Uncertainty Decomposition Research Articles

Decomposing high uncertainty in greenhouse gas mitigation pathways in emerging regions: An approach to evaluate risks toward carbon neutrality

In the context of ambitious greenhouse gas (GHG) mitigation strategies in emerging regions, addressing the prevailing uncertainty and its key influential factors is crucial. While uncertainty analysis of GHG mitigation pathways has been extensively explored, the systematic identification and quantification of pivotal factors has been notably absent. This study introduces a novel methodology that combines Quasi-Monte Carlo simulation with Sobol variance decomposition, which identifies key influential factors and traces the flow of uncertainties. Applied in Anhui Province, a rapidly developing region in China, our findings indicate an uncertain GHG emission proportion of 6.2 % by 2030, escalating to 68.6 % by 2060, with a 95 % confidence interval. This uncertainty results in a cumulative projection error of 2.1 billion tons of CO2e from 2020 to 2070. The per capita GDP factor emerges as the predominant influence, alongside the increasing impact of renewable energy factor and UHV import electricity factor. In our uncertainty flow analysis, the energy transformation sector is identified as the principal contributor to total uncertainty, driven significantly by economic and energy-related factors. These results underscore the critical need for policymakers in emerging regions to incorporate uncertainty decomposition analysis into their strategic planning to mitigate risks in GHG reduction efforts.

Quantitative analysis of spatiotemporal coverage and uncertainty decomposition in OCO-2/3 XCO2 across China

The Orbiting Carbon Observatory 2/3 (OCO-2/3) employs a full-physics inversion algorithm and estimates the column-averaged dry air mole fraction of carbon dioxide (XCO2). This research focuses on the spatiotemporal coverage and associated uncertainties of OCO-2/3's XCO2 measurements within the Chinese region. We undertook an extensive statistical examination of the daily, weekly, 16-day, and monthly spatiotemporal coverage of XCO2 across China, employing data from both OCO-2 and OCO-3 and their amalgamated datasets. Additionally, we used a posterior error analysis method to rigorously evaluate the uncertainties induced by various input parameters in the XCO2 inversion model across different regions in China. Our findings reveal that OCO-2's spatial coverage spans 2.3–53.8% in China at a spatial resolution of 1° × 1°, and OCO-3's spatial coverage spans 3.3 and 47.4% across these time scales in China. Notably, the combined coverage rates of both satellites are significantly higher, ranging from 5.4 to 72.6%. Our analysis also reveals a gradual decrease in XCO2 coverage and inversion rates from north to south and west to east across China. A significant portion of the uncertainties in OCO-2/3 XCO2 measurements, over 90%, were attributed to primary error sources such as instrument, aerosol, and CO2 prior profile. Aerosol-induced errors show regional variations, with higher levels observed in Southeast China. Compared to TCCON data, the accuracy of XCO2 measurements in the two Chinese sites was lower than the global average. Our research identifies the spatiotemporal distribution and uncertainty decomposition of carbon satellites at a regional scale in China, providing an essential reference for future research.

The uncertainty of quantum states with respect to the projective measurement

The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it systematically with respect to given projective measurement. Some basic concepts about uncertainty are reformulated in this context. We prove and get the form of the uncertainty preserving operations. The quantum states with maximal uncertainty are characterized. A universal decomposition of uncertainty into classical uncertainty and quantum uncertainty is provided. Furthermore, a unified and general relation among uncertainty, coherence and coherence of assistance is established. These results are independent of any explicit uncertainty measure. At last, we propose a new uncertainty measure called the geometric uncertainty based on the fidelity and link it with the geometric coherence.

Evaluating vegetation vulnerability under compound dry and hot conditions using vine copula across global lands

With global warming, climate extremes are intensifying, particularly compound dry and hot events (CDHEs), which would severely impact vegetation growth. However, quantitatively evaluating vegetation vulnerability to CDHEs remains challenging in global lands. A conditional probability model was constructed using the vine copula function to evaluate responses of vegetation to CDHEs based on the Standardized Moisture Anomaly Index (SZI), the Standardized Temperature Index (STI), and the kernel Normalized Difference Vegetation Index (kNDVI). The results show that vegetation growth is more susceptible to dry and hot conditions in arid and semi-arid regions than in sub-humid and humid regions. In terms of vegetation types, shrubs, savanna, grass, and crops are more susceptible to CDHEs than to individual dry or hot events, especially in water-limited regions. In arid regions, the vegetation vulnerability for open shrubs, closed shrubs, savanna, and grass under extreme CDHEs would correspondingly increase by 45%, 23%, 15%, and 12% compared with dry conditions, indicating the necessity to consider both dry and hot conditions simultaneously when evaluating vegetation dynamics to climatic extremes. In semi-arid and sub-humid regions, broadleaf forests show higher vulnerability to CDHEs than needleleaf forests. However, evergreen broadleaf forests show the lowest vulnerability and higher resistance to CDHEs in humid regions. The Analysis of Variance (ANOVA)-based uncertainty decomposition results show that copula combination sets in vine copula trees and vine copula structures are the two main uncertainty sources, accounting for about 60%. Despite with uncertainty, the modeling results show consistent vegetation loss probability patterns simulated with different structures of the vine copula model, indicating the robustness and reliability of the results. The findings provide a profound comprehension of ecosystems’ response mechanisms to compound extremes, which are essential to developing effective mitigation and adaptation strategies against the impact of future climate change.

Understanding anxiety through uncertainty quantification.

Uncertainty has been a central concept in psychological theories of anxiety. However, this concept has been plagued by divergent connotations and operationalizations. The lack of consensus hinders the current search for cognitive and biological mechanisms of anxiety, jeopardizes theory creation and comparison, and restrains translation of basic research into improved diagnoses and interventions. Drawing upon uncertainty decomposition in Bayesian Decision Theory, we propose a well-defined conceptual structure of uncertainty in cognitive and clinical sciences, with a focus on anxiety. We discuss how this conceptual structure provides clarity and can be naturally applied to existing frameworks of psychopathology research. Furthermore, it allows formal quantification of various types of uncertainty that can benefit both research and clinical practice in the era of computational psychiatry.

Informing synthetic passive microwave predictions through Bayesian deep learning with uncertainty decomposition

Abstract Space-borne passive microwave (PMW) data provide rich information on atmospheric state, including cloud structure and underlying surface properties. However, PMW data are sparse and limited due to low Earth orbit collection, resulting in coarse Earth system sampling. This study demonstrates that Bayesian deep learning (BDL) is a promising technique for predicting synthetic microwave (MW) data and its uncertainties from more ubiquitously available geostationary infrared observations. Our BDL models decompose predicted uncertainty into aleatoric (irreducible) and epistemic (reducible) components, providing insights into uncertainty origin and guiding model improvement. Low and high aleatoric uncertainty values are characteristic of clear sky and cloudy regions, respectively, suggesting that expanding the input feature vector to allow richer information content could improve model performance. The initially high average epistemic uncertainty metrics quantified by most models indicate that the training process would benefit from a greater data volume, leading to improved performance at most studied MW frequencies. Using quantified epistemic uncertainty to select the most useful additional training data (a training dataset size increase of 3.6%), the study reduced the mean absolute error and root mean squared error by 1.74% and 1.38%, respectively. The broader impact of this study is the demonstration of how predicted epistemic uncertainty can be used to select targeted training data. This allows for the curation of smaller, more optimized training datasets and also allows for future active learning studies.

Uncertainties in wave-driven longshore sediment transport projections presented by a dynamic CMIP6-based ensemble

In this study four experiments were conducted to investigate uncertainty in future longshore sediment transport (LST) projections due to: working with continuous time series of CSIRO CMIP6-driven waves (experiment #1) or sliced time series of waves from CSIRO-CMIP6-Ws and CSIRO-CMIP5-Ws (experiment #2); different wave-model-parametrization pairs to generate wave projections (experiment #3); and the inclusion/exclusion of sea level rise (SLR) for wave transformation (experiment #4). For each experiment, a weighted ensemble consisting of offshore wave forcing conditions, a surrogate model for nearshore wave transformation and eight LST models was used. The results of experiment # 1 indicated that the annual LST rates obtained from a continuous time series of waves were influenced by climate variability acting on timescales of 20-30 years. Uncertainty decomposition clearly reveals that for near-future coastal planning, a large part of the uncertainty arises from model selection and natural variability of the system (e.g., on average, 4% scenario, 57% model, and 39% internal variability). For the far future, the total uncertainty consists of 25% scenario, 54% model and 21% internal variability. Experiment #2 indicates that CMIP6 driven wave climatology yield similar outcomes to CMIP5 driven wave climatology in that LST rates decrease along the study area’s coast by less than 10%. The results of experiment #3 indicate that intra- and inter-annual variability of LST rates are influenced by the parameterization schemes of the wave simulations. This can increase the range of uncertainty in the LST projections and at the same time can limit the robustness of the projections. The inclusion of SLR (experiment #4) in wave transformation, under SSP1-2.6 and SSP5-8.5 scenarios, yields only meagre changes in the LST projections, compared to the case no SLR. However, it is noted that future research on SLR influence should include potential changes in nearshore profile shapes.

Comparative evaluation of uncertainty estimation and decomposition methods on liver segmentation

PurposeDeep neural networks need to be able to indicate error likelihood via reliable estimates of their predictive uncertainty when used in high-risk scenarios, such as medical decision support. This work contributes a systematic overview of state-of-the-art approaches for decomposing predictive uncertainty into aleatoric and epistemic components, and a comprehensive comparison for Bayesian neural networks (BNNs) between mutual information decomposition and the explicit modelling of both uncertainty types via an additional loss-attenuating neuron.MethodsExperiments are performed in the context of liver segmentation in CT scans. The quality of the uncertainty decomposition in the resulting uncertainty maps is qualitatively evaluated, and quantitative behaviour of decomposed uncertainties is systematically compared for different experiment settings with varying training set sizes, label noise, and distribution shifts.ResultsOur results show the mutual information decomposition to robustly yield meaningful aleatoric and epistemic uncertainty estimates, while the activation of the loss-attenuating neuron appears noisier with non-trivial convergence properties. We found that the addition of a heteroscedastic neuron does not significantly improve segmentation performance or calibration, while slightly improving the quality of uncertainty estimates.ConclusionsMutual information decomposition is simple to implement, has mathematically pleasing properties, and yields meaningful uncertainty estimates that behave as expected under controlled changes to our data set. The additional extension of BNNs with loss-attenuating neurons provides no improvement in terms of segmentation performance or calibration in our setting, but marginal benefits regarding the quality of decomposed uncertainties.

Evidential Conditional Neural Processes

The Conditional Neural Process (CNP) family of models offer a promising direction to tackle few-shot problems by achieving better scalability and competitive predictive performance. However, the current CNP models only capture the overall uncertainty for the prediction made on a target data point. They lack a systematic fine-grained quantification on the distinct sources of uncertainty that are essential for model training and decision-making under the few-shot setting. We propose Evidential Conditional Neural Processes (ECNP), which replace the standard Gaussian distribution used by CNP with a much richer hierarchical Bayesian structure through evidential learning to achieve epistemic-aleatoric uncertainty decomposition. The evidential hierarchical structure also leads to a theoretically justified robustness over noisy training tasks. Theoretical analysis on the proposed ECNP establishes the relationship with CNP while offering deeper insights on the roles of the evidential parameters. Extensive experiments conducted on both synthetic and real-world data demonstrate the effectiveness of our proposed model in various few-shot settings.

Eliciting second-order beliefs

We study elicitation of subjective beliefs of an agent facing ambiguity (model uncertainty): the agent has a non-singleton set of (first order) priors on an event and a second-order distribution on these priors. Such a two-stage decomposition of uncertainty and non-reduction of subjective compound lotteries resulting from non-neutrality to the second-order distribution plays an important role in resolving the Ellsberg Paradox. However, a key unanswered question is whether we can actually observe and separate the sets of first and second order subjective probabilities. We answer this question and show that it is indeed possible to pin the two sets down uniquely and therefore separate them meaningfully. We introduce prize variations and ensure that the tangent plane at any point on the surface of the certainty-equivalent function is reported truthfully. Any basis for this plane consists of derivatives in two different directions, and these combine first and second order beliefs in different ways. We show that this is enough to ensure that reporting both sets of beliefs truthfully is uniquely optimal. The technique requires knowledge of the changes in certainty equivalent of a mixture of acts as a result of variations in prizes, which we also elicit.

Uncertainty Decomposition to Understand the Influence of Water Systems Model Error in Climate Vulnerability Assessments

AbstractClimate vulnerability assessments rely on water infrastructure system models that imperfectly predict performance metrics under ensembles of future scenarios. There is a benefit to reduced complexity system representations to support these assessments, especially when large ensembles are used to better characterize future uncertainties. An important question is whether the total uncertainty in the output metrics is primarily attributable to the climate ensemble or to the systems model itself. Here we develop a method to address this question by combining time series error models of performance metrics with time‐varying Sobol sensitivity analysis. The method is applied to a reduced complexity multi‐reservoir systems model of the Sacramento‐San Joaquin River Basin in California to demonstrate the decomposition of flood risk and water supply uncertainties under an ensemble of climate change scenarios. The results show that the contribution of systems model error to total uncertainty is small (∼5%–15%) relative to climate based uncertainties. This indicates that the reduced complexity systems model is sufficiently accurate for use in the context of the vulnerability assessment. We also observe that climate uncertainty is dominated by the choice of general circulation model and its interactive effects with the representative concentration pathway (RCP), rather than the RCP alone. This observation has implications for how climate vulnerabilities should be interpreted.

Deep Learning based Uncertainty Decomposition for Real-time Control

Data-driven control in unknown environments requires a clear understanding of the involved uncertainties for ensuring safety and efficient exploration. While aleatoric uncertainty that arises from measurement noise can often be explicitly modeled given a parametric description, it can be harder to model epistemic uncertainty, which describes the presence or absence of training data. The latter can be particularly useful for implementing exploratory control strategies when system dynamics are unknown. We propose a novel method for detecting the absence of training data using deep learning, which gives a continuous valued scalar output between 0 (indicating low uncertainty) and 1 (indicating high uncertainty). We utilize this detector as a proxy for epistemic uncertainty and show its advantages over existing approaches on synthetic and real-world datasets. Our approach can be directly combined with aleatoric uncertainty estimates and allows for uncertainty estimation in real-time as the inference is sample-free unlike existing approaches for uncertainty modeling. We further demonstrate the practicality of this uncertainty estimate in deploying online data-efficient control on a simulated quadcopter acted upon by an unknown disturbance model.

Measuring Global Macroeconomic Uncertainty and Cross-Country Uncertainty Spillovers

We propose an approach for jointly measuring global macroeconomic uncertainty and bilateral spillovers of uncertainty between countries using a global vector autoregressive (GVAR) model. Over the period 2000Q1–2020Q4, our global index is able to summarize a variety of uncertainty measures, such as financial-market volatility, economic-policy uncertainty, survey-forecast-based measures and econometric measures of macroeconomic uncertainty, showing major peaks during both the global financial crisis and the COVID-19 pandemic. Global spillover effects are quantified through a novel GVAR-based decomposition of country-level uncertainty into the contributions from all countries in the global model. We show that this approach produces estimates of uncertainty spillovers which are strongly related to the structure of the global economy.

Path Tracking Control for Underactuated Vehicles With Matched-Mismatched Uncertainties: An Uncertainty Decomposition Based Constraint-Following Approach

This paper presents a robust path tracking control method by utilizing the ideology of constraint-following approach for uncertain underactuated autonomous vehicles. The uncertainties are bounded with an unknown boundary. They do not all fall within the range space of the input matrix. Based on kinematic relations between the desired path and vehicle, the path tracking task is transformed into an equality constraint of the vehicle lateral dynamics states. The control goal is to make the underactuated vehicle follow the constraint, thus realizing the desired tracking performance. The constraint-following robust control (CFRC) is designed in two steps. First, a servo control design for the nominal system is devised without considering uncertainty and initial constraint deviation. Second, the uncertainty is meticulously decomposed into matched and mismatched portions based on the geometric structural characteristics of the constraint dynamics system. As a result, since the mismatched uncertainty is orthogonal to the constraint-following geometric space, it “disappears” in the stability analysis. The matched uncertainty is estimated by a self-adjusting leakage type adaptive law. On this basis, a robust control is designed based on the estimated matched uncertainty. Through Lyapunov minimax analysis, the proposed control method guarantees the approximate constraint-following performance. Finally, the TruckSim–Simulink co-simulations and real vehicle experiments are presented. The results show that the proposed control can robustly realize excellent tracking performance in the presence of time-vary uncertainties.

Shell-model study on properties of proton dripline nuclides with Z, N = 30–50 including uncertainty analysis * *Supported by the National Natural Science Foundation of China (11775316, 11825504, 11961141004), the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2016TQ03N575), the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006)

The binding and proton separation energies of nuclides with are investigated based on the shell model, with an uncertainty analysis via statistical methods. Several formulas are used to obtain the binding and proton separation energies according to shell-model calculations. The non-parametric bootstrap method is applied to establish an uncertainty decomposition and recomposition framework. Moreover, this is used to estimate the stability of proton(s) emission for each nuclide. Two formulas for calculating the binding energies with a systematic uncertainty of MeV are proposed, and a reliable extrapolation ability is examined. These binding energy formulas deduce similar forms for their respective and energies, which predict the extension of the nuclear boundary of this region. A good description of the binding and proton separation energies is provided. The one- and two-proton separation energies and partial half-lives of proton emission are predicted, thus revealing a new dripline. Furthermore, there are 30 unstable nuclides predicted to be bound against proton(s)-emission. These nuclear properties will be useful in nuclear astrophysics.

Bio-inspired structure reference model oriented robust full vehicle active suspension system control via constraint-following

It is hard to realize the bio-inspired structure (BIS) directly in the vehicle suspension due to space limitation, even though the beneficial nonlinearity of BIS for anti-vibration has been extensively proved. This paper adopts active suspension control to take the advantage of BIS on anti-vibration to improve vehicle comfort, i.e., formulating the ideal BIS dynamics model as nonholonomic servo constraints and then designing the control via constraint-following to drive the dynamics of full vehicle active suspension system (FVASS) to follow the servo constraints. It is of novelty for this study to introduce the constraint-following controls (CFC) into the linear FVASS to follow the servo constraints, considering possibly fast time-varying uncertainties including large mismatched portions. The CFC views the nonlinear control problem from a new perspective of servo constraint. This leads to a simple and natural control that is capable of ‘exactly’ following the servo constraints of nonlinear BIS in the second-order form without the requirement of linearization and/or nonlinear cancellation. Furthermore, a robust CFC is designed based on an uncertainty decomposition technique to consider possibly fast time-varying uncertainties including large mismatched portions, which are unavoidable in underactuated systems but are usually ignored or assumed very small in existing studies. The proposed robust CFC is proved to be able to fulfill the control task with controllable constraint-following error by the Lyapunov stability analysis, even in the presence of uncertainties. Experimental and simulation results reveal the validity of the proposed approach in improving vehicle suspension performance.

Decomposing crop model uncertainty: A systematic review

Crop models are essential tools for analysing the effects of climate variability, change on crop growth and development and the potential impact of adaptation strategies. Despite their increasing usage, crop model estimations have implicit uncertainties which are difficult to classify and quantify. Failure to address these uncertainties may result in poor advice to policymakers and stakeholders for the development of adaptation strategies. Since the 1990s, the number of crop model uncertainty assessments that consider different sources of model uncertainty (model structure, model parameters and model inputs such as climate, soil, and crop management practices) has increased significantly. We present the outcomes of a systematic review focused on uncertainty assessments of crop model outputs (mainly grain yield) and crop model uncertainty decomposition. We reviewed 277 articles from 1991 to 2019 which included studies conducted in 82 countries (460 locations) across all continents. 57% of the articles have been published between 2015 and 2019. 52% of the studies focus on input uncertainty assessments with climate change projections as the most frequently considered source of input uncertainty. Only 28% and 20% of the studies, respectively, dealt with uncertainties related to model parameters and model structure. The latter was mainly quantified using multi-model ensembles. Over half the studies were carried out in European and Asian countries, 34% and 23%, respectively. Most articles estimated model uncertainty focusing on the grain yield of major cereal crops (wheat > maize > rice) using the Decision Support System for Agrotechnology Transfer (DSSAT) model. Sensitivity analysis was the most used technique to quantify the contribution of different sources of uncertainty although the range of approaches for uncertainty quantification was wide. There is a need for standard procedures to estimate crop model uncertainty and evaluate estimates. We discuss the challenges of quantifying the components of uncertainty within crop models and identify research needs to better understand sources of uncertainty and thus improve the accuracy of crop models.

Incomplete‐information games in large populations with anonymity

The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent‐specific micro component, with a law of large numbers for the latter. This macro–micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their beliefs about the cross‐section distribution of types and other macro variables, and by their beliefs about the cross‐section distribution of other agents' strategies. Any probability distribution over cross‐section distributions of types and other macro variables is compatible with a fully specified belief system, but not every function from types to such probability distributions is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of such a function with a common prior.

Decomposing Satellite-Based Classification Uncertainties in Large Earth Science Datasets

Collection of increasingly voluminous multispectral data from multiple instruments with high spatial resolution has posed both an opportunity and a challenge for maximizing their utilization, analysis, and impact. Obtaining accurate estimates of precipitation globally with high temporal resolution is crucial for assessing multiscale hydrologic impacts and providing a constraint for development of numerical models of the atmosphere that provide weather and climate predictions. Precipitation type classification plays an important role in constraining both the inverse problem in satellite precipitation retrievals and latent heat transfer within weather prediction simulations. Precipitation type, however, is often reported deterministically, without uncertainty attached to an estimate. Machine learning techniques are capable of extracting content of interest from large datasets and accurately retrieving discrete and continuous properties of physical systems, but with limited insights to the retrieval components—such as errors and the physical relationship between the observed and retrieved properties. To address this shortcoming, we perform precipitation type classification to introduce a novel tool for decomposing errors of satellite-retrieved products. We use Bayesian neural networks to map global precipitation measurement mission microwave imager observations to dual-frequency precipitation radar-derived precipitation type, which perform comparably to deterministic models, but with the added benefit of providing well-calibrated uncertainties. Through uncertainty decomposition, we demonstrate well-calibrated uncertainties as useful for making decisions concerning high uncertainty predictions, model selection, targeted data analysis, and data collection and processing. Additionally, our Bayesian models enable mathematical confirmation of a data distribution change as the cause for an unacceptable decline in model accuracy.

Eliciting Second-Order Beliefs

We study elicitation of subjective beliefs of an agent facing ambiguity (model uncertainty): the agent has a non-singleton set of (first-order) priors on an event and a second-order prior on these first-order belief-states. Such a two-stage decomposition of uncertainty and non-reduction of compound lotteries resulting from nonneutrality to the second-order distribution plays an important role in resolving the Ellsberg Paradox. The problem of eliciting beliefs on unobservable belief-states with ambiguity-sensitive agents is novel, and we introduce new elicitation techniques using report-dependent prize variations. We construct a direct revelation mechanism that induces truthful reporting of the first-order belief states as well as the secondorder distribution on the belief-states as the unique best response. The technique requires knowledge of the sensitivity function to second-order distribution (capturing ambiguity attitude) and the vN-M utility function, which we also elicit.