Summed versus estimated factor scores: Considering uncertainties when using observed scores.

Seismic fragility analysis is a complex process involving different sources of uncertainties. In this paper, an alternative procedure for seismic fragility analysis based on the uniform design method (UD) is proposed. UD is used to generate a reasonable sample to build probabilistic seismic demand models (PSDMs), which are used to generate the fragility curves of a cable-stayed bridge. Sensitivity analyses of different uncertainties are carried out by comparison of the fragility curves for different components. It is concluded that (1) the UD method can consider different sources of uncertainties in fragility analysis with reasonable accuracy; (2) the bridge system is more fragile than any component of bridges; and (3) the damage probability of fragility considering uncertainty in the ground motion, geometry, and material is larger than that considering only the uncertainty in the ground motion.

State updating in a distributed hydrological model by ensemble Kalman filtering with error estimation

Purpose This study aims to investigate how different sources of uncertainty hinder the measurement and reporting of greenhouse gas (GHG) emissions in the steel supply chain (SC). It also examines how information processing mechanisms can support SC planning and help organizations manage these uncertainties. Design/methodology/approach A qualitative approach is used, based on semi-structured interviews with 16 informants from 12 European companies operating at different positions in the steel SC, including raw material producers, manufacturers, logistics providers, wholesalers and service partners. Grounded in the organizational information processing theory, the study analyzes how uncertainty affects emissions-related information processing and planning decisions. Findings The study identifies six key sources of uncertainty that hinder emissions measurement and reporting in the steel SC. These uncertainties manifest differently across procurement, production, distribution and sales planning stages. The findings illustrate how organizations can respond through information processing mechanisms that support emissions-related planning tasks and help integrate decarbonization goals into SC decision-making. In this study, procurement planning emerged as a particularly critical stage, where targeted information processing mechanisms can help mitigate emissions-related uncertainties. Research limitations/implications This study contributes to research on sustainable SC management and SC planning by identifying key factors that generate emissions-related uncertainty and highlighting how information processing can support decarbonization efforts. Practical implications Organizations can benefit from understanding how uncertainties related to GHG emissions measurement and reporting emerge and intensify. The study suggests several information processing mechanisms that can help organizations mitigate these challenges through SC planning and inform policymaking for better carbon management. Originality/value This research contributes to the understanding of how different sources of uncertainty emerge and complicate GHG emissions measurement and reporting in the steel SC.

Uncertainty analysis has become an important topic in environmental research. Uncertainty in hydrological modeling, in general, has been studied by investigating mainly the influence of the parameter uncertainty on the uncertainty of the simulated outputs. This paper focuses essentially on the impact of point input uncertainty on fully distributed hydrological modeling and proposes an integrated approach to cope with input and parameter uncertainty. The approach uses Bayesian theory in two steps: first, to compute the uncertainty in input forcing data, and second, to compute the hydrological parameter uncertainty and the uncertainties of a lumped‐error term that include other sources of errors: response errors and model error. The method is applied with a fully distributed model: WaSiM‐ETH. The results show that the methodology proposed here is a valuable tool to assess different sources of uncertainty in hydrological modeling and show the effects of uncertainty in the input forcing when a fully distributed, physically based hydrological model is used.

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

Assessment of uncertainties and variations in PV modules degradation rates and lifetime predictions using physical models

A major challenge in the identification of material properties is handling different sources of uncertainty in the experiment and the modelling of the experiment for estimating the resulting uncertainty in the identified properties. Numerous improvements in identification methods have provided increasingly accurate estimates of various material properties. However, characterizing the uncertainty in the identified properties is still relatively crude. Different material properties obtained from a single test are not obtained with the same confidence. Typically the highest uncertainty is associated with respect to properties to which the experiment is the most insensitive. In addition, the uncertainty in different properties can be strongly correlated, so that obtaining only variance estimates may be misleading. A possible approach for handling the different sources of uncertainty and estimating the uncertainty in the identified properties is the Bayesian method. This method was introduced in the late 1970s in the context of identification [1] and has been applied since to different problems, notably identification of elastic constants from plate vibration experiments [2]-[4]. The applications of the method to these classical pointwise tests involved only a small number of measurements (typically ten natural frequencies in the previously cited vibration test) which facilitated the application of the Bayesian approach. For identifying elastic constants, full field strain or displacement measurements provide a high number of measured quantities (one measurement per image pixel) and hence a promise of smaller uncertainties in the properties. However, the high number of measurements represents also a major computational challenge in applying the Bayesian approach to full field measurements. To address this challenge we propose an approach based on the proper orthogonal decomposition (POD) of the full fields in order to drastically reduce their dimensionality. POD is based on projecting the full field images on a modal basis, constructed from sample simulations, and which can account for the variations of the full field as the elastic constants and other parameters of interest are varied. The fidelity of the decomposition depends on the number of basis vectors used. Typically even complex fields can be accurately represented with no more than a few dozen modes and for our problem we showed that only four or five modes are sufficient [5]. To further reduce the computational cost of the Bayesian approach we use response surface approximations of the POD coefficients of the fields. We show that 3rd degree polynomial response surface approximations provide a satisfying accuracy. The combination of POD decomposition and response surface methodology allows to bring down the computational time of the Bayesian identification to a few days. The proposed approach is applied to Moire interferometry full field displacement measurements from a traction experiment on a plate with a hole. The laminate with a layup of [45,- 45,0]s is made out of a Toray® T800/3631 graphite/epoxy prepreg. The measured displacement maps are provided in Figure 1. The mean values of the identified properties joint probability density function are in agreement with previous identifications carried out on the same material. Furthermore the probability density function also provides the coefficient of variation with which the properties are identified as well as the correlations between the various properties. We find that while the longitudinal Young's modulus is identified with good accuracy (low standard deviation), the Poisson's ration is identified with much higher uncertainty. Several of the properties are also found to be correlated. The identified uncertainty structure of the elastic constants (i.e. variance co-variance matrix) has potential benefits to reliability analyses, by allowing a more accurate description of the input uncertainty. An additional advantage of the Bayesian approach is that it provides a natural way (in the form of the prior probability density function) for accounting for prior information that may be available on the material properties thought. This is of great interest for reducing the uncertainty on properties that can only be determined with low confidence from the plate with a hole experiment, such as Poisson's ratio or transverse Young's modulus in our case.

Abstract. Water management in sub-Saharan African river basins is challenged by an uncertain future climatic, social and economical patterns potentially causing diverging water demands and availability, and by multi-stakeholder dynamics, resulting in evolving conflicts and tradeoffs. In such contexts, a better understanding of the sensitivity of water management to the different sources of uncertainty can support policymakers in identifying robust water supply policies balancing optimality and low vulnerability against likely adverse future conditions. This paper contributes an integrated decision-analytic framework combining an optimization, robustness, sensitivity, and uncertainty analysis to retrieve the main sources of vulnerability to optimal and robust reservoir operating policies across multi-dimensional objective spaces. We demonstrate our approach on the lower Umbeluzi river basin, Mozambique, which an archetypal example of sub-Saharan river basin, where surface water scarcity compounded by substantial climatic variability, uncontrolled urbanization rate, and agricultural expansion are hampering the Pequenos Libombos dam's ability to supply the agricultural, energy, and urban sectors. We adopt an Evolutionary Multi-Objective Direct Policy Search (EMODPS) optimization approach for designing optimal operating policies, whose robustness against social, agricultural, infrastructural, and climatic uncertainties is assessed via robustness analysis. We then implement the generalized likelihood uncertainty estimation (GLUE) and PAWN uncertainty and sensitivity analysis methods for disentangling the main challenges to the sustainability of the operating policies and quantifying their impacts on the urban, agricultural, and energy sectors. Numerical results highlight the importance of a robustness analysis when dealing with uncertain scenarios, with optimal non-robust reservoir operating policies largely being dominated by robust control strategies across all stakeholders. Furthermore, while robust policies are usually vulnerable only to hydrological perturbations and are able to sustain the majority of population growth and agricultural expansion scenarios, non-robust policies are sensitive also to social and agricultural changes and require structural interventions to ensure stable supply.

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.

Often quantities of interest in psychology cannot be observed directly. These unobservable quantities, known as latent variables, tend to be complex, often multidimensional, constructs. In many cases these constructs are categorical, such that individuals belong to mutually exclusive and exhaustive unobservable subgroups. Latent class analysis (LCA) is a statistical approach to modeling a discrete latent variable using multiple, discrete observed variables as indicators. Examples of latent class variables that appear in the psychology literature include temperament type, substance use behavior, teaching style, stages of change in the transtheoretical model, and latent classes of risk. The first section of this chapter provides a conceptual introduction to the concept of a latent class followed by a technical introduction to the mathematical model, including multiple-groups LCA and LCA with covariates. This is followed by a discussion of parameter restrictions, model selection, and goodness-of-fit. The second section demonstrates LCA using the empirical example of depression subtypes in adolescence. Five latent classes were identified based on responses to eight questionnaire items assessing depression symptoms: Non-depressed (characterized by a low probability of reporting all eight depression symptoms), sad, disliked, sad + disliked, and depressed (characterized by a high probability of reporting all eight depression symptoms). The third section presents longitudinal extensions of the model, including repeated-measures LCA and latent transition analysis (LTA). The empirical example is extended to examine change in depression subtypes over time. The final sections describe recent extensions to the latent class model and areas that merit additional research in the future. Keywords: latent class analysis; latent transition analysis; latent variable model; categorical data

ABSTRACTMigration to and from Scotland might be affected by the outcome of the 2014 Scottish referendum on the constitutional future of the United Kingdom. This potential change in migration has not been thoroughly analysed to date. The aim of this paper is thus to present a set of predictions of the possible effects of Scottish independence on internal and international migration. In particular, different sources of uncertainty of future migration flows are examined. The presented forecasts are based on the available historical data on migration flows, as well as on the opinions of a panel of experts on future migration trends. Bayesian statistical inference is used to combine different sources of uncertainty in a coherent manner. The results indicate that there is substantial uncertainty about future migration to and from Scotland, which increases with the forecast horizon. The most uncertain flow is international immigration to Scotland. Emigration from Scotland is more likely than not to increase in the near future, whereas migration between Scotland and the rest of the UK is expected to remain at similar levels to the present, irrespective of the outcome of the 2014 independence referendum. © 2014 The Authors. Population, Space and Place Published by John Wiley & Sons Ltd.

Most simulation studies in factor analysis follow a process of constructing population correlation matrices from the common-factor model and generating sample correlation matrices from the population matrices. In the common-factor model, the population correlation matrix is perfectly fit by the model's containing common and unique factors. However, since no mathematical model accounts exactly for the real-world phenomena that it is intended to represent, the Tucker-Koopman-Linn model (1969) is more realistic for generating correlation matrices than the conventional common-factor model because the former incorporates model error. In this paper, a procedure for generating population and sample correlation matrices with model error by combining the Tucker-Koopman-Linn model and Wijsman's algorithm (1959) is presented. The SAS/IML program for generating correlation matrices is described, and an example is also provided.

Estimates of longitudinal change in the parameters of latent (i.e. unobserved) variables, including means, are affected by non-response on the items or indicators of the latent variable. This study used Monte Carlo simulation and a numeric example to compare four ordinal item non-response methods: non-negative matrix factorization (NNMF), multiple imputation with conditional proportional odds model (POM), full information maximum likelihood (FIML) and complete-case analysis, when estimating the longitudinal change in latent variable means. The mean squared error for the NNMF method was more than 40% lower than for the FIML and POM methods when the latent variable correlations over time were strong, percentage of missing data was 25% or more, and sample size was large. The NNMF method is a promising method to address item non-response. It is relatively efficient when sample size is large, and the percentage of missing data is high but has limitations under other data-analytic conditions.

The pharmacokinetic parameter estimation problem is reexamined within the framework of stochastic dynamic systems. Using this formalism, two sources of uncertainty are incorporated into the parameter estimation procedure: measurement error and process or model error. Consideration is given to linear dynamic models, with both model and measurement error terms modeled as Gaussian random processes. The maximum likelihood estimate of the parameters is obtained by using the Kaiman filter formulation of the model to compute the likelihood function which is then maximized by direct nonlinear optimization. This approach to maximum likelihood estimation, given process or model error as well as output error, is evaluated using several simulated pharmacokinetic parameter estimation problems.

Sustainable environmental management often involves long-term time horizons and multiple conflicting objectives and, by nature, is affected by different sources of uncertainty. Many sources of uncertainty, such as climate change or government policies, cannot be addressed using probabilistic models, and, therefore, they can be seen to contain deep uncertainty. In this setting, the variety of possible future states is represented as a set of scenarios lacking any information about the likelihood of occurring. Integrating deep uncertainty into multiobjective decision support increases complexity, calling for the elaboration of appropriate methods and tools. This paper proposes a novel interactive multi-scenario multiobjective approach to support decision-making and trade-off analysis in sustainable forest landscape planning under multiple sources of uncertainty. It includes new preference simulation models aimed at reducing the decision-maker’s cognitive load and supporting the preference elicitation process. The proposed approach is applied in a case study of long-term forest landscape planning with four sustainability objectives in 12 scenarios and a forestry expert as the decision-maker. The approach is demonstrated to be efficient in exploring trade-offs in different scenarios, helping the expert gain deep insights into the problem, understand the consequences of alternative strategies, and find the most preferred robust strategy.