mobius framework allows for quick develoment of models based on ODE- and discrete-timestep equations. One can build and explore many model structures with only small modifications to the model code. Model run speed is fast, making it feasible to do extensive automated parameter space exploration, for instance using optimizers or MCMC algorithms. The framework can compile models to a format where they are accessible for interaction using the Python scripting language. Moreover, several calibration and uncertainty analysis tools in Python are already set up so that they can be used with any Mobius model. This can then be used to evaluate model structures using Bayesian methods. We show an example of evaluating a few DOC catchment models using this framework. Modelling frameworks are a good alternative to one-size-fits-all models, and we hope Mobius will be a useful tool for promoting more robust modelling. </p>

A probabilistic framework for Bayesian inference and uncertainty analysis is developed. It allows inverse problems to be addressed in experimental situations where data are scarce and uncertainty is ubiquitous. The uncertainty characterization subproblem of the NASA Langley Multidisciplinary Uncertainty Quantification Challenge serves as the motivating application example. From the responses of a computational model, the goal is to learn about unknown model inputs that are subject to multiple types of uncertainty. This objective is interpreted and solved as Bayesian multilevel model calibration. The zero-noise or “perfect” data limit is investigated. Thereby, the likelihood function is defined as a solution to forward uncertainty propagation. Posterior explorations are based on suitable Markov chain Monte Carlo algorithms and stochastic likelihood simulations. An unforeseen finding in this context is that the posterior distribution can only be sampled with a certain degree of fidelity. Partial data augmentation is introduced as a means to improve the error statistics of likelihood estimations and the fidelity of posterior computations.

Hybrid wind energy forecasting and analysis system based on divide and conquer scheme: A case study in China

In 2019, the International Atomic Energy Agency launched a coordinated research project titled “Advancing the State of the Practice in Uncertainty and Sensitivity Methodologies for Severe Accident Analysis in Water Cooled Reactors of CANDU Types.” This project involved participation from 22 organizations representing 18 member states. The purpose of the project was to advance the understanding and characterization of the sources of uncertainty and assess their impacts on key water-cooled reactor figures of merit predicted by severe accident (SA) codes. Three organizations from three member states participated in the CANada Deuterium Uranium (CANDU) exercise: Canadian Nuclear Laboratories, Canada; Korea Atomic Energy Research Institute, Republic of Korea; and University Politehnica of Bucharest, Romania. Each contributor used its own SA code and uncertainty analysis tools and selected its own uncertain input variables with associated probability distributions. All three participants performed a station blackout scenario for a generic CANDU 6 station, using similar normal operating conditions and analysis assumptions. This paper presents the results of the uncertainty and sensitivity calculations from each contributor and discusses the key findings, lessons learned, and future work.

SWMM (Stormwater Management Model) is one of the most widely used computation tools in urban water resources management. Traditionally, the choice of rainfall data for calibrating the SWMM model has been arbitrary, lacking clarity on the most suitable rainfall types. In addition, the simplification in the SWMM hydrological module of the rainfall–runoff process, coupled with measurement errors, introduces a high level of uncertainty in the calibration. This study investigates the influences of rainfall types on the highly uncertain SWMM model calibration by implementing the Bayesian inference theory. A Bayesian SWMM calibration framework was established, in which an advanced DREAM(zs) (Differential Evolution Adaptive Metropolis, Version ZS) sampling method was used. The investigation focused on eight key hydrological parameters of SWMM. The impact of rainfall types was analyzed using nine rainfall intensities and three rainfall patterns. Results show that rainfall events equivalent to a one-year return period (R5, 42.70 mm total depth) or higher generally yield the most accurate parameters, with posterior distribution standard deviations reduced by 40–60% compared to low-intensity rainfalls. Notably, three parameters (impervious area percentage [Imperv], storage depth of impervious area [S-imperv], and Manning’s coefficient of impervious area [N-imperv]) demonstrated consistent accuracy irrespective of rainfall intensity, with a coefficient of variation below 0.05 for Imperv and S-imperv across all rainfall intensities. Furthermore, it was found that rainfall events with double peaks resulted in more satisfactory calibration compared to single or triple peaks, reducing the standard deviation of the Width parameter from 168.647 (single-peak) to 110.789 (double-peak). The findings from this study could offer valuable insights for selecting appropriate rainfall events before SWMM model calibration for more accurate predictions when it comes to urban non-point pollution control strategies and watershed management.