Uncertainty Distribution Research Articles

Organotypic sinonasal airway culture systems are predictive of the mucociliary phenotype produced by bronchial airway epithelial cells

Differentiated air–liquid interface models are the current standard to assess the mucociliary phenotype using clinically-derived samples in a controlled environment. However, obtaining basal progenitor airway epithelial cells (AEC) from the lungs is invasive and resource-intensive. Hence, we applied a tissue engineering approach to generate organotypic sinonasal AEC (nAEC) epithelia to determine whether they are predictive of bronchial AEC (bAEC) models. Basal progenitor AEC were isolated from healthy participants using a cytological brushing method and differentiated into epithelia on transwells until the mucociliary phenotype was observed. Tissue architecture was assessed using H&E and alcian blue/Verhoeff–Van Gieson staining, immunofluorescence (for cilia via acetylated α-tubulin labelling) and scanning electron microscopy. Differentiation and the formation of tight-junctions were monitored over the culture period (day 1–32) by quantifying trans-epithelial electrical resistance. End point (day 32) tight junction protein expression was assessed using Western blot analysis of ZO-1, Occludin-1 and Claudin-1. Reverse transcription qPCR-array was used to assess immunomodulatory and autophagy-specific transcript profiles. All outcome measures were assessed using R-statistical software. Mucociliary architecture was comparable for nAEC and bAEC-derived cultures, e.g. cell density P = 0.55, epithelial height P = 0.88 and cilia abundance P = 0.41. Trans-epithelial electrical resistance measures were distinct from day 1–14, converged over days 16–32, and were statistically similar over the entire culture period (global P < 0.001). This agreed with end-point (day 32) measures of tight junction protein abundance which were non-significant for each analyte (P > 0.05). Transcript analysis for inflammatory markers demonstrated significant variation between nAEC and bAEC epithelial cultures, and favoured increased abundance in the nAEC model (e.g. TGFβ and IL-1β; P < 0.05). Conversely, the abundance of autophagy-related transcripts were comparable and the range of outcome measures for either model exhibited a considerably more confined uncertainty distribution than those observed for the inflammatory markers. Organotypic air–liquid interface models of nAEC are predictive of outcomes related to barrier function, mucociliary architecture and autophagy gene activity in corresponding bAEC models. However, inflammatory markers exhibited wide variation which may be explained by the sentinel immunological surveillance role of the sinonasal epithelium.

Burden of foodborne disease due to bacterial hazards associated with beef, dairy, poultry meat, and vegetables in Ethiopia and Burkina Faso, 2017

Foodborne disease is a significant global health problem, with low- and middle-income countries disproportionately affected. Given that most fresh animal and vegetable foods in LMICs are bought in informal food systems, much the burden of foodborne disease in LMIC is also linked to informal markets. Developing estimates of the national burden of foodborne disease and attribution to specific food products will inform decision-makers about the size of the problem and motivate action to mitigate risks and prevent illness. This study provides estimates for the burden of foodborne disease caused by selected hazards in two African countries (Burkina Faso and Ethiopia) and attribution to specific foods. Country-specific estimates of the burden of disease in 2010 for Campylobacter spp., enterotoxigenic Escherichia coli (ETEC), Shiga-toxin producing E. coli and non-typhoidal Salmonella enterica were obtained from WHO and updated to 2017 using data from the Global Burden of Disease study. Attribution data obtained from WHO were complemented with a dedicated Structured Expert Judgement study to estimate the burden attributable to specific foods. Monte Carlo simulation methods were used to propagate uncertainty. The burden of foodborne disease in the two countries in 2010 was largely similar to the burden in the region except for higher mortality and disability-adjusted life years (DALYs) due to Salmonella in Burkina Faso. In both countries, Campylobacter caused the largest number of cases, while Salmonella caused the largest number of deaths and DALYs. In Burkina Faso, the burden of Campylobacter and ETEC increased from 2010 to 2017, while the burden of Salmonella decreased. In Ethiopia, the burden of all hazards decreased. Mortality decreased relative to incidence in both countries. In both countries, the burden of poultry meat (in DALYs) was larger than the burden of vegetables. In Ethiopia, the burdens of beef and dairy were similar, and somewhat lower than the burden of vegetables. The burden of foodborne disease by the selected pathogens and foods in both countries was substantial. Uncertainty distributions around the estimates spanned several orders of magnitude. This reflects data limitations, as well as variability in the transmission and burden of foodborne disease associated with the pathogens considered.

Modelling the spatial distribution of the classification error of remote sensing data in cocoa agroforestry systems

Cocoa growing is one of the main activities in humid West Africa, which is mainly grown in pure stands. It is the main driver of deforestation and encroachment in protected areas. Cocoa agroforestry systems which have been promoted to mitigate deforestation, needs to be accurately delineated to support a valid monitoring system. Therefore, the aim of this research is to model the spatial distribution of uncertainties in the classification cocoa agroforestry. The study was carried out in Côte d’Ivoire, close to the Taï National Park. The analysis followed three steps (i) image classification based on texture parameters and vegetation indices from Sentinel-1 and -2 data respectively, to train a random forest algorithm. A classified map with the associated probability maps was generated. (ii) Shannon entropy was calculated from the probability maps, to get the error maps at different thresholds (0.2, 0.3, 0.4 and 0.5). Then, (iii) the generated error maps were analysed using a Geographically Weighted Regression model to check for spatial autocorrelation. From the results, a producer accuracy (0.88) and a user’s accuracy (0.91) were obtained. A small threshold value overestimates the classification error, while a larger threshold will underestimate it. The optimal value was found to be between 0.3 and 0.4. There was no evidence of spatial autocorrelation except for a smaller threshold (0.2). The approach differentiated cocoa from other landcover and detected encroachment in forest. Even though some information was lost in the process, the method is effective for mapping cocoa plantations in Côte d’Ivoire.

Feeding ecology of the endangered Himalayan Gray Langur Semnopithecus ajax in Chamba, Himachal Pradesh, India

This study on the feeding ecology of Himalayan Gray Langur or the Chamba Sacred Langur Semnopithecus ajax is a crucial baseline step as very little is known about this species due to its long taxonomic uncertainty and limited distribution range. This study was done in Kalatop-Khajjiar Wildlife Sanctuary, Chamba, Himachal Pradesh using scan sampling method. A total of 71 scan samples were collected in the study area from September 2020 to November 2020 focusing on the autumn diet of the species. Group size, group composition, and distribution of the langurs were also recorded. Totally, 20 species of plants belonging to 15 different botanical families were recorded which contribute to the diet. Hedera nepalensis, Quercus oblongata, and Ilex dipyrena formed the major components of the diet. The langurs consumed a substantial portion of leaves (84.32%), followed by fruits and flowers. Mature leaves being a part of the diet of langurs has proven the broaden repertoires of langurs inhabiting the Himalayan landscape. Also, a difference in the diet composition of two study groups was recorded which might be the result of varying distribution with respect to elevation.

Belief-Informed Robust Decision Making (BIRDM): Assessing changes in decision robustness due to changing distributions of deep uncertainties

Robust Decision Making (RDM) is an established framework for decision making under deep uncertainty. RDM relies on the idea of scenario neutrality, namely that decision robustness is not affected by how scenarios are generated if these are uniformly distributed and span a sufficiently large range of future states of the world. Several authors have shown that scenario neutrality may not hold, but they did so by adopting either new or computationally expensive modeling. We introduce the Belief-Informed Robust Decision Making (BIRDM) framework to assess how robustness might change under an arbitrary large number of non-uniform distributions at virtually no additional costs with respect to RDM. We apply BIRDM to a flood management problem and find that alternative distributions change the robustness and ranking of measures. BIRDM allows identifying what distributions lead to these changes and under what set of distributions a measure has a specific robustness and rank.

A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions.

Enhanced index tracking problem is the issue of selecting a tracking portfolio to outperform the benchmark return with a minimum tracking error. In this paper, we address the enhanced index tracking problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. First, we propose a nonlinear uncertain optimization model, i.e., uncertain mean-absolute downside deviation enhanced index tracking model. Then, we give the analytical solution of the proposed optimization model when stock returns take linear uncertainty distributions. Based on the solution, we find that tracking portfolio frontier is a continuous curve composed of at most n-1 different line segments. Furthermore, we give the condition that tracking portfolio return and risk increase with benchmark return and risk, respectively. Finally, we offer some experiments and show that our proposed model is effective in controlling the tracking error.

Configuration of urban water eutrophication abatement systems using a novel regression-based optimization scheme.

A novel regression-based target-oriented robust optimization (R-TORO) framework is introduced to obtain robust designs of surface water eutrophication abatement systems during the early stages of urban water planning. The proposed framework can process a manifold of data for estimating the relationships of system elements and the uncertainty distribution of imprecise parameters, a novel extension of the canonical TORO framework. A demonstrative case study about an early-stage urban water infrastructure planning for abating Phosphorous (P) accumulation in urban waters is employed to demonstrate the R-TORO framework. The following system targets are considered: target cost and target water cycle sustainability index (WCSI). The findings show that the abatement of P accumulation in soil contributes the largest to WCSI. Consequently, the R-TORO-generated system design suggests the implementation of impervious local roads connected to sewers with improved P removal. The simulated/estimated performance of the eutrophication abatement system design obtained using the R-TORO are as follows: import of water=2.88 × 106m3/y; export of P=4.96 × 106gP/y; P concentration in recreational lake=0.04mgP/l; P concentration in canal system=0.30mgP/l; P accumulation in lake sediments=0.08gP/m2,y; P accumulation in canal sediments=1.18gP/m2,y; P accumulation in soil=0.01gP/m2,y.

An uncertain support vector machine based on soft margin method.

Traditional support vector machines (SVMs) play an important role in the classification of precise data. However, due to various reasons, available data are sometimes imprecise. In this paper, uncertain variables are adopted to describe the imprecise data, and an uncertain support vector machine (USVM) is built for linearly alpha-nonseparable sets based on soft margin method, where a penalty coefficient is utilized as the trade-off between the maximum margin and the sum of slack variables. Then the equivalent crisp model is derived based on the inverse uncertainty distributions. Numerical experiments are designed to illustrate the application of the soft margin USVM. Finally, metrics, such as accuracy, precision, and recall are used to evaluate the robustness of the proposed model.

Exploring the uncertainty in projected wheat phenology, growth and yield under climate change in China

Exploring and quantifying the uncertainties in climate impact assessment with multiple climate-crop models is crucial to reducing the total uncertainty and guiding adaptation strategies for crop production. Here, we carried out a climate-crop ensemble simulation to measure the uncertainty in estimated climate impacts on China's wheat productivity by the 2050s. The ensemble included the simulations conducted with the three-DSSAT wheat model ensemble. As for the future climate, five Global Climate projections (GCMs) under two Representative Concentration Pathways (RCP4.5 and 8.5) and two CO2 concentrations were selected. Our results indicate that the median of simulated yield change was between 4.5% ∼ 5.5%, and -7.7% ∼ -5.6% respectively under elevated and current CO2 concentrations by 2050s compared to 1981–2010. The median of simulated phenology change was nearly -12 ∼ -10 d In percentage terms, higher uncertainty in national yield change was observed compared to phenology change. The total relative contributions of climate projections, crop models, and RCP scenarios have been more than 70% of the total uncertainty of national phenology and yield change. Crop models have accounted for the largest uncertainty of irrigated yield, while crop models and climate projections almost contributed a similar share of the total uncertainty of rainfed yield. These findings highlight the distribution of uncertainty and sources of uncertainty both at the national and grid scales, which would provide a more comprehensive understanding of uncertainties in future yield prediction. Our results also showed that larger uncertainty has been observed in warmer regions (growing season average temperature > 20 °C) than in cooler regions, while the wet regions (growing season rainfall > 400 mm) would suffer smaller uncertainty than dry regions. These findings emphasize the relationships between uncertainty and climate factors, which offers insights for improving crop models and designing adaptation strategies.

Distributionally robust OPF in distribution network considering CVaR-averse voltage security

The uncertain generations of renewable energy sources (RES) bring considerable challenges to voltage security in distribution networks. This paper proposes a conditional value at risk (CVaR)-averse distributionally robust chance constrained optimal power flow (CVaR-DRCC-OPF) which considers the voltage regulation from a risk perspective. The CVaR of voltage violation is proposed to act as an additional penalty term in the objective. Compared to the conventional chance-constrained OPF, the CVaR-averse penalty term quantifies the voltage violation better, especially for the uncertainty distribution function with a long tail. In addition, this paper develops a moment-based ambiguous set of the uncertainty distribution functions. By applying the duality theory, we reformulate the proposed OPF as a second-order cone programming (SOCP), which can be solved in polynomial processing time. Simulation results on the modified 118-bus distribution system show the efficiency and superiority of the proposed CVaR-DRCC-OPF in distribution network voltage regulation over other benchmark models.

An online adaptive plan library approach for intensity modulated proton therapy for head and neck cancer

Background and purposeIn intensity modulated proton therapy (IMPT), the impact of setup errors and anatomical changes is commonly mitigated by robust optimization with population-based setup robustness (SR) settings and offline replanning. In this study we propose and evaluate an alternative approach based on daily plan selection from patient-specific pre-treatment established plan libraries (PLs). Clinical implementation of the PL strategy would be rather straightforward compared to daily online re-planning. Materials and methodsFor 15 head-and-neck cancer patients, the planning CT was used to generate a PL with 5 plans, robustly optimized for increasing SR: 0, 1, 2, 3, 5 mm, and 3% range robustness. Repeat CTs (rCTs) and realistic setup and range uncertainty distributions were used for simulation of treatment courses for the PL approach, treatments with fixed SR (fSR3) and a trigger-based offline adaptive schedule for 3 mm SR (fSR3OfA). Daily plan selection in the PL approach was based only on recomputed dose to the CTV on the rCT. ResultsCompared to using fSR3 and fSR3OfA, the risk of xerostomia grade ≥ II & III and dysphagia ≥ grade III were significantly reduced with the PL. For 6/15 patients the risk of xerostomia and/or dysphagia ≥ grade II could be reduced by > 2% by using PL. For the other patients, adherence to target coverage constraints was often improved. fSR3OfA resulted in significantly improved coverage compared to PL for selected patients. ConclusionThe proposed PL approach resulted in overall reduced NTCPs compared to fSR3 and fSR3OfA at limited cost in target coverage.

Western U.S. Geologic Deformation Model for Use in the U.S. National Seismic Hazard Model 2023

Abstract Fault geometry and slip rates are key input data for geologic deformation models, which are a fundamental component of probabilistic seismic hazard analyses (PSHAs). However, geologic sources for PSHA have traditionally been limited to faults with field-based slip rate constraints, which results in underrepresentation of known, but partially characterized, active faults. Here, we evaluate fault geometries and geologic fault slip rates for the western United States to construct a new geologic deformation model for the U.S. National Seismic Hazard Model 2023 update (NSHM23). In previous NSHM iterations, only faults with published geologic slip rates were included. In the NSHM23 fault sections database compilation, this inclusion criterion was expanded to include faults without known slip rates. In this updated geologic deformation model, preferred slip rates and associated uncertainty distributions are incorporated for faults with slip rates derived from field studies. For faults without site-specific slip rates, we evaluate a suite of uncertainty distributions derived from broad slip rate categories in the U.S. Geological Survey Quaternary Fault and Fold Database. Preferred slip rate distributions are selected via comparison with geodetic strain rates in tectonic subregions. The resultant moment of the geologic deformation model is generally in deficit compared with the geodetic moment within each region. Primary advances in the NSHM23 geologic deformation model include the following: (1) slip rates are presented as preferred values with uncertainties rather than single values; (2) the representation of the western U.S. active fault network is more complete; and (3) the geologic deformation model leverages geodetic information to assess regional constraints on geologic fault slip rates.

Stochastic optimization models for location and inventory prepositioning of disaster relief supplies

We consider the problem of preparing for a disaster season by determining where to open warehouses and how much relief item inventory to preposition in each. Then, after each disaster, prepositioned items are distributed to demand nodes during the post-disaster phase, and additional items are procured and distributed as needed. There is often uncertainty in the disaster level, affected areas’ locations, the demand for relief items, the usable fraction of prepositioned items post-disaster, procurement quantity, and arc capacity. To address uncertainty, we propose and analyze two-stage stochastic programming (SP) and distributionally robust optimization (DRO) models, assuming known and unknown (ambiguous) uncertainty distributions. The first and second stages correspond to pre- and post-disaster phases, respectively. We also propose a model that minimizes the trade-off between considering distributional ambiguity and following distributional belief. We obtain near-optimal solutions of our SP model using sample average approximation and propose a computationally efficient decomposition algorithm to solve our DRO models. We conduct extensive experiments using a hurricane season and an earthquake as case studies to investigate these approaches computational and operational performance.

Bayesian rule in the framework of uncertainty theory

In Bayesian rule an unknown parameter is thought to be a quantity whose variation can be characterized by a prior distribution. Then some data are observed from a population whose distribution function is indexed by the unknown parameter and then the prior distribution is updated according to the observed data. The updated prior distribution is named as the posterior distribution. Based on uncertainty theory, this paper first makes a connection between posterior uncertainty distribution and likelihood function, and proposes a new method to obtain the posterior uncertainty distribution from the prior uncertainty distribution with given observed data. Some examples with special uncertainty distributions are employed to explain the calculation. Furthermore, an uncertain urn problem is provided to illustrate the application of the new method.

Uncertainty propagation in pore water chemical composition calculation using surrogate models

Performance assessment in deep geological nuclear waste repository systems necessitates an extended knowledge of the pore water chemical conditions prevailing in host-rock formations. In the last two decades, important progress has been made in the experimental characterization and thermodynamic modeling of pore water speciation, but the influence of experimental artifacts and uncertainties of thermodynamic input parameters are seldom evaluated. In this respect, we conducted an uncertainty propagation study in a reference geochemical model describing the pore water chemistry of the Callovian-Oxfordian clay formation. Nineteen model input parameters were perturbed, including those associated to experimental characterization (leached anions, exchanged cations, cation exchange selectivity coefficients) and those associated to generic thermodynamic databases (solubilities). A set of 13 quantities of interest were studied by the use of polynomial chaos expansions built non-intrusively with a least-squares forward stepwise regression approach. Training and validation sets of simulations were carried out using the geochemical speciation code PHREEQC. The statistical results explored the marginal distribution of each quantity of interest, their bivariate correlations as well as their global sensitivity indices. The influence of the assumed distributions for input parameters uncertainties was evaluated by considering two parametric domain sizes.

Probabilistic forecasting of rainfall response in a Danish stormwater tunnel

• Development of a non-linear SDE-model of rainfall response in a stormwater tunnel. • A modified maximum-likelihood estimation of the non-linear SDE-model. • Probabilistic l -step forecasting with the non-linear SDE-model. • Evaluation of the uncertainty in rainfall response forecasts. Sustainable urban drainage is an economically expensive necessity, partially due to the operation of water pumps. Reliable forecasting of stormwater response following a rainfall event has the potential to reduce those expenses, because it can be used in model predictive control schemes that optimize the energy consumption of pumps significantly better than the commonly applied real-time control systems. Urban drainage systems are traditionally designed around highly complex, deterministic models where an assessment of the uncertainty of the stormwater forecast is either absent or relies on computation–heavy simulations. With offset in a Danish stormwater tunnel, we propose a much faster, but reliable, non-linear continuous-discrete-time state-space model based on stochastic differential equations which can generate probabilistic forecasts that contain complete information about the distribution of uncertainty. We explain step-by-step how the model structure is built from simple physical assumptions, then how the parameters are estimated from maximum likelihood principles and finally we demonstrate the forecasting capabilities of the model. We believe this model would be well-suited for a subsequent model predictive control scheme.

Probabilistic Day-Ahead Inertia Forecasting

Power system inertia is declining and is increasingly variable and uncertain in regions where the penetration of non-synchronous generation and interconnectors is growing. This presents a challenge to power system operators who must take appropriate actions to ensure the stability and security of power systems relying on short-term forecasts of the system’s inertial response. Existing models to forecast inertia fail to quantify uncertainty, which may prevent their utilization given the risk aversion of the system operators when handling stability issues. This paper is the first to develop a model to produce calibrated, data-driven probabilistic forecasts of the inertia contribution of transmission-connected synchronous generators. The model provides a necessary tool for system operators to quantify forecast uncertainty, allowing them to manage the risk of frequency instability cost-effectively. The paper demonstrates that the assumption of a Gaussian distribution of uncertainty applied in existing models is not acceptable to accurately forecast the inertial response and provides a satisfactory forecast model by combining non-parametric density forecasting with parametric tail distributions. Moreover, the paper shows that satisfactory predictive performance can only be achieved by adopting a rolling horizon forecast approach to deal with the rapidly changing characteristics of the inertial response in power systems.

A methodology for integrating the characterization factors uncertainty into life cycle assessments

The need to consider the uncertainty associated with the data used to compute characterization factors has been recognized as a requirement to fully address uncertainty in a life cycle assessment study. However, most of these studies focus on the uncertainty associated with data collected in the Inventory Analysis step, leaving the uncertainty in the parameters used in the Impact Assessment step without analysis. This study addresses this gap and presents a methodology for analyzing the uncertainty related to the characterization factors. This methodology departs from the traditionally deterministic life cycle assessment and explores Monte Carlo simulation to develop a stochastic life cycle assessment. The proposed methodology is applied to the comparison of two pulp bleaching techniques, Elemental Chlorine Free and Total Chlorine Free, to demonstrate how this methodology can be used in a decision-making process. The analysis of the stochastic results indicate that switching from Elemental Chlorine Free to Total Chlorine Free is not the most effective strategy when trying to decrease the overall environmental impact associated with the production of bleached pulp since the two techniques have significantly equal single scores. The proposed methodology and its application to a case study showed the importance of integrating uncertainty analysis into life cycle assessment studies. This integration would be more straightforward if impact assessment methods provided uncertainty distributions for the characterization factors used.

Sensitivity and uncertainty of the IFR-1 BISON benchmark

The fuel performance code BISON is being used to evaluate metallic fuel for a new fast-spectrum test reactor called the Versatile Test Reactor, which is being considered for adoption by the US Department of Energy. To quantify the accuracy of BISON predictions, researchers at Oak Ridge National Laboratory have been developing a series of benchmarks based on legacy metallic fuel experiments. As part of this effort, the sensitivity of BISON predictions to variations in model inputs and the uncertainties associated with BISON predictions must be established. This paper summarizes efforts to perform a comprehensive sensitivity analysis (SA) and uncertainty quantification (UQ) on a benchmark based on the IFR-1 experiment.For the SA, at least one input was chosen from every BISON model and physics module used in the benchmark. The inputs were varied individually in a series of BISON simulations. The resulting variations in benchmark predictions were normalized to calculate sensitivities. These sensitivities were then used to inform input selections for the UQ.The UQ was performed using the Monte Carlo UQ method. A literature review was conducted to estimate uncertainty distributions for the selected inputs, and values were sampled randomly from each distribution in a series of BISON simulations. Variations in the benchmark predictions were used to estimate uncertainty distributions and confidence intervals. It was found that nearly 100% of the benchmark predictions matched the corresponding legacy values within the confidence intervals. However, this is at least partially because the confidence intervals associated with benchmark predictions were wide. The uncertainty contributions of assumptions in the benchmark, experimental uncertainties, and BISON models were quantified. Some analysis was performed to identify inputs that contributed to the uncertainties. Finally, recommendations are made for future benchmark and future BISON development.

Constrained tracking control of stochastic multivariable nonlinear systems via Gaussian process predictions

To overcome the difficulty of propagating the stochastic uncertainties through a nonlinear model for successful online implementation of the stochastic nonlinear model predictive control (SNMPC) framework, this paper proposes the utilisation of Gaussian processes (GPs) in the context of SNMPC for the stochastic multivariable nonlinear systems to track a given trajectory in the presence of stochastic uncertainties and system constraints. Taking advantage of the GP regression which not only provides predictions, but also uncertainty quantification in the function estimation, the proposed GP-SNMPC architecture exploits the probability distribution of stochastic uncertainties and utilises the predictions provided by the GPs to formulate the model cost and constraint functions, which yields a tractable framework for handling nonlinear constrained control problems with Gaussian parametric uncertainties. By employing a cancellation strategy, the control law consists of two components, that is, tracking control law and disturbance rejection control law. Theoretical results regarding the performance bounds of the closed-loop system are derived. Numerical examples are provided to verify the effectiveness of the proposed GP-SNMPC scheme.