Quantitative Evaluation Of Uncertainty Research Articles

Horizon auto-picking with quantitative uncertainty evaluation by using a modified VQ-VAE framework

Abstract In this paper, we propose a novel approach of deep-learning-based seismic horizon auto-picking that introduces a modified vector quantized variational autoencoder (VQ-VAE) framework to improve the accuracy of seismic horizon interpretation and, for the first time, quantitatively evaluate the uncertainty of the auto-picked horizon by exploiting the concept of entropy. Compared with the conventional VQ-VAE approach, the proposed method not only modifies the VQ-VAE model with more deep-learning channels at each layer of the network to enhance the performance of horizon auto-picking within the VQ-VAE framework, but also extends the 1D seismic labels with more continuous samplings within a single trace to boost the stability of auto-picked horizon in geologically complex settings and also significantly suppress the resulting uncertainty. To further improve the resulting accuracy in geologically complex settings, we introduce the directional structure tensor to extract a more reliable initial horizon and, moreover, a dilated horizon searching strategy to extend the capacity of the proposed method in dealing with the large fault displacement and reducing the computational cost simultaneously. Additionally, the resulting uncertainty quantitatively measured by entropy can also serve as an effective indicator to enable a further refinement of the auto-picked result accordingly. Both 2D example and 3D field applications are carried out to validate the effectiveness of the proposed method.

Uncertainty evaluation approach based on Shannon entropy for upscaled land use/cover maps

ABSTRACT Understanding the scale of land use/cover (LULC) map and its impacts on representing LULC is central to address earth observation issues. However, there is an absence of quantitative uncertainty evaluation of upscaled maps to be used over decades. An approach based on the Shannon entropy theory was then proposed to tackle this issue by reporting categorical heterogeneity information contained in upscaled pixels. The Majority Rule-Based aggregation algorithm was performed to generate upscaled maps at different widely used scales using a national LU map. The results reveal that substantial uncertainties inevitably exist in the upscaled maps. Additionally, the analysts demonstrate that the proposed approach can-and-indeed accurately provide spatially uncertain information of upscaled maps. These findings suggest that this approach is necessary for users to most effectively use these maps in earth observation models and should be extensively used in the future work.

Macroeconomic Uncertainty and Empirical Research Results of its Quantitative Measurement in Georgia

The present article describes the approaches and definition of the concept of uncertainty proposed by its authors, a quantitative evaluation of uncertainty, and materials of the empirical study used to explore the said issues on the example of macroeconomics of Georgia. We hope that the views given in the article will be useful for developing countries, particularly for the economic policy-makers in the post-communist states, as well as for the academic and scientific circles engaged in the studies of the above-listed issues.

A framework for rapid on-board deterministic estimation of occupant injury risk in motor vehicle crashes with quantitative uncertainty evaluation

Accurate on-board occupant injury risk prediction of motor vehicle crashes (MVCs) can decrease fatality rates by providing critical information timely and improving injury severity triage rates. The present implemented prediction algorithms in vehicle safety systems are probabilistic and rely on multi-variate logistic regression of real-world vehicle collision databases. As a result, they do not utilize important vehicle and occupant features and tend to overgeneralize the solution space. This study presents a framework to address these problems with deterministic and computationally efficient lumped parameter model simulations driven by a database of vehicle crash tests. A 648-case mixed database was generated with finite element and multi-body models and validated under the principal directions of impact with experimental results for a single vehicle body type. Using the finite element database, we developed lumped parameter models for four principal modes of impact (i.e., frontal, rear, near side and far side) with parameters identified via genetic algorithm optimization. To obtain confidence bounds for the injury risk prediction, the parameter uncertainty and model adequacy were evaluated with arbitrary and bootstrapped polynomial chaos expansion. The developed algorithm was able to achieve over triage rates of 17.1% ± 8.5%, whilst keeping the under triage rates below 8% on a finite element-multi body model database of a single vehicle body type. This study demonstrated the feasibility and importance of using low-complexity deterministic models with uncertainty quantification in enhanced occupant injury risk prediction. Further research is required to evaluate the effectiveness of this framework under a wide range of vehicle types. With the flexibility of parameter adjustment and high computational efficiency, the present framework is generic in nature so as to maximize future applicability in improved on-board triage decision making in active safety systems.

Quantitative Characterization of Uncertainty in the Concentration-Response Relationship between Long-Term PM2.5 Exposure and Mortality at Low Concentrations.

Extensive epidemiologic evidence supports a linear, no-threshold concentration-response (C-R) relationship between long-term exposure to fine particles (PM2.5) and mortality in the United States. While examinations of the C-R relationship are designed to assess the shape of the C-R curve, they do not provide the information needed to quantitatively characterize uncertainty at specific PM2.5 concentrations, which is often needed in the context of risk assessments and benefits analyses. We developed a novel approach, using information that is typically available in published epidemiologic studies, to quantitatively characterize uncertainty at different concentrations along the PM2.5 concentration distribution. Our approach utilizes the annual mean PM2.5 concentration and corresponding standard deviation from a published epidemiologic study to estimate the standard deviation of hypothetical PM2.5 concentration distributions defined at 0.1 μg/m3 increments. The hypothetical distributions are then used to derive adjusted uncertainty estimates in the reported effect estimate at low concentrations (i.e., concentrations lower than the annual mean observed in the study). We demonstrate the application of this method in six individual epidemiologic studies that examined the relationship between long-term PM2.5 exposure and mortality and were conducted in different geographic locations worldwide and at different PM2.5 concentrations. This new method allows for a more comprehensive quantitative evaluation of uncertainty in the shape of the C-R relationship between long-term PM2.5 exposure and mortality at concentrations below the mean annual concentrations observed in current studies.

Quantitative uncertainty evaluation of seismic facies classification: A case study from northeast China

Reservoir characterization in the early stage of oilfield exploration generally has enormous uncertainty because few geophysical and well data are typically available. The uncertainty when classifying the facies with seismic data propagates throughout the processes of seismic facies classification, causing errors in the final evaluation of geologic features in an area. To quantitatively evaluate the uncertainty in seismic facies classification, we have analyzed prestack seismic data and well observations in a tight reservoir from northeast China and calculated the uncertainties throughout the process. To achieve this, the facies probabilities conditioned on different properties in each step of seismic facies classification were first derived using a probabilistic multistep inversion. Second, the associated uncertainty and maximum a posterior (MAP) of facies probabilities were evaluated by means of entropy and reconstruction rate, which assessed the degree of similarity between MAP and facies sequence within the range [0, 1]. This enabled us to investigate the influence of the uncertainty propagation on seismic facies classification. The uncertainty of the inversion results for the target reservoir was finally characterized by the calculated entropy and its indicator transform. Additionally, parameter spaces of well-log and upscaled elastic properties were restricted according to the data distribution characteristics in the crossplot. Parameter vectors that were outside the restricted scopes were excluded, reducing the computational time and uncertainty. We determined that quantitative uncertainty evaluation by entropy with a probabilistic multistep approach enabled us to explore much more details of the uncertainty propagation in the processes of seismic reservoir characterization. It should be the method of choice for risk of management and decision making in reservoir assessment.

Uncertainty and sensitivity analysis of normalization factors to methodological assumptions

Normalisation is an optional step of a life cycle assessment, supporting the interpretation of the results of the characterization in terms of relative environmental relevance of the impacts. Normalisations factors (NFs) are calculated as results of regional/global inventories of emission and resources characterized through impact assessment methods. Several methodological assumptions are needed for building the inventory, as presented in Sala et al. (Int J Life Cycle Assess 20:1568–1585, 2015). NFs for EU27 have been calculated for 2010 compliant with ILCD recommendations defining a methodological approach for sources selection and the use of proxy indicators. Qualitative and quantitative uncertainty evaluation is needed for assessing the robustness of final figures. The present work aims at quantifying the influence of key methodological choices on the variability of the normalisation factors. Five sources of uncertainty have been analyzed in this work: (F1) the selection of the sources of data; (F2) the classification of data as life cycle inventory (LCI) elementary flows; (F3) the classification of substances for characterization; (F4) the specification of the emission compartments and (F5) the use of spatially differentiated characterization factors. The sensitivity of the normalization factors to such uncertainties were assessed through a global sensitivity method, for the impact categories acidification (ACID), terrestrial eutrophication (ET), marine eutrophication (EM), photochemical ozone formation (POF), respiratory inorganics/particulate matter (RIPM) and water depletion (WD). The results demonstrate the need of thorough uncertainty and sensitivity analysis for supporting the use of NFs. Uncertainties are high for the impact categories respiratory inorganics (RIPM) and water depletion (WD) and improvement of these categories is a priority. For RIPM this is explained by the high variability amongst the characterization factors for PM2.5 and PM10, together with the contextual lack of information about the height of the emission source in the inventory. For WD this is explained by variability of the regionalized factors available within the ILCD. For ACID, ET and EM the uncertainty is relatively low and generally completely led by factors F1 and F2. However, regionalized characterization factors were not tested for ACID and ET, therefore the results might be underestimating the overall uncertainty. For what concerns POF, the main source of uncertainty—amongst those included in the analysis—is the selection of the data source. Overall, improvements in the spatial resolution of the inventory are needed in order to confine uncertainty. This would allow the use of characterization factors specific for emission source typology and geographical location. The uncertainty associated with the methodological choices made for calculating normalization factors (Sala et al. in Int J Life Cycle Assess 20:1568–1585, 2015) was assessed. Generally, the value calculated by Sala et al. (Int J Life Cycle Assess 20:1568–1585, 2015) compare well against average and median values estimated in this analysis for ACID, ET, EM and POF. Instead, the impact categories RIPM and WD show different patterns. For RIPM, although the average value is very similar to the normalization factor reported by Sala et al. (Int J Life Cycle Assess 20:1568–1585, 2015), the median value is far lower. For what concerns WD, the median value is much higher. Future improvements of the normalization factors should therefore prioritize the development of more detailed inventories of emissions by including higher substance resolution, height of emission as well as the use of spatially differentiated characterization factors. To support the interpretation of normalized results, we recommend that the normalization factors from Sala et al. (Int J Life Cycle Assess 20:1568–1585, 2015) are applied together with two additional sets of normalization factors i.e. the ‘median values’ and the set of ‘average + standard deviation’ values, so to better capture their uncertainty. Similarly, the interpretation of the results should build on the qualitative estimates of robustness provided by Sala et al. (Int J Life Cycle Assess 20:1568–1585, 2015).

Improving uncertainty evaluation of process models by using pedigree analysis. A case study on CO2 capture with monoethanolamine

This article aims to improve uncertainty evaluation of process models by combining a quantitative uncertainty evaluation method (data validation) with a qualitative uncertainty evaluation method (pedigree analysis). The approach is tested on a case study of monoethanolamine based postcombustion CO2 capture from a coal power plant. Data validation was used to quantitatively assess the uncertainty of the inputs and outputs of the MEA model. Pedigree analysis was used to qualitatively assess the uncertainty in the current knowledge base on MEA carbon capture systems, the uncertainty in the MEA process model, and the uncertainty of the MEA model results. The pedigree review was done by 13 international experts in the field of postcombustion carbon capture with chemical solvents.The data validation showed that our MEA model is accurate in predicting specific reboiler duty, and CO2 stream purity (4% and 1% difference respectively between model and pilot plant results), but in first instance it was less accurate in predicting liquid over gas ratio, and cooling water requirement (54% and 23% difference respectively between model and pilot plant results). The pedigree analysis complemented these results by showing that there was fairly high uncertainty in the thermodynamic, and chemistry submodels, as reflected in the low pedigree scores on most indicators. Therefore, the model was improved to better resemble pilot plant results.The results indicate that using a pedigree approach improved uncertainty evaluation in three ways. First, by highlighting sources of uncertainty that quantitative uncertainty analysis does not take into account, such as uncertainty in the knowledge base regarding a specific phenomenon. Second, by providing a systematic approach to uncertainty evaluation, thereby increasing the awareness of modeller and model user. And finally, by presenting the outcomes in easy to understand numerical scores and colours, improving the communication of model uncertainty. In combination with quantitative validation efforts, the pedigree approach can provide a strong method to gain deep insight into the strengths and weaknesses of a process model, and to communicate this to policy and decision-makers.

Uncertainty Analysis in Geological Modeling for Coalbed Methane

The complexity of geological conditions results in ambiguity and uncertainty when interpreting geological data, bring difficulties to geological modeling, so quantitative evaluation of uncertainty of various geological parameters is important to establish accurate geological modeling. M coalbed methane field in eastern Australia was selected as an example to explain this process. The parameters and these uncertainty ranges were discussed firstly. And then, the impacts on calculated reserves of parameter uncertainty were analyzed. A better effect was attained in M coalbed methane field with this method.

Impact of missing data on the estimation of ecological indicators from satellite ocean-colour time-series

Ocean-colour remote sensing provides high-resolution and global-coverage of chlorophyll concentration, which can be used to estimate ecological indicators and to study inter-annual and long-term trends in the state of the marine ecosystem. To date, the record of ocean-colour observations is a rich one, including data from a number of sensors spanning more than three decades. The ESA Ocean-Colour Climate Change Initiative has advanced seamless merging of ocean-colour observations from missions during the period 1990s to 2010s. However, comparison of these more recent observations with records from 1970s to 1980s remains a complex undertaking, particularly for absolute values of chlorophyll concentration, primarily due to differences in the sensors. A further impediment to the analysis of the past records is the non-uniform distribution of gaps in the observations, in both time and space dimensions, when data from two or more sensors are compared. Here, we use the CZCS gap distribution from the Coastal Zone Color Scanner (CZCS, 1978–1986) as a mask to evaluate the impact that missing data may have on the estimation of six ecological indicators, when using the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) data set. Specifically, we evaluate the precision and accuracy of indicators by computing the root-mean-square-error (RMSE) and the bias arising purely from missing data. We develop an original resampling method allowing comparison of indicator estimates between SeaWiFS reference time-series and SeaWiFS time-series with CZCS-like gaps. We reduce some of the sampling gaps by applying a linear interpolation procedure, and compute multi-year averages of the indicators for every one-by-one degree pixel where sufficient data are available. Indicators from SeaWiFS reference and SeaWiFS with CZCS-like gaps are compared. Lowest uncertainty arising from missing data is observed in the indicators of annual mean and median chlorophyll concentration (global mean RMSE of 8% and |bias| ≤1%), whilst higher uncertainty is recorded for the peak chlorophyll values and the duration of the phytoplankton growing period (global mean RMSE of 33 and 47% respectively and |bias| ≤20%). Timing of initiation of the increasing phase of chlorophyll concentration in the seasonal cycle and timing of peak chlorophyll are subject to a global mean RMSE of nearly two months and a bias of two weeks or less. The present quantitative evaluation of uncertainty due to missing data demonstrates that, when pooled to create a nine-year climatology at 8-day temporal resolution, the coverage of CZCS is adequate for many climate-related studies on the marine ecosystem. Phytoplankton annual mean biomass can be estimated with low error in approximately 95% of the global oceans (i.e. regions where the indicators can be estimated with RMSE values of less than 30% and bias within ±10%), and the phenological patterns can be estimated with low error in approximately 25% of the global oceans.

Bayesian Analysis of A Rat Formaldehyde DNA–Protein Cross-Link Model

As the initial effort in a multi-step uncertainty analysis of a biologically based cancer model for formaldehyde, a Markov chain Monte Carlo (MCMC) analysis was performed for a compartmental model that predicts DNA–protein cross-links (DPX) produced by formaldehyde exposure. The Bayesian approach represented by the MCMC analysis integrates existing knowledge of the model parameters with observed, formaldehyde-DPX-specific data, providing a statistically sound basis for estimating model output uncertainty. Uncertainty and variability were evaluated through a hierarchical structure, where interindividual variability was considered for all model parameters and that variability was assumed to be uncertain on population levels. The uncertainty of the population mean and that of the population variance were significantly reduced through the MCMC analysis. Our investigation highlights several issues that must be dealt with in many real-world analyses (e.g., issues of parameters' nonidentifiability due to limited data) while demonstrating the feasibility of conducting a comprehensive quantitative uncertainty evaluation. The current analysis can be viewed as a case study, for a relatively simple model, illustrating some of the constraints that analysts will face when applying Bayesian approaches to biologically or physiologically based models of increasing complexity.

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

Abstract Ground-validation (GV) radar-rain products are often utilized for validation of the Tropical Rainfall Measuring Mission (TRMM) space-based rain estimates, and, hence, quantitative evaluation of the GV radar-rain product error characteristics is vital. This study uses quality-controlled gauge data to compare with TRMM GV radar rain rates in an effort to provide such error characteristics. The results show that significant differences of concurrent radar–gauge rain rates exist at various time scales ranging from 5 min to 1 day, despite lower overall long-term bias. However, the differences between the radar area-averaged rain rates and gauge point rain rates cannot be explained as due to radar error only. The error variance separation method is adapted to partition the variance of radar–gauge differences into the gauge area–point error variance and radar-rain estimation error variance. The results provide relatively reliable quantitative uncertainty evaluation of TRMM GV radar-rain estimates at various time scales and are helpful to understand better the differences between measured radar and gauge rain rates. It is envisaged that this study will contribute to better utilization of GV radar-rain products to validate versatile space-based rain estimates from TRMM, as well as the proposed Global Precipitation Measurement satellite and other satellites.

Confident Interpretation of Bayesian Decision Tree Ensembles for Clinical Applications

Bayesian averaging (BA) over ensembles of decision models allows evaluation of the uncertainty of decisions that is of crucial importance for safety-critical applications such as medical diagnostics. The interpretability of the ensemble can also give useful information for experts responsible for making reliable decisions. For this reason, decision trees (DTs) are attractive decision models for experts. However, BA over such models makes an ensemble of DTs uninterpretable. In this paper, we present a new approach to probabilistic interpretation of Bayesian DT ensembles. This approach is based on the quantitative evaluation of uncertainty of the DTs, and allows experts to find a DT that provides a high predictive accuracy and confident outcomes. To make the BA over DTs feasible in our experiments, we use a Markov Chain Monte Carlo technique with a reversible jump extension. The results obtained from clinical data show that in terms of predictive accuracy, the proposed method outperforms the maximum a posteriori (MAP) method that has been suggested for interpretation of DT ensembles.

Quantitative estimation of uncertainty in human risk analysis

This paper is aimed to candidate the use of an ISO standard procedure (Guide to the Expression of Uncertainty in Measurement, GUM) for quantitative evaluation of uncertainty in Human Risk estimation under chronic exposure to a hazardous chemical compound. Risk was evaluated by using the usual methodologies: the deterministic reasonable maximum exposure (RME) and the statistical Monte Carlo method; in both cases the procedures to evaluate the uncertainty on risk values are detailed. The paper put in evidence that the procedure is able to single out the variables that contribute mostly to the uncertainty. The obtained results show that the application of GUM procedure is easy and straightforward to estimate the uncertainty value on the results of risk estimation. The procedure is applied to a real case concerning the ingestion of milk contaminated by dioxins in a northern part of Italy; the risk value resulted to be over the minimal threshold of 10 −6 with 20–80% confidence.

Spatial Prediction of Heavy Metal Pollution for Soils in Peri-Urban Beijing, China Based on Fuzzy Set Theory

ABSTRACT Fuzzy classification combined with spatial prediction was used to assess the state of soil pollution in the peri-urban Beijing area. Total concentrations of As, Cr, Cd, Hg, and Pb were determined in 220 topsoil samples (0–20 cm) collected using a grid design in a study area of 2600 km 2 . Heavy metal concentrations were grouped into three classes according to the optimum number of classes and fuzziness exponent using the fuzzy c -mean (FCM) algorithm. Membership values were interpolated using ordinary kriging. The polluted soils of the study area induced by the measured heavy metals were concentrated in the northwest corner and eastern part, especially the southeastern part close to the urban zone, whereas the soils free of pollution were mainly distributed in the southwestern part. The soils with potential risk of heavy metal pollution were located in isolated spots mainly in the northern part and southeastern corner of the study region. The FCM algorithm combined with geostatistical techniques, as compared to conventional single geostatistical kriging methods, could produce a prediction with a quantitative uncertainty evaluation and higher reliability. Successful prediction of soil pollution achieved with FCM algorithm in this study indicated that fuzzy set theory had great potential for use in other areas of soil science.