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Variance global sensitivity (VGS) is defined by the mean square difference between output expectation and conditional one on input realization, and it can calculate the mean contribution of the input within its distribution region and guide the effective modulation of output variance. The Monte Carlo simulation (MCS) and quasi MCS are commonly used to estimate VGS, but they are time-consuming respectively due to double-loop framework and computation related to input dimension. Thus, a novel method is proposed to estimate VGS by elaborately using Bayesian updating. In the proposed algorithm, the input realizations are firstly treated as observations to construct a likelihood function. Then by Bayesian updating, all conditional output expectations on different input realizations, which are required in estimating VGS and most time-consuming, can be obtained as the posterior and estimated by the sample of simulating the output expectation. The proposed algorithm shares the sample of solving output expectation to obtain all conditional ones required for solving VGS, which makes the computational effort of estimating VGS equivalent to that of estimating output expectation, thus improving the efficiency of estimating VGS. Numerical and engineering examples fully substantiate the novelty and effectiveness of this algorithm. [ABSTRACT FROM AUTHOR]

We provide a unified analysis of dynamically consistent menu preferences in which an agent may exhibit a preference for flexibility, a preference for commitment, or both. Our work generalizes prior results, which investigated this problem for an agent who always exhibits preference for flexibility. By using two types of consistency conditions, we characterize an agent with a subjective state space who reacts to information about her subjective states in a dynamically consistent way. We apply our results to the uncertain strength of temptation and the anticipating regret representations, and characterize a dynamically consistent updating of the no-uncertainty representation. [ABSTRACT FROM AUTHOR]

Model updating (i.e., inverse problems) involving high-dimension and nonlinearity plays an increasingly important role in various research fields, e.g., digital twin model updating. Bayesian updating has become a robust and rigorous probabilistic means for parameter uncertainty quantification. However, it remains a challenging task to simultaneously ensure theoretically rigorous and computationally efficient solving of inverse problems involving high-dimensionality and nonlinearity. To address the issue, by applying the basic idea of subset simulation (SuS) to the ensemble Kalman filter (EnKF) that is computationally efficient and applicable to high-dimensional inverse problems, we designed an efficient Monte Carlo method, termed ensemble Kalman filter with subset simulation (EnKF-SuS). In EnKF-SuS, SuS provides a rigorous theoretical basis for guiding EnKF to adaptively search and explore the true target space(s), while avoiding the disadvantages of Markov chain Monte Carlo (MCMC)-based sampling methods by utilizing EnKF to generate updated ensemble samples. The performance of EnKF-SuS was validated and analyzed through three case studies involving multimodal posterior, strongly nonlinear, or high-dimensional problems. Moreover, based on a simplified model for longitudinal response analysis of shield tunnels, we present the application of EnKF-SuS in model updating using centrifuge data and field data, respectively. Results indicate that EnKF-SuS can accurately and efficiently sample from general target posterior distributions, especially in the tested strongly nonlinear or high-dimensional problems, and it is computationally one to two orders of magnitude faster than tested with MCMC-sampling methods. [ABSTRACT FROM AUTHOR]

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters, making the slope reliability assessment closer to the engineering reality. However, multi-source information (including test data, monitored data, field observation and slope survival records) is rarely used in current probabilistic back-analysis. Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved. In this paper, a framework by integrating a modified Bayesian Updating with Subset simulation (mBUS) method with adaptive Conditional Sampling (aCS) algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction. Within this framework, the high-dimensional probabilistic back-analysis problem can be easily tackled, and the multi-source information (e.g. monitored pressure heads and slope survival records) can be fully used in the back-analysis. A real Taoyuan landslide case in Taiwan, China is investigated to illustrate the effectiveness and performance of the established framework. The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations. Furthermore, the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12, 2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City, Taiwan, China.

We estimate the value of information to farmers from a soybean rust sentinel plot monitoring network. Monitoring provides value over time from farmers learning about their risk of infection and contemporaneously from farmers making more profitable fungicide applications. Optimizing the spatial configuration of the network reveals the value of information plateaus at around $920 million with around 75 sentinel plots. The optimal spatial distribution of sentinel plots differs substantially from historical placements. Optimal sentinel plot placement would have included fewer plots in the Southern United States, where the risk of infection is relatively high, and more in the Midwest, where soybean production is relatively high. [ABSTRACT FROM AUTHOR]

Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian‐like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian‐like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability. I examine empirical work that sheds light on the idea that animals can make decisions in a Bayesian‐like manner. I show evidence that animals are sensitive to variation in reward options and can make probabilistic inferences, two foundations of Bayesian‐like estimation. I also show that Bayesian models often predict the behavior of individuals in different environmental contexts. [ABSTRACT FROM AUTHOR]

Prioritizing multiple potentially unstable slopes based on varying levels of criticality is an essential approach when resources are limited. This study presents a framework for planning the prioritization of unstable rock slope remediation. The prioritization of mitigation measures for these slopes is determined using deformation values derived from indirect information, such as rock classification systems. To demonstrate the application of this framework, a case study involving unstable rock slopes in southwestern China is presented. Initially, the most appropriate estimation model was chosen from among six candidates for estimating the deformation modulus of the unstable rock mass in the slope, utilizing indirect information. Subsequently, the deformation modulus, updated through Bayesian analysis, was employed to generate the corresponding deformation distributions for the rock slopes. Compared to traditional quantitative methods, the proposed framework is adaptable to various working conditions and yields more definitive results. The indirect data used in this framework are cost-effective, enabling the assessment of all unstable slopes. Moreover, the effect of the amount of indirect data and prior information on slope remediation prioritization is discussed. The proposed framework offers a valuable tool for decision-makers in planning and prioritizing mitigation measures.

The probability analysis of ground deformation is becoming a trend to estimate and control the risk brought by shield tunnelling. The gap parameter is regarded as an effective tool to estimate the ground loss of tunnelling in soft soil. More specifically, ω, which is a gap parameter component defined as the over (or insufficient) excavation due to the change in the posture of the shield machine, may contribute more to the uncertainty of the ground loss. However, the existing uncertainty characterization methods for ω have several limitations and cannot explain the uncertain correlations between the relevant parameters. Along these lines, to better characterize the uncertainty of ω, the multivariate probability distribution was developed in this work and a dynamic prediction was proposed for it. To attain this goal, 1 523 rings of the field data coming from the shield tunnel between Longqing Road and Baiyun Road in Kunming Metro Line 5 were utilized and 44 parameters including the construction, stratigraphic, and posture parameters were collected to form the database. According to the variance filter method, the mutual information method, and the value of the correlation coefficients, the original 44 parameters were reduced to 10 main parameters, which were unit weight, the stoke of the jacks (A, B, C, and D groups), the pressure of the pushing jacks (A, C groups), the chamber pressure, the rotation speed, and the total force. The multivariate probability distribution was constructed based on the Johnson system of distributions. Moreover, the distribution was satisfactorily verified in explaining the pairwise correlation between ω and other parameters through 2 million simulation cases. At last, the distribution was used as a prior distribution to update the marginal distribution of ω with any group of the relevant parameters known. The performance of the dynamic prediction was further validated by the field data of 3 shield tunnel cases.

Recently, the application of Bayesian updating to predict excavation-induced deformation has proven successful and improved prediction accuracy significantly. However, updating the ground settlement profile, which is crucial for determining potential damage to nearby infrastructures, has received limited attention. To address this, this paper proposes a physics-guided simplified model combined with a Bayesian updating framework to accurately predict the ground settlement profile. The advantage of this model is that it eliminates the need for complex finite element modeling and makes the updating framework user-friendly. Furthermore, the model is physically interpretable, which can provide valuable references for construction adjustments. The effectiveness of the proposed method is demonstrated through two field case studies, showing that it can yield satisfactory predictions for the settlement profile.

The accurate prediction of short-term platform motions in a real environment is crucial for the safe design, operation, and maintenance of floating offshore wind turbines (FOWTs). Numerical simulations of motions are typically associated with high uncertainties due to abstracted theoretical models, empirical parameters, initial environment parameters, etc. Therefore, it is necessary to integrate other sources of information associated with less uncertainty, e.g., monitoring data, for accurate predictions. In this paper, we propose a probabilistic prediction based on the Bayesian approach that logically integrates motion monitoring data with simulated motion predictions of FOWTs, considering uncertainties in the environment model, structural properties, motion prediction method, monitoring data, etc. The approach consists of constructing a prior probability density function (PDF) of a random variable (which characterizes the largest value of the initial motion response) via numerical simulations and a likelihood function based on platform motion monitoring data and deriving a posterior PDF of the random variable by Bayesian updating. Then, posterior distributions of short-term extreme motion responses are derived using the posterior PDF of the random variable, representing lower uncertainty and improved accuracy. A Metropolis–Hastings algorithm is adopted to obtain PDFs of complex probability distributions. The effectiveness of the approach is demonstrated on a real FOWT platform in Scotland. The proposed probabilistic prediction approach results in posterior distributions of short-term extreme platform motions associated with less uncertainty and higher accuracy, which is attributed to integrating prior knowledge with monitoring data. [ABSTRACT FROM AUTHOR]

Applications of Bayesian updating commonly treat soil parameters as random variables. A significant issue with this is that soil parameters are highly subjective. Therefore, using traditional parameter-based models, Bayesian analysis starts from a subjective prior and it is unclear how this may influence the overall results of a study. In this paper, Bayesian updating is combined with a data-driven method, known as CRACA (i.e., CReep And Consolidation Analysis), for predicting the settlement of embankments on soft soil. Importantly, the method directly ingests measured oedometer data and, therefore, avoids the subjectivity involved in parameter selection. Because parameters are not used, scaling factors are introduced that account uncertainty associated with the laboratory measurements and the automated interpretation process. These factors have an initial value of unity (returning the prior) and are updated in a Bayesian framework as settlement monitoring data are revealed over time to improve future forecasts. The model was applied to an embankment case history and was shown to result in a rapid improvement in the accuracy and a narrowing of the 95% confidence interval as settlement monitoring data are revealed to the model. [ABSTRACT FROM AUTHOR]

The rapid development of electric vehicles (EVs) has created more possibilities for their flexible participation in electric power dispatching. Considering the clustering and fast mobility of EVs coinciding with real-time market requirements for responsive demands, a bidding strategy is proposed in this paper to assist EV aggregators with submitting reasonable quotations for the real-time market. Based on Bayesian updating, the strategy in this paper considers relevant factors such as aggregator cost and expected return. First, a quotation strategy in electricity spot market is proposed for EV aggregators. Second, the applicable scope of the strategy is given under different scenarios. Then, the objective function of learning is proposed, and the specific process of Bayesian updating is demonstrated. Finally, a case study of the aggregator quotation strategy based on Bayesian updating is simulated to verify the effectiveness and feasibility of the proposed strategy, which helps improve the bidding success rate of EVs and peak-to-valley balance of the grid. [ABSTRACT FROM AUTHOR]

Abstract Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian‐like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian‐like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability.

Probabilistic inverse-analysis is an essential approach to infer statistical characteristics of uncertain soil parameters, making the slope reliability assessment closer to engineering reality. However, current probabilistic inverse analysis rarely integrates multi-source information, including monitored data, field observation information, and slope survival records. Conducting the probabilistic inverse-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating the multi-source information is a challenging issue due to the involvement of thousands of random variables and the evaluation of high-dimensional likelihood functions. In this paper, a modified Bayesian updating with subset simulation (mBUS) method is combined with adaptive conditional sampling (aCS) algorithm to establish a framework for probabilistic inverse analysis of spatially variable soil parameters and reliability prediction of slopes. The effectiveness of this framework is validated using a highway slope as a case study. The research results show that the posterior statistical characteristics of soil parameters obtained by integrating multi-source information are in good agreement with field observation results. Additionally, the probability of slope failure under heavy rainfall on September 12, 2004 with the updated soil parameters is 23.1 %, which is in line with the actual slope instability. Within this framework, multi-source information can be fully utilized to address high-dimensional probabilistic inverse analysis problems.

Shapley value-based explainable AI has recently attracted significant interest. However, the computational complexity of the Shapley value grows exponentially with the number of players, resulting in high computational costs that prevent its widespread practical application. To address this challenge, various approximation methods have been proposed in the literature for computing the Shapley value, such as linear Shapley computation, sampling-based Shapley computation, and several estimation-based approaches. Among these methods, the sampling approach exhibits non-zero bias and variance and is sufficiently universal to be used with almost any AI algorithm. However, it suffers from unstable interpretability results and slow convergence in high-dimensional problems. To address these problems, we propose integrating a sequential Bayesian updating framework into the Shapley sampling approach. The core idea of this method is to dynamically update probabilities based on each sample’s Shapley value combined with a selection strategy. Both theoretical analysis and empirical results show that this method significantly improves the convergence speed and interpretability compared to the original sampling approach.

Understanding consciousness is central to understanding human nature. We have competing theories of consciousness. In interdisciplinary consciousness studies most believe that consciousness can be naturalized (i.e., consciousness depends in some substantial way on processes in — or states of — the brain). For roughly two decades, proponents of almost every theory have focused on collecting empirical support for their preferred theory, on the tacit assumption that empirical evidence will resolve the debates. Yet, it remains unclear how empirical evidence can do this in practice. Here I address this issue by offering (a sketch of) a methodology to quantify the divergent sets of empirical support proposed in favor of extant theories of consciousness. This in turn forms the foundation for a process of inference to the best explanation inspired by Bayesian confirmation theory. In interdisciplinary consciousness studies we are blessed with an abundance of theories, but we have reached a point where, going forward, it would be beneficial to focus on the most promising ones. Methods for assessment and comparison are necessary to identify which those are. While future refinement is likely, the methodology for assessment and comparison proposed here is a first step toward a novel way of approaching this through a quantification of empirical support for theories of consciousness. [ABSTRACT FROM AUTHOR]

This paper presents a new way to determine road profile and detect bridge damage using accelerations from a fleet of passing vehicles. Using off-bridge data, a Bayesian approach updates estimates of the road profile and vehicle properties. The profile elevations and vehicle properties are shown to be insensitive to random noise in acceleration measurements. On-bridge data, with recently updated vehicle properties, are used to estimate bridge damage. Bearing damage and local crack damage in a bridge are simulated. For bearing damage, the results show that this method can quantify the damage level of a bearing and infer other bridge properties. For local crack damage, the levels and the location of the damage are inferred from the simulated measurements. [ABSTRACT FROM AUTHOR]

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Abstract Background The main task of applied sport science is to inform decision-making in sports practice, that is, enabling practitioners to compare the expectable outcomes of different options (e.g. training programs). Main Body The “evidence” provided may range from group averages to multivariable prediction models. By contrast, many decisions are still largely based on the subjective, experience-based judgement of athletes and coaches. While for the research scientist this may seem “unscientific” and even “irrational”, it is important to realize the different perspectives: science values novelty, universal validity, methodological rigor, and contributions towards long-term advancement. Practitioners are judged by the performance outcomes of contemporary, specific athletes. This makes out-of-sample predictive accuracy and robustness decisive requirements for useful decision support. At this point, researchers must concede that under the framework conditions of sport (small samples, multifactorial outcomes etc.) near certainty is unattainable, even with cutting-edge methods that might theoretically enable near-perfect accuracy. Rather, the sport ecosystem favors simpler rules, learning by experience, human judgement, and integration across different sources of knowledge. In other words, the focus of practitioners on experience and human judgement, complemented—but not superseded—by scientific evidence is probably street-smart after all. A major downside of this human-driven approach is the lack of science-grade evaluation and transparency. However, methods are available to merge the assets of data- and human-driven strategies and mitigate biases. Short Conclusion This work presents the challenges of learning, forecasting and decision-making in sport as well as specific opportunities for turning the prevailing “evidence vs. eminence” contrast into a synergy.

The inter-well connectivity calculated from reservoir dynamic production data reflects formation heterogeneity quantitatively. Currently, the calculated inter-well connectivity between pair wells is mainly used as a tool for water flood management but not for quantitative reservoir characterization. This study proposes an innovative, dynamic data integration workflow that can integrate inter-well connectivity with a static reservoir model. In the workflow, the first step is calculating the inter-well connectivity vectors from the reservoir pairwise injector and producer wells. The second step covers interpolation in the domain of interest. The third step is to update the permeability model based on the Bayesian updating method. The result of this study shows that integrating the calculated inter-well connectivity with the static models enhances model reliability and it also provides an insight to deeper geological understanding reflected from dynamic data integration in reservoir modeling.

Understanding consciousness is central to understanding human nature. We have competing theories of consciousness. In interdisciplinary consciousness studies most believe that consciousness can be naturalized (i.e., consciousness depends in some substantial way on processes in — or states of — the brain). For roughly two decades, proponents of almost every theory have focused on collecting empirical support for their preferred theory, on the tacit assumption that empirical evidence will resolve the debates. Yet, it remains unclear how empirical evidence can do this in practice. Here I address this issue by offering (a sketch of) a methodology to quantify the divergent sets of empirical support proposed in favor of extant theories of consciousness. This in turn forms the foundation for a process of inference to the best explanation inspired by Bayesian confirmation theory. In interdisciplinary consciousness studies we are blessed with an abundance of theories, but we have reached a point where, going forward, it would be beneficial to focus on the most promising ones. Methods for assessment and comparison are necessary to identify which those are. While future refinement is likely, the methodology for assessment and comparison proposed here is a first step toward a novel way of approaching this through a quantification of empirical support for theories of consciousness.

Soil spatial variability has essential influence on the reliability of geotechnical structures. Karhunen–Loève (KL) series expansion is an effective approach to characterize such features of soil properties. Acquiring solution for Fredholm integral equation of the second type is a necessary prerequisite; however, the corresponding analytical expressions are only available for limited circumstances. To overcome this challenge, a newly proposed method called Chebyshev–Galerkin–KL expansion was developed to discretize the random fields of soil parameters, from which the approximated eigenvalues and eigenfunctions can be obtained using the Chebyshev orthogonal polynomials of the second kind combined with Galerkin technique. Application of the proposed approach is illustrated through reliability analysis of an unsaturated slope example under different rainfall patterns, where the uncertainty in selection of a "best" soil-water characteristic curve (SWCC) model and statistical uncertainties in SWCC model parameters are taken into account. Results show that the developed approach is feasible to generate random fields with sufficient accuracy. Under a constant rainfall duration, the Advanced pattern may lead to shallow landslide with the highest probability, followed by Intermediate and Delayed. It should be noted that Bayesian inference and determination of optimal SWCC model should be carried out prior to reliability analysis. Otherwise, the landslide risk level would be exaggerated. [ABSTRACT FROM AUTHOR]

Background: The main task of applied sport science is to inform decision-making in sports practice, that is, enabling practitioners to compare the expectable outcomes of different options (e.g. training programs). Main Body: The "evidence" provided may range from group averages to multivariable prediction models. By contrast, many decisions are still largely based on the subjective, experience-based judgement of athletes and coaches. While for the research scientist this may seem "unscientific" and even "irrational", it is important to realize the different perspectives: science values novelty, universal validity, methodological rigor, and contributions towards long-term advancement. Practitioners are judged by the performance outcomes of contemporary, specific athletes. This makes out-of-sample predictive accuracy and robustness decisive requirements for useful decision support. At this point, researchers must concede that under the framework conditions of sport (small samples, multifactorial outcomes etc.) near certainty is unattainable, even with cutting-edge methods that might theoretically enable near-perfect accuracy. Rather, the sport ecosystem favors simpler rules, learning by experience, human judgement, and integration across different sources of knowledge. In other words, the focus of practitioners on experience and human judgement, complemented—but not superseded—by scientific evidence is probably street-smart after all. A major downside of this human-driven approach is the lack of science-grade evaluation and transparency. However, methods are available to merge the assets of data- and human-driven strategies and mitigate biases. Short Conclusion: This work presents the challenges of learning, forecasting and decision-making in sport as well as specific opportunities for turning the prevailing "evidence vs. eminence" contrast into a synergy. Key Points: Generally, decision making in sports practice is based on "evidence " from scientific research or on "eminence" based on experience and subjective human judgment. Under the framework conditions of sport—specifically complexity and sparse data—both come with limitations that lead to considerable uncertainty when making decisions in practice. A broader range of strategies, smart strategy combinations and critical evaluation of performance under real-world conditions contribute to better decisions and better outcomes in the field of sport and exercise. [ABSTRACT FROM AUTHOR]

The uncertainty in the concrete compressive strength is one of the most challenging issues in safety checking of existing reinforced concrete (RC) buildings. The concrete compressive strength used in the assessment can highly influence the vulnerability results and thus the retrofit strategies. The need to use less expensive and less invasive in situ measurements such as the non-destructive tests should be balanced with a careful check of their structural reliability. The compressive concrete strength is characterized herein based on a large database of both in situ destructive and non-destructive results measured on the same structural members. The data are obtained from existing RC buildings mainly located in the Campania region, Southern Italy. Probabilistic linear and multilinear regression models are developed for calculating the compressive concrete strength based on non-destructive tests. Furthermore, the implementation of the concrete strength based on ultrasonic test results are investigated together with the relative measurement error through a fully probabilistic workflow. Accordingly, the relative weights of non-destructive data for calculating concrete compressive strength are estimated and compared with those recommended by the Italian national code. The results demonstrate that the effective weights of the non-destructive data are very close to the code-based recommendation. [ABSTRACT FROM AUTHOR]

The accurate prediction of short-term platform motions in a real environment is crucial for the safe design, operation, and maintenance of floating offshore wind turbines (FOWTs). Numerical simulations of motions are typically associated with high uncertainties due to abstracted theoretical models, empirical parameters, initial environment parameters, etc. Therefore, it is necessary to integrate other sources of information associated with less uncertainty, e.g., monitoring data, for accurate predictions. In this paper, we propose a probabilistic prediction based on the Bayesian approach that logically integrates motion monitoring data with simulated motion predictions of FOWTs, considering uncertainties in the environment model, structural properties, motion prediction method, monitoring data, etc. The approach consists of constructing a prior probability density function (PDF) of a random variable (which characterizes the largest value of the initial motion response) via numerical simulations and a likelihood function based on platform motion monitoring data and deriving a posterior PDF of the random variable by Bayesian updating. Then, posterior distributions of short-term extreme motion responses are derived using the posterior PDF of the random variable, representing lower uncertainty and improved accuracy. A Metropolis–Hastings algorithm is adopted to obtain PDFs of complex probability distributions. The effectiveness of the approach is demonstrated on a real FOWT platform in Scotland. The proposed probabilistic prediction approach results in posterior distributions of short-term extreme platform motions associated with less uncertainty and higher accuracy, which is attributed to integrating prior knowledge with monitoring data.

Accurate prediction of ground surface settlements induced by shield construction is of great significance for ensuring the safety of shield construction. This paper proposes a ground surface settlement prediction method for shield tunneling based on Bayesian updating. The sequential observation data during the advance of excavation is utilized to update the key soil parameters, leading to a more accurate settlement prediction for the subsequent excavation stages. Response surfaces are constructed to replace the finite element model as the forward models for higher computational efficiency. A tunnel excavation project in Hangzhou, China, is selected to illustrate the effectiveness of the proposed method. The shield excavation face passes through four soil layers, and two soil parameters (i.e., Young’s modulus and friction angle) of these soil layers are selected as random variables to be updated. The results show that the soil parameters can be effectively updated based on the observation data at multiple points and various excavation stages. The predictions of ground surface settlements are improved by using the updated soil parameters. The prediction accuracy of the proposed method increases as more stages of observation data are sequentially obtained and incorporated.

The nation's transportation systems are complex and are some of the highest valued and largest public assets in the United States. As a result of repeated natural hazards and their significant impact on transportation functionality and the socioeconomic health of communities, transportation resilience has gained increasing attention in recent years. Previous studies on transportation resilience have heavily emphasized network functionality during and/or following a scenario hazard event by implicitly assuming that sufficient knowledge of structural capacity and environmental/service conditions is available at the time of an extreme event. However, such assumptions often fail to consider uncertainties that arise when an extreme hazard event occurs in the future. Thus, it is essential to quantify and reduce uncertainties to better prepare for extreme events and accurately assess transportation resilience. To this end, this paper proposes a dynamic Bayesian network-based resilience assessment model for a large-scale roadway network that can explicitly quantify uncertainties in all phases of the assessment and investigate the role of inspection and monitoring programs in uncertainty reduction. Specifically, the significance of data reliability is investigated through a sensitivity analysis, where various sets of data having different reliabilities are used in updating system resilience. To evaluate the effectiveness of the model, a benchmark problem involving a highway network in South Carolina, USA is utilized, showcasing the systematic quantification and reduction of uncertainties in the proposed model. The benchmark problem result shows that incorporating monitoring and inspection data on important variables could improve the accuracy of predicting the seismic resilience of the network. It also suggests the need to consider equipment reliability when designing monitoring and inspection programs. With the recent development of a wide range of monitoring and inspection techniques, including nondestructive testing, health monitoring equipment, satellite imagery, LiDAR, etc., these findings can be useful in assisting transportation managers in identifying necessary equipment reliability levels and prioritizing inspection and monitoring efforts. [ABSTRACT FROM AUTHOR]

Decisions in management and finance rely on information that often includes win-lose feedback (e.g., gains and losses, success and failure). Simple reinforcement then suggests to blindly repeat choices if they led to success in the past and change them otherwise, which might conflict with Bayesian updating of beliefs. We use finite mixture models and hidden Markov models, adapted from machine learning, to uncover behavioral heterogeneity in the reliance on difference behavioral rules across and within individuals in a belief-updating experiment. Most decision makers rely both on Bayesian updating and reinforcement. Paradoxically, an increase in incentives increases the reliance on reinforcement because the win-lose cues become more salient. This paper was accepted by Gustavo Manso, finance. Funding: C. Alós-Ferrer gratefully acknowledges financial support from the Deutsche Forschungsgemeinschaft under [Grant AL1169/4], part of the research unit "Psychoeconomics" (FOR 1882). Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2022.4584. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a validation process in order to assess the predictive capabilities of a single degree-of-freedom oscillator. Model validation is understood here as the process of determining the accuracy with which a model can predict observed physical events or important features of the physical system. Therefore, assessment of the model needs to be performed with respect to the conditions under which the model is used in actual simulations of the system and to specific quantities of interest used for decision-making. Model validation also supposes that the model be trained and tested against experimental data. In this work, virtual data are produced from a non-linear single degree-of-freedom oscillator, the so-called oracle model, which is supposed to provide an accurate representation of reality. The mathematical model to be validated is derived from the oracle model by simply neglecting the non-linear term. The model parameters are identified via Bayesian updating. This calibration process also includes a modeling error due to model misspecification and modeled as a normal probability density function with zero mean and standard deviation to be calibrated.

In reality, sellers face challenges in obtaining perfect demand information. Demand is influenced not only by price but also by behavioral factors such as reference effects, which complicate optimal pricing for enterprises. To address this problem, we propose a dynamic pricing model that incorporates demand learning and considers consumer reference effects. Using the Bayesian method and based on historical sales and prices, sellers can learn about demand patterns. We analyze the model to determine the existence of an optimal solution and provide an algorithm to solve it. Our numerical simulation demonstrates that the total consumer demand and the impact of price on demand remain relatively stable over time. However, the factors influencing the reference effects exhibit greater variability. Sellers can also gain insights into market demand through their learning behavior in each phase and adjust production based on market size. For instance, our simulation shows an increase in market demand over time, allowing the seller to adjust the production plan according to the demand change. [ABSTRACT FROM AUTHOR]

Reliability updating can improve the failure probability estimates of structural systems when new observations are obtained. At present, an efficient reliability updating method is one that transforms the equality observation information into the inequality type by introducing an auxiliary variable and then employs structural reliability methods to perform reliability updating. For this method, the computation of posterior failure probability Pr(F|Z) , where Z is an observation event, requires two reliability analysis processes to estimate Pr(Z) and Pr(F∩Z) , respectively. To improve the efficiency, this paper develops a reliability updating method with output observations, where the computation of Pr(Z) and Pr(F∩Z) is integrated into one system reliability problem, which is then solved by adaptive kriging with truncated candidate region (AKTCR). A composite adaptive learning process is developed to construct the kriging model, which can provide accurate estimates for both Pr(Z) and Pr(F∩Z). In this way, the proposed method can also deal with the problem of multiple failure modes and multiple observation events. In addition, a combined global and local sampling method is embedded into the proposed algorithm to reduce the size of candidate sample pool and improve the modeling efficiency. Finally, three examples can prove the efficiency and accuracy of the proposed reliability updating method. In this work, we present a reliability updating framework for structural systems with output observations based on kriging. Although mathematical models often replace physical systems for reliability analysis, deviation between the real physical system and its model is inevitable. Thus, it is very necessary to reevaluate the failure probability of a structural system with the available observations when its model is used. In general, these observations can be collected from various sensors, such as force sensors, accelerometers, and so on. Once observations are obtained, the likelihood function and therefore the transformed inequality limit state function can be constructed, and reliability updating can be performed. Given that many models of physical systems are still expensive, such as the finite-element model, a kriging model is adopted to replace the expensive forward model and fit the inequality limit state function for simulation. Our reliability updating framework is also applicable to cases where there are multiple failure modes and multiple observation events. We expect our reliability updating framework can significantly save computational costs in engineering practice. [ABSTRACT FROM AUTHOR]

Reassessment of infrastructure buildings has become an essential approach to deal with increasing traffic loads on ageing infrastructure buildings and to verify the service-life of those structures. Good estimation of the actual material properties is highly relevant for reliable structural reassessment. Although this holds for all building materials, the importance of good parameter estimation is of special importance for concrete structures, where the strength properties show relatively high variation and where the nominal strength properties tend to be too conservative. Modern design guidelines allow to make use of scientific methods such as Bayesian Updating of material properties to enable a more realistic consideration of the actual material properties in the reassessment of existing structures. However, guidelines for application and experience with those methods are not yet reported much or are rather vague [1]. The presented study focuses on the effect of the Bayesian Updating process for material parameters with special emphasis on the number and sampling location of test specimens as well as on the accuracy and confidence in the obtained posterior distribution, since sampling also includes a certain margin of uncertainty. The investigation on the methodological potential and on the uncertainty margin in the updating process in this contribution uses a batch of 14 test results on the concrete compressive strength obtained from drill cores along with the inherent measurement uncertainties from the testing procedure. After a short review of Bayes’ Theorem, the Markov Chain Monte Carlo Method (MCMC) and the bootstrap methodology, all combinations of subsamples of size 1, 3 and 5 specimens were built and provided to the Bayes’ updating procedure via MCMC to determine the posterior distributions. The series of obtained posterior distributions for a certain subsample was used to determine the uncertainty in the Bayesian Updating process by evaluation of the scatter in the expected value, the standard deviation and the 5 %-quantile of the updated distribution. The simulations show the importance of an adequate sample size and quantify the uncertainties arising from the limited number of observations.

A novel methodology for the fatigue life uncertainty quantification of anisotropic structures is presented in this work. The concept of the equivalent initial flaw size distribution (EIFSD) is employed to overcome the difficulties in small cracks detection and fatigue prediction. This EIFSD concept is combined with the dual boundary element method (DBEM) to provide an efficient methodology for modelling the fatigue crack growth. Bayesian inference is used to infer the EIFSD based on inspection data from the routine maintenance of the structure, simulated with the DBEM. A large amount of DBEM simulations were required for the Bayesian inference. Therefore, surrogate models are used as part of the inference to further improve computational efficiency. A numerical example featuring an anisotropic plate is investigated for demonstrating the proposed methodology. When considering a low level of uncertainty in the crack propagation parameters, an error of 0.12% was found between the estimated fatigue life obtained using the proposed method compared to actual fatigue life, and only 0.35% error when considering high level of uncertainty. The application of the estimated fatigue life can be used to determine an appropriate inspection interval for aircraft maintenance. [ABSTRACT FROM AUTHOR]

In this study, a new method for multihazard risk assessment of an overhead transmission line grid located over a relatively large area is proposed. The main task of this method was to assess annual risk for overhead transmission lines using failure rates estimated from historical failure data and then modifying these estimated failure rates by reanalysis data and a Bayesian updating scheme. For this purpose, a comprehensive database of structural failures was collected for climatic, geologic, and man-made hazards to overhead transmission lines. Risk denotes the probability of exceeding the sum of direct losses due to repair costs of overhead transmission line components and indirect losses due to energy not supplied or unplanned power-off after outages. The performance of the proposed method was evaluated in a case study of a target area. The results showed that climatic hazards contributed the most to total losses in the study area. Furthermore, when using indirect losses to estimate the annual loss, the average annual loss may increase by up to about 45% relative to direct losses, depending on the type of hazard. This demonstrates the importance of investigating indirect losses from structural failures in the risk assessment of overhead transmission lines. [ABSTRACT FROM AUTHOR]

This paper explores the transferability of the Multiple Discrete-Continuous Extreme Value (MDCEV) model for activity type and duration using various transfer methods and sample sizes. This study employs the data of travel demand studies in two major cities, Shiraz and Mashhad in Iran. The model is first developed for Shiraz and then transferred to Mashhad. The adopted transfer methods are transfer scaling, Bayesian updating, combined transfer estimation, and joint context estimation. Aggregate and disaggregate transfer measures are adopted to examine the transferred models' general prediction and policy predictability. The results indicate the joint context estimation method's superiority in terms of estimation and policy prediction powers. The available massive data to the authors enabled measuring the value of sample size in this study. The sample size sensitivity analysis revealed a decrease in the marginal gain of the transferred model's performance as the sample size increases. Remarkably, the transferred model outperforms even the locally estimated model when 1) advanced transfer techniques are applied (i.e., the combined transfer estimation and the joint context estimation), and 2) the application context sample size is large enough (i.e., more than 30 percent).

The recent seismic events that occurred in South Korea have increased the interest in the re-evaluation of the seismic capacity of nuclear power plant (NPP) equipment, which is often conservatively estimated. To date, various approaches—including the Bayesian method proposed by the United States (US) Electric Power Research Institute —have been developed to quantify the seismic capacity of NPP equipment. Among these, the Bayesian approach has advantages in accounting for both prior knowledge and new information to update the probabilistic distribution of seismic capacity. However, data availability and region-specific issues exist in applying this Bayesian approach to Korean NPP equipment. Therefore, this paper proposes to construct an earthquake experience database by combining available earthquake records at Korean NPP sites and the general location of equipment within NPPs. Also, for the better representation of the seismic demand of Korean earthquake datasets, which have distinct seismic characteristics from those of the US at a high-frequency range, a broadband frequency range optimization is suggested. The proposed data construction and seismic demand optimization method for seismic capacity re-evaluation are demonstrated and tested on a 480 V motor control center of a South Korea NPP.

The parametric probability-box model, often abbreviated as "p-box" is frequently used to characterize epistemic uncertainties. However, structural reliability analysis with p-box uncertainties can often be computationally intensive. This paper presents an efficient method to accurately compute the bounds of failure probabilities within this context. The method's key innovation lies in its ability to achieve high efficiency with only a single round of model evaluations. First, the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM) with Bivariate Dimension Reduction Method (BDRM) is employed for precise reliability assessment, where a single-round of model evaluations are carried out. Subsequently, Bayesian Updating (BU) is applied to adjust the weights obtained from BDRM in response to changes in input variables, while ensuring the invariance of integration points. Following this adjustment, the FEM-MEM is once again employed to compute the failure probability after the information change, without necessitating additional model evaluations. To compute the bounds of failure probabilities, a Kriging model is employed to construct a surrogate relationship between the interval variables and failure probabilities. The accuracy and efficiency of the proposed method are demonstrated through numerical examples, with comparisons made against pertinent double-loop method. • The weights of BDRM are updated via Bayesian updating with the information change. • The proposed method conduct reliability assessment with only single round of LSF evaluations. • The Kriging model provides accurate upper and lower bounds of reliability index with minimal training data. • The proposed method allows for the robust and accurate results involving p-box uncertainties. [ABSTRACT FROM AUTHOR]

Precisely assessing statistical parameters to characterize spatial soil variability presents a significant challenge in probabilistic slope stability analysis, primarily due to inherent soil uncertainties and limited field-specific data. Probabilistic back analysis, recognized as an effective and reliable technique, offers a rational method for utilizing observational data to invert parameters of geomaterial properties. Nevertheless, previous investigations into parameter inversion for slope stability analysis have seldom considered the coupling of hydro-mechanical characteristics in reservoir landslides. This study proposes a novel integrated Bayesian framework to perform back analysis of reservoir landslides, incorporating the spatial variability of hydro-mechanical parameters. Within this framework, a hypoplastic constitutive model is developed to characterize the step-like deformation of the reservoir slope. The posterior knowledge of the saturated permeability coefficient and shear strength parameters is obtained by collecting field monitoring data of the underground water level and ground displacement. The Maliulin landslide, located in the Three Gorges Reservoir area of China, is adopted as an illustrative example to validate the proposed framework through back analysis of spatially variable soil parameters and probabilistic stability analysis. The results demonstrate that the proposed Bayesian updating framework significantly reduces the uncertainties associated with statistical values of soil parameters, providing more accurate and reasonable updated soil parameters for probabilistic slope stability analysis. [ABSTRACT FROM AUTHOR]

This study develops an efficient Bayesian updating method with monitoring data for predicting the deformation of high rock slopes induced by excavation. The importance ranking based on random forest is introduced to identify the key rock parameters as random variables in the Bayesian updating. The surrogate models using support vector machine are constructed to approximate the physical numerical models using FLAC3D for evaluating slope deformation. A practical example involving deformation prediction of the excavated left-bank rock slope for the well-known Baihetan hydropower station in southwest China is presented. The results indicate that the developed Bayesian updating method can efficiently and accurately update the posterior distributions of rock parameters and predict the deformation of high rock slopes induced by excavation. Incorporating the monitoring data of displacement into the Bayesian updating can effectively reduce the uncertainty of rock parameters and displacement prediction. As a result, the displacement predictions made by the Bayesian updating are closer to the monitoring data than the prior displacement predictions. In addition, incorporating more monitoring data of displacement from the previous excavation stages produces more accurate displacement predictions for subsequent excavation stages. • An efficient Bayesian updating method for predicting slope deformation is developed. • The excavated left-bank rock slope for Baihetan hydropower station is investigated. • Bayesian updating can efficiently and accurately predict deformation of high rock slopes. • The predictions made by Bayesian updating are more accurate than prior predictions. • Incorporating more monitoring data produces more accurate prediction results. [ABSTRACT FROM AUTHOR]

This study aims to the understanding of the impact of uncertainties related to constitutive model parameters on the cyclic response of CuAlBe Shape Memory Alloy (SMA) strands, and to define an adequate methodology for constructing the strands, thereby reducing uncertainty in their behavior. Employing a Bayesian framework and utilizing experimental data from tensile tests, the prior knowledge of mechanical properties at the wire level is updated. Various scenarios are explored, including model parameter updating for wires tested at different strain levels and from the same and different heat treatment batches. The updated model parameters are then used in a strand model, considering two scenarios: the strand is constructed from pieces cut from a single wire, post-heat treatment; or from pieces cut from wires from different heat treatment batches. The study concludes proposing a practical methodology to define test conditions for CuAlBe SMA wires and guidelines for the utilization of experimental data to predict bounds in the cyclic response of CuAlBe SMA strands. • Formulates robust tuning of constitutive relationships for CuAlBe SMA wires. • Proposes a Bayesian framework based on cyclic response of CuAlBe SMA wires. • Experimental data from different strain levels and heat treatment batches are used. • Uncertainties in wires are propagated to strands. • A practical methodology is proposed to predict bounds in the strand's cyclic response. [ABSTRACT FROM AUTHOR]

It has been more than a decade since sequential indicator simulation was proposed to model geological features. Due to its simplicity and easiness of implementation, the algorithm attracts the practitioner's attention and is rapidly becoming available through commercial software programs for modeling mineral deposits, oil reservoirs, and groundwater resources. However, when the algorithm only uses hard conditioning data, its inadequacy to model the long-range geological features has always been a research debate in geostatistical contexts. To circumvent this difficulty, one or several pieces of soft information can be introduced into the simulation process to assist in reproducing such large-scale settings. An alternative format of Bayesian sequential indicator simulation is developed in this work that integrates a log-linear pooling approach by using the aggregation of probabilities that are reported by two sources of information, hard and soft data. The novelty of this revisited Bayesian technique is that it allows the incorporation of several influences of hard and soft data in the simulation process by assigning the weights to their probabilities. In this procedure, the conditional probability of soft data can be directly estimated from hard conditioning data and then be employed with its corresponding weight of influence to update the weighted conditional portability that is simulated from the same hard conditioning and previously simulated data in a sequential manner. To test the algorithm, a 2D synthetic case study is presented. The findings showed that the resulting maps obtained from the proposed revisited Bayesian sequential indicator simulation approach outperform other techniques in terms of reproduction of long-range geological features while keeping its consistency with other expected local and global statistical measures. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a validation process in order to assess the predictive capabilities of a single degree-of-freedom oscillator. Model validation is understood here as the process of determining the accuracy with which a model can predict observed physical events or important features of the physical system. Therefore, assessment of the model needs to be performed with respect to the conditions under which the model is used in actual simulations of the system and to specific quantities of interest used for decision-making. Model validation also supposes that the model be trained and tested against experimental data. In this work, virtual data are produced from a non-linear single degree-of-freedom oscillator, the so-called oracle model, which is supposed to provide an accurate representation of reality. The mathematical model to be validated is derived from the oracle model by simply neglecting the non-linear term. The model parameters are identified via Bayesian updating. This calibration process also includes a modeling error due to model misspecification and modeled as a normal probability density function with zero mean and standard deviation to be calibrated. [ABSTRACT FROM AUTHOR]

Reassessment of infrastructure buildings has become an essential approach to deal with increasing traffic loads on ageing infrastructure buildings and to verify the service-life of those structures. Good estimation of the actual material properties is highly relevant for reliable structural reassessment. Although this holds for all building materials, the importance of good parameter estimation is of special importance for concrete structures, where the strength properties show relatively high variation and where the nominal strength properties tend to be too conservative. Modern design guidelines allow to make use of scientific methods such as Bayesian Updating of material properties to enable a more realistic consideration of the actual material properties in the reassessment of existing structures. However, guidelines for application and experience with those methods are not yet reported much or are rather vague [1]. The presented study focuses on the effect of the Bayesian Updating process for material parameters with special emphasis on the number and sampling location of test specimens as well as on the accuracy and confidence in the obtained posterior distribution, since sampling also includes a certain margin of uncertainty. The investigation on the methodological potential and on the uncertainty margin in the updating process in this contribution uses a batch of 14 test results on the concrete compressive strength obtained from drill cores along with the inherent measurement uncertainties from the testing procedure. After a short review of Bayes' Theorem, the Markov Chain Monte Carlo Method (MCMC) and the bootstrap methodology, all combinations of subsamples of size 1, 3 and 5 specimens were built and provided to the Bayes' updating procedure via MCMC to determine the posterior distributions. The series of obtained posterior distributions for a certain subsample was used to determine the uncertainty in the Bayesian Updating process by evaluation of the scatter in the expected value, the standard deviation and the 5 %-quantile of the updated distribution. The simulations show the importance of an adequate sample size and quantify the uncertainties arising from the limited number of observations. [ABSTRACT FROM AUTHOR]

Ageing infrastructure is becoming an increasing challenge as a result of deterioration and greater loading demands. Modern cities were built on top of complex underground infrastructure networks many of which are still in-service beyond their design life. The safety assessment of underground structures is of utmost importance to avoid catastrophic failures and develop cost-effective renewal and rehabilitation strategies. However, the lack of design documentation and absence of data on the level of structural deterioration make determination of current structural capacity a challenge. This paper presents a probabilistic based assessment framework for underground utility service pits using Bayesian updating technique, which is used to refine the probabilistic distribution of material properties from the prior distribution constructed using published data. A case study of an underground pit located in Central Melbourne is provided. Extensive experimental testing was conducted to characterise the material properties and a full-scale masonry wall was tested to understand the failure mode due to earth pressure and traffic load. The test data was used in strength prediction models to achieve a more accurate estimate for wall capacity. Further, the strength degradation models were integrated to develop the time-dependent material models, which were eventually used to compute reliability index. [ABSTRACT FROM AUTHOR]