Probabilistic Uncertainty Research Articles

Reasoning with PCP-Nets

We introduce PCP-nets, a formalism to model qualitative conditional preferences with probabilistic uncertainty. PCP-nets generalise CP-nets by allowing for uncertainty over the preference orderings. We define and study both optimality and dominance queries in PCP-nets, and we propose a tractable approximation of dominance which we show to be very accurate in our experimental setting. Since PCP-nets can be seen as a way to model a collection of weighted CP-nets, we also explore the use of PCP-nets in a multi-agent context, where individual agents submit CP-nets which are then aggregated into a single PCP-net. We consider various ways to perform such aggregation and we compare them via two notions of scores, based on well known voting theory concepts. Experimental results allow us to identify the aggregation method that better represents the given set of CP-nets and the most efficient dominance procedure to be used in the multi-agent context.

A method to devise multiple model structures for urban flood inundation uncertainty

The interaction between the sewer network and the overland runoff is challenging to study due to the complex flow exchange between the two systems during flooding. The complexity increases when dealing with sub-catchments that contain separated urban satellite areas that share the sewer network. Under this context it is possible to devise likely model structures which render determinist approaches spuriously precise. In this paper, a methodology is proposed for to devise multiple model structures for urban flood inundation uncertainty. Seven different model structures are assembled and validated in a case study Baiersdorf for the flood event from 21st of 2007 to produce a probabilistic flood inundation uncertainty map. The results show that the flood inundation extent uncertainty differs across the study area. The overall flood extent uncertainty covers 14.15% of the inundation area. The highest uncertainty is found to be 30.87% at the North part up of the study area. Many small areas of high uncertainty are concentrated in the main urban area, and close to most of the upstream boundary conditions. It is conducted that the highest uncertainties are likely to be found downstream of the coupling points of the 2D overland flow with either the 1D sewer system or the 1D overland flow network. These results highlight the need to consider multiple model structures when estimating the uncertainty of the flood inundation extents.

Probabilistic Assessment and Uncertainty Analysis of CO2 Storage Capacity of the Morrow B Sandstone—Farnsworth Field Unit

This paper presents probabilistic methods to estimate the quantity of carbon dioxide (CO2) that can be stored in a mature oil reservoir and analyzes the uncertainties associated with the estimation. This work uses data from the Farnsworth Field Unit (FWU), Ochiltree County, Texas, which is currently undergoing a tertiary recovery process. The input parameters are determined from seismic, core, and fluid analyses. The results of the estimation of the CO2 storage capacity of the reservoir are presented with both expectation curve and log probability plot. The expectation curve provides a range of possible outcomes such as the P90, P50, and P10. The deterministic value is calculated as the statistical mean of the storage capacity. The coefficient of variation and the uncertainty index, P10/P90, is used to analyze the overall uncertainty of the estimations. A relative impact plot is developed to analyze the sensitivity of the input parameters towards the total uncertainty and compared with Monte Carlo. In comparison to the Monte Carlo method, the results are practically the same. The probabilistic technique presented in this paper can be applied in different geological settings as well as other engineering applications.

Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile

We used the lumped rainfall–runoff hydrologic models Génie Rural à 4, 5, 6 paramètres Journalier (GR4J, GR5J and GR6J) to evaluate the most robust model for simulating discharge on four forested small catchments (<40 ha) in south-central Chile. Different evapotranspiration methods were evaluated: Oudin, Hargreaves–Samani and Priestley–Taylor. Oudin’s model allows the achievement of the highest efficiencies in the flow simulation. The more sensitive parameters for each model were identified through a Generalized Probability Uncertainty Estimation (GLUE) model. Our results demonstrate that the three hydrological models were capable of efficiently simulating flow in the four study catchments. However, the GR6J model obtained the most satisfactory results in terms of simulated to measured streamflow closeness. In general, the three models tended to underestimate peak flow, as well as underestimate and overestimate flow events in most of the in situ observations, according to the probability of non-exceedance. We also evaluated the models’ performance in a simulation of summer discharge due to the importance of downstream water supply in the months of greatest scarcity. Again, we found that GR6J obtained the most efficient simulations.

Computing the Number of Failures for Fuzzy Weibull Hazard Function

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number (TFN) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (GMVD) method. The results show that for certain weighting factor of the GMVD, the cores of these fuzzy numbers of failures are identical.

Distributionally Robust Microgrid Formation Approach for Service Restoration Under Random Contingency

When a major outage occurs in a distribution system due to extreme events, service restoration (SR) strategies pick up critical loads after isolating the faults that have occurred. However, in extreme conditions, traditional SR strategies could pose potential security risks to restored services due to subsequent contingencies in succeeding events. To address this challenge, we propose a microgrid-based SR methodology that aims to enhance the preparedness of microgrids during unfolding extreme events. The proposed SR strategy comprises microgrid formation (MF) and sequential service restoration (SSR) steps. The MF makes the benefit of topology switching, generator allocation, and load demand response. Additionally, the uncertainty of line failure probability is considered, and a distributionally robust optimization model is proposed to maximize the expected load restoration with regard to the worst-case distribution of contingencies. Then, the SSR is formulated as a mixed-integer linear program model to yield proper load switching sequences and generation of power sources for sequentially restoring the outage system. The proposed SR measure enhances the system resilience by the proactive formation of microgrids, reducing the impact of cascading phenomenon when lines with high failure probability are tripped. The effectiveness of the proposed method is validated by numerical simulations.

A data-centric approach to generative modelling for 3D-printed steel.

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products.

Effectiveness of the Preventive Intervention of Chromosomal Disorders of Iran's Community Genetics Program: Application of Bayesian Network.

Background: Evidence-based policymaking for the genetic preventive interventions at the community level requires information on the effectiveness of interventions in the operational areas taking into account the characteristics of health system and customer behaviour. These information are limited in many low- and middle-income countries. In this study, we estimated the effectiveness of preventive interventions for chromosomal disorders using the conceptual framework of Iran’s community genetics program (ICGP) using a Bayesian Network as a modeling method in limited access situation to the complete and accurate observational data. Methods: Expert elicitation method based on global and national scientific evidences was applied to determine the structure of the Bayesian Network (BN) and to quantify the probability of nodes. The nomological and face validity of the network was checked. Also, a sensitivity analysis against the sources of uncertainty of probabilities was conducted. Results: By ICGP interventions, 63% (95% CI, 0.55-0.71) of all chromosomal disorders can be prevented, which is responsible for 80% (95% CI, 0.76-0.84) and 38% (95% CI, 0.31-0.45) reduction of expected baseline birth prevalence of trisomis and other autosomal disorders, respectively. Improving the access to and the uptake of screening service can also result in a 12% and 11% increase in effectiveness, respectively. Conclusion: Effectiveness of ICGP’s intervention is between the same interventions’ effectiveness in Western Europe and the Eastern Mediterranean region. Opportunities for increasing the uptake of and the access to the interventions are strengthening the public genetic literacy and implantation of a system of laboratory sample transfer at the side of the utilization of telehealth for delivering the counseling services at remote areas.

Data-Driven System Dynamics Model for Simulating Water Quantity and Quality in Peri-Urban Streams

Holistic water quality models to support decision-making in lowland catchments with competing stakeholder perspectives are still limited. To address this gap, an integrated system dynamics model for water quantity and quality (including stream temperature, dissolved oxygen, and macronutrients) was developed. Adaptable plug-n-play modules handle the complexity (sources, pathways) related to both urban and agricultural/natural land-use features. The model was applied in a data-rich catchment to uncover key insights into the dynamics governing water quality in a peri-urban stream. Performance indicators demonstrate the model successfully captured key water quantity/quality variations and interactions (with, e.g., Nash-Sutcliff Efficiency ranging from very good to satisfactory). Model simulation and sensitivity results could then highlight the influence of stream temperature variations and enhanced heterotrophic respiration in summer, causing low dissolved oxygen levels and potentially affecting ecological quality. Probabilistic uncertainty results combined with a rich dataset show high potential for ammonium uptake in the macrophyte-dominated reach. The results further suggest phosphorus remobilization from streambed sediment could become an important diffuse nutrient source should other sources (e.g., urban effluents) be mitigated. These findings are especially important for the design of green transition solutions, where single-objective management strategies may negatively impact aquatic ecosystems.

Epistemic uncertainty quantification in deep learning classification by the Delta method

The Delta method is a classical procedure for quantifying epistemic uncertainty in statistical models, but its direct application to deep neural networks is prevented by the large number of parameters P. We propose a low cost approximation of the Delta method applicable to L2-regularized deep neural networks based on the top K eigenpairs of the Fisher information matrix. We address efficient computation of full-rank approximate eigendecompositions in terms of the exact inverse Hessian, the inverse outer-products of gradients approximation and the so-called Sandwich estimator. Moreover, we provide bounds on the approximation error for the uncertainty of the predictive class probabilities. We show that when the smallest computed eigenvalue of the Fisher information matrix is near the L2-regularization rate, the approximation error will be close to zero even when K≪P. A demonstration of the methodology is presented using a TensorFlow implementation, and we show that meaningful rankings of images based on predictive uncertainty can be obtained for two LeNet and ResNet-based neural networks using the MNIST and CIFAR-10 datasets. Further, we observe that false positives have on average a higher predictive epistemic uncertainty than true positives. This suggests that there is supplementing information in the uncertainty measure not captured by the classification alone.

Optimal Reserve and Energy Scheduling for a Virtual Power Plant Considering Reserve Activation Probability

With the increasing share of variable and limitedly predictable renewable energy in power systems worldwide, ensuring reserve capacity to maintain the balance of supply and demand becomes more important. On the other hand, the development of the virtual power plant model (VPP) allows renewable sources and energy storage to participate in reserve service. This paper addresses the optimal reserve bidding strategy problem of a VPP comprising of renewable energy resources (RESs), energy storage systems (ESSs), and several customers. The VPP participates in balance capacity (BC), day-ahead (DA), and intra-day (ID) markets. The scheduling problem is formulated as a two-stage chance-constrained optimization model taking the uncertainty of RESs production, load consumption, and probability of reserve activation into account. The response of VPP after its reserve capacity is called and generated is also considered to increase the operational flexibility of VPP. The proposed model is implemented on a test VPP system, and the effects of RESs sizing, ESSs sizing, and the probability of reserve activation are analyzed. Results indicate that the proposed model can perform well under real-world conditions.

Probabilistic modeling and reliability-based design optimization of a ground source heat pump system

The optimization design of a ground source heat pump (GSHP) system can be crucial in improving its performance and economic competitiveness. The effect of probabilistic uncertainties of design variables in a GSHP system was analyzed using reliability-based design optimization (RBDO) method. An analytical borehole heat transfer model was selected as the frame of energy simulation in this work. With the goal to minimize the cumulative costs over a 20-year lifespan of the GSHP system, a non-linear optimization was carried out under three constraint factors imposed on the internal flow in ground heat exchanger: The inlet water temperature, water pressure losses and Reynolds number to ensure turbulent flow. Three design variables including depth of boreholes, ground pipe radius and mass flow rate, and two random variables at the installation site, including the groundwater velocity and ground thermal conductivity were considered in this investigation. Different uncertainty levels were assigned into the probability indexes of all five variables, which were studied under multiple reliability levels of all three constraints. Results showed that uncertainties of variables can strongly affect the system reliability and total cost determination. The compromised increment of system cost to ensure the reliability was discussed, and the optimal combinations of design variables (borehole depth, pipe radius and mass flow rate) were also given under different designing scenarios.

Uncertainty of Integral System Safety in Engineering

Abstract The probabilistic safety analysis evaluates system reliability and failure probability by using statistics and probability theory. However, it cannot estimate the system safety uncertainties due to variabilities of probabilities in different system states. The article first summarizes how the information entropy expresses the probabilistic uncertainties due to nonuniform probability distributions of system states. Next, it argues that the conditional entropy of system operational and failure states appropriately describes both system redundancy and robustness. Finally, the article concludes that the probabilistic uncertainties of reliability, redundancy, and robustness jointly define the integral system safety. The concept of integral system safety allows for more precise definitions of efficient system functional properties, system configuration evaluation, optimal component selection, optimization, and decision making in engineering.

Belief eXtropy: Measure uncertainty from negation

As the duality and complement of the Shannon entropy, the eXtropy is proposed in this years. The eXtropy also can be explained from the perspective of negation, which can be seen as an entropy with one-step negation operation of elements. The Dempster–Shafer theory (DST), as the generalization of probability theory (PT), it can express the more uncertain information than the Bayesian distribution. It contains the uncertainty of the event probability expressed in the Bayesian distribution and the uncertainty of the Bayesian distribution. Based on above, this article proposes a new belief entropy in DST called SU entropy, which is the first belief entropy to use the elements rather than mass functions. And then, a new negation of non-specificity part in DST is proposed, which is the first time to research the negation of non-specificity alone. Finally, a new belief eXtropy was proposed. It is different from the traditional eXtropy thinking, but from the perspective of elements’ negation. After verification, it has a satisfying performance in measurement uncertainty in DST. At the end of the paper, we discuss how to understand eXtropy from the perspective of negation, and the future research direction for the new belief eXtropy.

Periodic dynamics for nonlocal Hopfield neural networks with random initial data

In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results.

A Bayesian surrogate constitutive model to estimate failure probability of elastomers

To calculate the uncertainty in the failure probability of elastomeric materials, a parametric and a non-parametric Bayesian-based stochastic constitutive model were evaluated. (i) A Bayesian linear regression calibration technique is created based on the Carroll model to construct a probabilistic hyper-elastic model in the parametric approach. The model was then calibrated using two methods: Maximum Likelihood Estimation (MLE) and Maximum a Posteriori (MAP) estimation, with the results compared. (ii) The Gaussian process (GP) is used in non-parametric hyper-parameters of the radial basis kernel computed using the limited-memory Broyden–Fletcher–Goldfarb–Shanno technique. Both models were trained and verified with regard to two sets of our experiments on silicon- and polyurethane-based elastomers to demonstrate their capabilities in modeling uncertainty propagation. Finally, failure probability analysis was carried out for these data sets using First Order Reliability Method (FORM) analysis and Crude Monte Carlo (CMC) simulation, with a limit state function based on the stochastic constitutive model at the failure point. Sensitivity analysis is also used to demonstrate the importance of Carroll model parameters in predicting failure likelihood. The results show that the parametric approach has great agreement with experimental data, not only for uncertainty quantification and model calibration, but also for calculating the failure probability of hyperelastic materials.

The impact of simulated soccer match-play on hip and hamstring strength in academy soccer players

ABSTRACT Introduction Together, the burden of hamstring and hip and groin injuries in soccer is substantial and the risk of re-injury in these areas is high. Reduced muscle strength has been identified as an important modifiable intrinsic risk factor of injury. However, little is known regarding the within-match changes in hip and hamstring muscle strength in order to inform early detection and management strategies. Methods Seventy-one male soccer players (age, 19.2 ± 0.9 yrs; height, 175.9 ± 5.8 cm; weight, 73 ±8.2 kg) from an international academy completed a fixed soccer-specific activity profile (SAFT90). Isometric hip and eccentric hamstring strength were measured after a standardised 5-min warm-up and repeated at half time and full time. Repeated-measures ANOVA were used to determine changes in muscle strength with magnitude-based decisions used to express probabilistic uncertainty. Results Findings indicate that i) there was likely to very likely substantial changes in isometric hip strength (−9.9–15.7%) and ii) no substantial changes in eccentric hamstring strength (−2.6–5.1%). Discussion By extrapolating these findings, it can be inferred that reduced isometric hip strength during match play may be one risk factor for injury, especially during periods of fixture congestion and practitioners should routinely assess muscle strength to inform training and match exposure based on player readiness. In doing so, it is likely that practitioners may enhance player availability and minimise injury incidence.

Deep Bayesian baseline for segmenting diabetic retinopathy lesions: Advances and challenges.

Early diagnosis of retinopathy is essential for preventing retinal complications and visual impairment due to diabetes. For the detection of retinopathy lesions from retinal images, several automatic approaches based on deep neural networks have been developed in the recent years. Most of the proposed methods produce point estimates of pixels belonging to the lesion areas and give no or little information on the uncertainty of method predictions. However, the latter can be essential in the examination of the medical condition of the patient when the goal is early detection of abnormalities. This work extends the recent research with a Bayesian framework by considering the parameters of a convolutional neural network as random variables and utilizing stochastic variational dropout based approximation for uncertainty quantification. The framework includes an extended validation procedure and it allows analyzing lesion segmentation distributions, model calibration and prediction uncertainties. Also the challenges related to the deep probabilistic model and uncertainty quantification are presented. The proposed method achieves area under precision-recall curve of 0.84 for hard exudates, 0.641 for soft exudates, 0.593 for haemorrhages, and 0.484 for microaneurysms on IDRiD dataset.

Final state sensitivity in noisy chaotic scattering

The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the dynamical behavior and it models their internal irregularities or their coupling with the environment. In these situations the unpredictability is affected by both the chaotic dynamics and the stochastic fluctuations. In the presence of noise two trajectories with the same initial condition can evolve in different ways and converge to a different asymptotic behavior. For this reason, even the exact knowledge of the initial conditions does not necessarily lead to the predictability of the final state of the system. Hence, the noise can be considered as an important source of unpredictability that cannot be fully understood using the conventional methods of nonlinear dynamics, such as the exit basins and the uncertainty exponent. By adopting a probabilistic point of view, we develop the concepts of probability basin, uncertainty basin and noise-sensitivity exponent, that allow us to carry out both a quantitative and qualitative analysis of the unpredictability on noisy chaotic scattering problems.

Naomi: a new modelling tool for estimating HIV epidemic indicators at the district level in sub-Saharan Africa.

IntroductionHIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small‐area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five‐year age groups.MethodsSmall‐area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district‐level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016–2018.ResultsAdult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty‐eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city.ConclusionsThe Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data.