Incorporating Model Uncertainty Research Articles

Battery state-of-health estimation incorporating model uncertainty based on Bayesian model averaging

Accurately estimating the state-of-health (SOH) of lithium-ion batteries is crucial for efficient, reliable, and safe use. However, the degradation of these batteries involves complex and intricate failure mechanisms that cannot be fully captured by a single model. To tackle this challenge, we propose an SOH estimation method based on Bayesian Model Averaging (BMA), which effectively accounts for both parameter and model uncertainties by combining estimations from different model implementations. It provides both point-value estimates and the probability distribution estimates, delivering results in a fraction of a second. Evaluated on three open-source datasets, the maximum absolute error of SOH estimation is within 0.03, and the Continuous Ranked Probability Score is within 0.015. Compared to optimal individual models, the proposed BMA method reduces the prediction error of point estimates by half to two-thirds. Additionally, the prediction error for probability estimation decreases by an order of magnitude. Moreover, the comparison studies with respect to the Gaussian Process Regression model and the Quantile Regression Forests model demonstrate the applicability and superiority of proposed method. These results highlight the potential of the BMA method to advance battery SOH estimation and facilitate reliable battery management.

Methods for Incorporating Model Uncertainty into Exoplanet Atmospheric Analysis

A key goal of exoplanet spectroscopy is to measure atmospheric properties, such as abundances of chemical species, in order to connect them to our understanding of atmospheric physics and planet formation. In this new era of high-quality JWST data, it is paramount that these measurement methods are robust. When comparing atmospheric models to observations, multiple candidate models may produce reasonable fits to the data. Typically, conclusions are reached by selecting the best-performing model according to some metric. This ignores model uncertainty in favor of specific model assumptions, potentially leading to measured atmospheric properties that are overconfident and/or incorrect. In this paper, we compare three ensemble methods for addressing model uncertainty by combining posterior distributions from multiple analyses: Bayesian model averaging, a variant of Bayesian model averaging using leave-one-out predictive densities, and stacking of predictive distributions. We demonstrate these methods by fitting the Hubble Space Telescope (HST) + Spitzer transmission spectrum of the hot Jupiter HD 209458b using models with different cloud and haze prescriptions. All of our ensemble methods lead to uncertainties on retrieved parameters that are larger but more realistic and consistent with physical and chemical expectations. Since they have not typically accounted for model uncertainty, uncertainties of retrieved parameters from HST spectra have likely been underreported. We recommend stacking as the most robust model combination method. Our methods can be used to combine results from independent retrieval codes and from different models within one code. They are also widely applicable to other exoplanet analysis processes, such as combining results from different data reductions.

Optimal payout strategies when Bruno de Finetti meets model uncertainty

Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal payout policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.

Data-driven probabilistic energy consumption estimation for battery electric vehicles with model uncertainty

ABSTRACT This paper presents a novel probabilistic data-driven approach to trip-level energy consumption estimation of battery electric vehicles (BEVs). As there are very few electric vehicle (EV) charging stations, EV trip energy consumption estimation can make EV routing and charging planning easier for drivers. In this research article, we propose a new driver behavior-centric EV energy consumption estimation model using probabilistic neural networks with model uncertainty. By incorporating model uncertainty into neural networks, we have created an ensemble of neural networks using Monte Carlo approximation. Our method comprehensively considers various vehicle dynamics, driver behavior, and environmental factors to estimate EV energy consumption for a given trip. We propose relative positive acceleration (RPA), average acceleration, and average deceleration as driver behavior factors in EV energy consumption estimation, and this paper shows that the use of these driver behavior features improves the accuracy of the EV energy consumption model significantly. Instead of predicting a single-point estimate for EV trip energy consumption, this proposed method predicts a probability distribution for the EV trip energy consumption. The experimental results of our approach show that our proposed probabilistic neural network with weight uncertainty achieves a mean absolute percentage error of 9.3% and outperforms other existing EV energy consumption models in terms of accuracy.

Robust adoption and valuation in tokenomics

This paper incorporates model uncertainty into the dynamic token-based platform adoption and valuation theory. We find that ambiguity slows down the tokenized platform adoption since users with the belief distortion tend to prevent the perturbation of the platform productivity, thus weakening the appreciation of the expected token price and the decline of the token carry cost due to the user-base growth. Moreover, as concerns regarding model uncertainty induce a trade-off between token price appreciation expectation and ambiguity hesitation, comparing the adoption speeds in the robust tokenized economy and the tokenless economy depends on the severity of the ambiguity aversion. Finally, ambiguity amplifies the user-base volatility of the tokenized economy, which, however, is still lower than that of the tokenless economy.

Addressing Uncertainty in Tool Wear Prediction with Dropout-Based Neural Network

Data-driven algorithms have been widely applied in predicting tool wear because of the high prediction performance of the algorithms, availability of data sets, and advancements in computing capabilities in recent years. Although most algorithms are supposed to generate outcomes with high precision and accuracy, this is not always true in practice. Uncertainty exists in distinct phases of applying data-driven algorithms due to noises and randomness in data, the presence of redundant and irrelevant features, and model assumptions. Uncertainty due to noise and missing data is known as data uncertainty. On the other hand, model assumptions and imperfection are reasons for model uncertainty. In this paper, both types of uncertainty are considered in the tool wear prediction. Empirical mode decomposition is applied to reduce uncertainty from raw data. Additionally, the Monte Carlo dropout technique is used in training a neural network algorithm to incorporate model uncertainty. The unique feature of the proposed method is that it estimates tool wear as an interval, and the interval range represents the degree of uncertainty. Different performance measurement matrices are used to compare the proposed method. It is shown that the proposed approach can predict tool wear with higher accuracy.

Active learning with Bayesian CNN using the BALD method for Hyperspectral Image Classification

Deep learning DL techniques have recently been used to examine the classification of remote sensing data like hyperspectral images HSI. However, DL models are difficult to obtain since they rely largely on a large number of labeled training data. Therefore, a current challenge in the field of HSI classification is how to effectively incorporate DL models in constrained labeled data. The Bayesian Convolutional Neural Networks BCNN method is robust against overfitting on small datasets. One of the key methods for automating data selection is active learning AL, which has gained popularity in recent decades. By choosing the most informative samples, AL aims to reduce the costly data labeling procedure and build a robust training set that is resource-efficient. In this work, we aim to improve the performance of BCNN using AL method to build a competitive classifier considering the Bayesian Active Learning Disagreement BALD acquisition function (Dropout Bayesian Active Learning by Disagreement), which incorporates model uncertainty information. In a previous work, BCNN was built and applied on Pavia datasets giving 99.7% classification accuracy. For comparison traditional BCNN with BALD, The techniques were applied on the Indian Pines dataset. The average accuracy of the classification had increased from 90% to 98% using BALD method.

Integrating fundamental model uncertainty in policy analysis: A Bayesian averaging approach combining CGE-models with metamodeling techniques

Sustainable economic development in the future is driven by public policy on regional, national and global levels. Therefore a comprehensive policy analysis is needed that provides consistent and effective policy support. However, a general problem facing classical policy analysis is model uncertainty. All actors, those involved in the policy choice and those in the policy analysis, are fundamentally uncertain which of the different models corresponds to the true generative mechanism that represents the natural, economic, or social phenomena on which policy analysis is focused. In this paper, we propose a general framework that explicitly incorporates model uncertainty into the derivation of a policy choice. Incorporating model uncertainty into the analysis is limited by the very high required computational effort. In this regard, we apply metamodeling techniques as a way to reduce computational complexity. We demonstrate the effect of different metamodel types using a reduced model for the case of CAADP in Senegal. Furthermore, we explicitly show that ignoring model uncertainty leads to inefficient policy choices and results in a large waste of public resources.

Bayesian model comparison for mortality forecasting

Abstract Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.

Analytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty

The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class of rotating shallow water models which are stochastically perturbed in order to incorporate model uncertainty into the underlying system. The stochasticity is chosen in a judicious way, by following the principles of location uncertainty, as introduced in Mémin (Geophys Astrophys Fluid Dyn 108(2):119–146, 2014). We prove that the resulting equation is part of a class of stochastic partial differential equations that have unique maximal strong solutions. The methodology is based on the construction of an approximating sequence of models taking value in an appropriately chosen finite-dimensional Littlewood-Paley space. Finally, we show that a distinguished element of this class of stochastic partial differential equations has a global weak solution.

Bayesian Model Averaging to Account for Model Uncertainty in Estimates of a Vaccine's Effectiveness.

PurposeVaccine effectiveness (VE) studies are often conducted after the introduction of new vaccines to ensure they provide protection in real-world settings. Control of confounding is often needed during the analyses, which is most efficiently done through multivariable modeling. When many confounders are being considered, it can be challenging to know which variables need to be included in the final model. We propose an intuitive Bayesian model averaging (BMA) framework for this task.Patients and MethodsData were used from a matched case–control study that aimed to assess the effectiveness of the Lyme vaccine post-licensure. Cases were residents of Connecticut, 15–70 years of age with confirmed Lyme disease. Up to 2 healthy controls were matched to each case subject by age. All participants were interviewed, and medical records were reviewed to ascertain immunization history and evaluate potential confounders. BMA was used to systematically search for potential models and calculate the weighted average VE estimate from the top subset of models. The performance of BMA was compared to three traditional single-best-model-selection methods: two-stage selection, stepwise elimination, and the leaps and bounds algorithm.ResultsThe analysis included 358 cases and 554 matched controls. VE ranged between 56% and 73% and 95% confidence intervals crossed zero in <5% of all candidate models. Averaging across the top 15 models, the BMA VE was 69% (95% CI: 18–88%). The two-stage, stepwise, and leaps and bounds algorithm yielded VE of 71% (95% CI: 21–90%), 73% (95% CI: 26–90%), and 74% (95% CI: 27–91%), respectively.ConclusionThis paper highlights how the BMA framework can be used to generate transparent and robust estimates of VE. The BMA-derived VE and confidence intervals were similar to those estimated using traditional methods. However, by incorporating model uncertainty into the parameter estimation, BMA can lend additional rigor and credibility to a well-designed study.

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin

This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model.

Robust reinsurance contract with asymmetric information in a stochastic Stackelberg differential game

In this paper, we determine a robust reinsurance contract from joint interests of the insurer and reinsurer under the framework of Stackelberg differential game. More specifically, the reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal proportional reinsurance to purchase. In order to defend the large shocks of wealth process, a loss-dependent premium principle is applied to the insurer. Meanwhile, we incorporate model uncertainty into the reinsurer's controlled surplus due to the asymmetric information. Under the time-consistent mean-variance criterion, we derive the robust reinsurance contract explicitly by solving the coupled extended Hamilton–Jacobi–Bellman systems. It is interesting to prove that the optimal premium control for the reinsurer is determined by a time-adjusted variance principle. In addition, we find that the reinsurer would like to raise the reinsurance price to guard against the model uncertainty, which consequently decreases the insurer's reinsurance demand. Finally, further analyses are provided to show the necessity of considering the model uncertainty; otherwise, the reinsurance company will suffer a great loss of utility.

Bayesian model uncertainty quantification for hyperelastic soft tissue models

Abstract Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g., recovered during surgery) cause considerable uncertainty in the identification. In this exploratory work, parameter uncertainty for incompressible hyperelasticity, often used for soft tissues, is addressed by a probabilistic identification approach based on Bayesian inference. Our study particularly focuses on the uncertainty of the model: we investigate how the identified uncertainties of the constitutive parameters behave when different forms of model uncertainty are considered. The model uncertainty formulations range from uninformative ones to more accurate ones that incorporate more detailed extensions of incompressible hyperelasticity. The study shows that incorporating model uncertainty may improve the results, but this is not guaranteed.

Narrow Money Demand in Indonesia and in Other Transitional Economies – Model Selection and Forecasting

Purpose: This paper aims to incorporate model uncertainty in variable selection and forecasting in the monetarist money demand model and check whether the emerging economies such as the Czech Republic, Poland, Hungary, Russia, Mexico, Brazil, Turkey, India, Republic of South Africa, and Indonesia follow this model in the long-run. The case of the United Kingdom serves as a benchmark for the study. Design/Methodology/Approach: In dynamic econometric modeling, the number of potential explanatory variables increases rapidly, and model uncertainty grows very fast. Consequently, empirical modeling of money demand needs a comprehensive strategy for model selection and forecasting. We use Bayesian averaging of classical estimates (BACE) as an appropriate model reduction strategy. The monetary model serves as the theoretical basis for empirical equilibrium error-correction models (EqCM) and employing the Bayesian averaging of classical estimates (BACE) approach for variable and model selection and forecasting. Findings: Four theoretical and competitive model specifications are proposed and empirically tested. We found that monetary systems in Indonesia and other analyzed economies are both stable and theory consistent. The forecasts generated for Indonesia are accurate. The robustness of the model selection based on the BACE procedure was strongly confirmed. Practical Implications: The proposed procedure is valid for practical application, particularly in dynamic model selection and forecasting. Originality/Value: The novelty of this research lies in employing the BACE approach to model the demand for money with the equilibrium error correction (EqCM) mechanism.

Accounting for model uncertainty in multiple imputation under complex sampling

AbstractMultiple imputation provides an effective way to handle missing data. When several possible models are under consideration for the data, multiple imputation is typically performed under a single‐best model selected from the candidate models. This single‐model selection approach ignores the uncertainty associated with the model selection and so leads to underestimation of the variance of multiple imputation estimator. In this article, we propose a new multiple imputation procedure incorporating model uncertainty in the final inference. The proposed method incorporates possible candidate models for the data into the imputation procedure using the idea of Bayesian model averaging. The proposed method is directly applicable to handling item nonresponse in survey sampling. Asymptotic properties of the proposed method are investigated. A limited simulation study confirms that our model averaging approach provides better estimation performance than the single‐model selection approach.

Leverage and valuation of hedge funds under model uncertainty

ABSTRACT We extend the model of dynamic leverage and valuation of hedge funds [Lan, Y., N. Wang, and J. Yang. 2013. The Economics of Hedge Funds.” Journal of Financial Economics 110: 300–323.] by incorporating model uncertainty. Our theoretical model predicts that concerns about model uncertainty induce risk-neutral managers to behave more endogenously risk-averse and to choose a more conservative leverage strategy. Moreover, it shows that model uncertainty may reduce the valuations of hedge funds, including incentive fees, and total fees for the manager as well as the investors' payoff, while model uncertainty has ambiguous effects on the valuations of managers' management fees. Finally, we find that model uncertainty significantly increases the break-even alpha at the founding of a hedge fund.

Uncertainty‐assisted deep vision structural health monitoring

AbstractComputer vision leveraging deep learning has achieved significant success in the last decade. Despite the promising performance of the existing deep vision inspection models, the extent of models’ reliability remains unknown. Structural health monitoring (SHM) is a crucial task for the safety and sustainability of structures, and thus, prediction mistakes can have fatal outcomes. In this paper, we use Bayesian inference for deep vision SHM models where uncertainty can be quantified using the Monte Carlo dropout sampling. Three independent case studies for cracks, local damage identification, and bridge component detection are investigated using Bayesian inference. Aside from better prediction results, the two uncertainty metrics, variations in softmax probability and entropy, are shown to have good correlations with misclassifications. However, modifying the decision or triggering human intervention can be challenging based on raw uncertainty outputs. Therefore, the concept of surrogate models is proposed to develop the models for uncertainty‐assisted segmentation and prediction quality tagging. The former refines the segmentation mask and the latter is used to trigger human interventions. The proposed framework can be applied to future deep vision SHM frameworks to incorporate model uncertainty in the inspection processes.

A recurrent reinforcement learning approach applicable to highly uncertain environments

Reinforcement learning has been a promising approach in control and robotics since data-driven learning leads to non-necessity of engineering knowledge. However, it usually requires many interactions with environments to train a controller. This is a practical limitation in some real environments, for example, robots where interactions with environments are restricted and time inefficient. Thus, learning is generally conducted with a simulation environment, and after the learning, migration is performed to apply the learned policy to the real environment, but the differences between the simulation environment and the real environment, for example, friction coefficients at joints, changing loads, may cause undesired results on the migration. To solve this problem, most learning approaches concentrate on retraining, system or parameter identification, as well as adaptive policy training. In this article, we propose an approach where an adaptive policy is learned by extracting more information from the data. An environmental encoder, which indirectly reflects the parameters of an environment, is trained by explicitly incorporating model uncertainties into long-term planning and policy learning. This approach can identify the environment differences when migrating the learned policy to a real environment, thus increase the adaptability of the policy. Moreover, its applicability to autonomous learning in control tasks is also verified.

Worst-Case Value at Risk and Portfolio Management: A Simple Method Incorporating Model Uncertainty

A kind of worst-case value-at-risk, GVaR, is defined to measure risk incorporating model uncertainty. Compared with most extant notions of worst-case VaR, GVaR can be computed by an explicit formula, and can be applied to large portfolios of several hundreds dimensions with low computational cost. It is robust for, but not limited to a set of VaRs based on normal distributions. We also reveal connections to robust portfolio optimization, which provides a tractable way to give optimal allocations under market ambiguity. Empirical analysis demonstrates that GVaR is a reliably robust risk measure.