Relevant Uncertainties Research Articles

Robust Product Line Design by Protecting the Downside While Minding the Upside

Many decisions must be made before relevant uncertainties are revealed; hence robustness approaches to decision making are often considered. There are two major approaches to robustness in the literature: (i) maximizing the value of the worst outcome and (ii) minimizing the maximum ex post regret of the decision. While the first approach seeks the best worst‐case outcome, it may result in substantial opportunity losses relative to the ex post optimal decision; this is particularly critical in new product design decisions as it leaves the leading firm exposed to a late entrant who designs its products after uncertainties are resolved. The second approach seeks to minimize these ex post opportunity losses, but it may expose the decision maker to greater downside risk, that is, lower outcome in the worst case. Most studies have examined one of these approaches in isolation; in contrast, in this study, we explore the trade‐offs between protecting upside regret and downside risk with a focus on a product line design (PLD) problem, which relies greatly on conjoint analysis data. The PLD problem may suffer from significant uncertainty in the partworth utilities which define the attribute‐level consumer preferences on a product for different population segments. Our numerical experiments, based on a real conjoint data set, show that neither robustness approaches dominates the other and hence our proposed approach uses both. We construct a Min‐Value vs. Max‐Relative‐Regret efficient frontier to narrow down the PLD choice and propose a metric to quantify the trade‐offs and finalize the selection.

Wave-packet continuum discretisation for nucleon–nucleon scattering predictions

In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon–nucleon (NN) scattering amplitudes with the wave-packet continuum discretisation method (WPCD). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit to explore the benefits of this inherent parallelism. From a theoretical perspective, the WPCD method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLOopt interaction to demonstrate that WPCD enables efficient computation of NN scattering amplitudes provided one can tolerate an averaged method error of 1–5 mb in the total cross section at scattering energies 0–350 MeV in the laboratory frame of reference. Considering only scattering energies ∼40–350 MeV, we find a smaller method error of ≲ 1–2 mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the WPCD method will be offset by the increased size of the resulting discretisation mesh. In practice, a GPU-implementation is mainly advantageous for matrices that fit in the fast on-chip shared memory. We find that WPCD is a promising method for computationally efficient, statistical analyses of nuclear interactions from effective field theory, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.

Evaluation of Testing Uncertainties for the Impact Resistance of Machine Guards

Abstract Machine guards provide protection against the ejection of parts during operation, such as chips or workpiece fragments. They are considered safe if the impact resistance is at least as high as the resulting projectile energy in the worst case of damage. To protect the machine operator, the impact resistance of machine guards is determined according to ISO standards. The bisection method can be used to determine the impact resistance through impact tests. However, this method is inaccurate for a small number of impact tests and does not indicate uncertainties in the determination. Moreover, the result of testing is validated in different ways depending on the standard utilized for testing. Relevant uncertainties affecting impact testing and a new probabilistic approach for assessing the impact resistance using the Recht and Ipson equation are presented. With multiple impact tests at different initial velocities a Recht and Ipson best-fit curve and a confidence interval for a ballistic limit can be obtained, which is used to determine the impact resistance by defining a velocity reduction coefficient. This method can be applied to any machine guard made of ductile material. This paper validates the Recht and Ipson method by performing impact tests with a standardized 2.5 kg projectile on polycarbonate sheets of different thicknesses. Determination of the ballistic limit showed good agreement with experimental results. With the ballistic limits, the velocity reduction coefficients have been found to determine the impact resistances. Therefore, an alternative method for standardized tests to determine the impact resistance was found.

Equity in medical education: Addressing microaggressions and discrimination on the wards

Purpose Existing frameworks to address instances of microaggressions and discrimination in the clinical environment have largely been developed for faculty and resident physicians, creating a lack of resources for medical students. Methods We implemented a workshop to prepare pre-clinical medical/dental students to recognize and respond to microaggressions. Participants in three cohorts from 2018 to 2020 completed pre- and post-workshop surveys assessing the prevalence of exposure to clinical microaggressions and the workshop’s effect on mitigating commonly perceived barriers to addressing microaggressions. Results Of 461 first-year medical and dental students who participated, 321 (69.6%) provided survey responses. Over 80% of students reported experiencing microaggressions, with women and URM students over-represented. After the workshop, participants reported significant reductions in barriers to addressing microaggressions and discrimination, including recognizing incidents, uncertainty of what to say or do, lack of allies, lack of familiarity with institutional policies, and uncertainty of clinical relevance. The workshop was similarly effective in-person and virtual formats. Conclusions Most medical/dental student respondents reported experiencing microaggressions in the clinical setting, particularly female and URM students. Our workshop mitigated most perceived challenges to responding to microaggressions. Future interventions across institutions should continue to equip students with the tools they need to address and respond to microaggressions.

Modelling approaches for histology-independent cancer drugs to inform NICE appraisals: a systematic review and decision-framework.

The first histology-independent marketing authorisation in Europe was granted in 2019. This was the first time that a cancer treatment was approved based on a common biomarker rather than the location in the body at which the tumour originated. This research aims to explore the implications for National Institute for Health and Care Excellence appraisals. Targeted reviews were undertaken to determine the type of evidence that is likely to be available at the point of marketing authorisation and the analyses required to support National Institute for Health and Care Excellence appraisals. Several challenges were identified concerning the design and conduct of trials for histology-independent products, the greater levels of heterogeneity within the licensed population and the use of surrogate end points. We identified approaches to address these challenges by reviewing key statistical literature that focuses on the design and analysis of histology-independent trials and by undertaking a systematic review to evaluate the use of response end points as surrogate outcomes for survival end points. We developed a decision framework to help to inform approval and research policies for histology-independent products. The framework explored the uncertainties and risks associated with different approval policies, including the role of further data collection, pricing schemes and stratified decision-making. We found that the potential for heterogeneity in treatment effects, across tumour types or other characteristics, is likely to be a central issue for National Institute for Health and Care Excellence appraisals. Bayesian hierarchical methods may serve as a useful vehicle to assess the level of heterogeneity across tumours and to estimate the pooled treatment effects for each tumour, which can inform whether or not the assumption of homogeneity is reasonable. Our review suggests that response end points may not be reliable surrogates for survival end points. However, a surrogate-based modelling approach, which captures all relevant uncertainty, may be preferable to the use of immature survival data. Several additional sources of heterogeneity were identified as presenting potential challenges to National Institute for Health and Care Excellence appraisal, including the cost of testing, baseline risk, quality of life and routine management costs. We concluded that a range of alternative approaches will be required to address different sources of heterogeneity to support National Institute for Health and Care Excellence appraisals. An exemplar case study was developed to illustrate the nature of the assessments that may be required. Adequately designed and analysed basket studies that assess the homogeneity of outcomes and allow borrowing of information across baskets, where appropriate, are recommended. Where there is evidence of heterogeneity in treatment effects and estimates of cost-effectiveness, consideration should be given to optimised recommendations. Routine presentation of the scale of the consequences of heterogeneity and decision uncertainty may provide an important additional approach to the assessments specified in the current National Institute for Health and Care Excellence methods guide. Further exploration of Bayesian hierarchical methods could help to inform decision-makers on whether or not there is sufficient evidence of homogeneity to support pooled analyses. Further research is also required to determine the appropriate basis for apportioning genomic testing costs where there are multiple targets and to address the challenges of uncontrolled Phase II studies, including the role and use of surrogate end points. This project was funded by the National Institute for Health Research (NIHR) Evidence Synthesis programme and will be published in full in Health Technology Assessment; Vol. 25, No. 76. See the NIHR Journals Library website for further project information.

Towards improved USLE-based soil erosion modelling in India: A review of prevalent pitfalls and implementation of exemplar methods

One of the most common approaches to modelling soil erosion worldwide has been the implementation of the original Universal Soil Loss Equation (USLE) and its revised version, the RUSLE. However, despite its widespread use, often there are discrepancies in the methods used to compute it and in the values elicited for the five individual factors that comprise this function. Such pitfalls subsequently skew the final results obtained and often many studies also fail to adequately examine the accuracy of the enumerated soil loss amounts. We examine these aspects with respect to the raft of USLE-based studies undertaken in India over the last few decades, reviewing a total of 100 investigations in this regard. Results reveal that almost all studies had either over- or underestimated at least one of the five factors, thereby possibly misrepresenting the actual soil loss occurring from their examined areas. Even more worryingly, most studies had failed to document their methods succinctly or in sufficient detail to ascertain their efficacies or provide viable templates for replication elsewhere. Our results also show a marked spatiality in the pursuance of such studies, with these being mostly undertaken in the eastern part of the country, even though the proportionate land affected by soil erosion is considerably less in this region. Thus regions where the USLE would be most pertinent for implementation towards land management have seen a lower number of applications. We hope that by avoiding the missteps highlighted in this paper and following the subsequently detailed exemplar methods of conducting such an investigation along with the relevant model accuracy and uncertainty checks, the USLE can be best utilised in these regions and in the rest of the country for soil erosion mitigation. Though focused on India, the methods outlined can also be used to conduct the most accurate possible USLE-based soil erosion modelling elsewhere.

Acoustic and thermal numerical modelling of transcranial ultrasound thermal therapy

Ultrasound has long been recognized as a therapeutic tool with potential to treat disorders throughout the brain. However, the attenuation and distortion of acoustic waves caused by the skull has been a significant challenge to the development and clinical application of transcranial ultrasound therapies. Numerical models, such as the use of finite difference method, can be prohibitively expensive in required computational resources. While some numerical models can be computationally prohibitive, the ray-tracing modelling method used in the CIVA Healthcare simulation platform has been shown to be an efficient and computationally inexpensive method of modelling transcranial focused ultrasound, and can be coupled to Pennes’ bioheat transfer equation to model temperature in biological tissue. The present work quantifies the sensitivity of transcranial ultrasound to clinically relevant uncertainties in the physical properties of the skull (i.e., shear conversion, wave speed), and combines the ray-tracing acoustic model with a numerical thermal model to provide a versatile and unified software platform for use in clinical ultrasound treatment planning. Results are compared with experimentally measured thermal rise from transcranial focused ultrasound using a clinical Insightec ExAblate 650 kHz 1000-element system, and shown to exhibit a high degree of accuracy. [This work is supported by the Focused Ultrasound Foundation.]

UNCERTAINTY ASSOCIATED WITH THE USE OF SOFTWARE SOLUTIONS UTILIZING DICOM RDSR FOR SKIN DOSE ASSESSMENT IN INTERVENTIONAL RADIOLOGY AND CARDIOLOGY.

The purpose of this work is to provide a comprehensive analysis of uncertainties associated with the use of software solutions utilizing DICOM RDSRs for skin dose assessment in the interventional fluoroscopic environment. Three different scenarios have been defined for determining the overall uncertainty, each with a specific assumption on the maximum deviations of factors affecting the calculated dose. Relative expanded uncertainty has been calculated using two approaches: the law of propagation of uncertainty and the propagation of distributions based on the Monte Carlo method. According to the propagation of uncertainty, it is estimated that the lowest possible relative expanded uncertainty of ~13% (at the 95% level of confidence, i.e. with the coverage factor of k=2 assuming normal distribution) could only be achieved if all sources of uncertainties are carefully controlled, whereas maximum relative expanded uncertainty could reach up to 61% if none of the influencing parameters are controlled properly. When the influencing parameters are reasonably well-controlled, realistic relative expanded uncertainty amounts to 28%. Values for the relative expanded uncertainty obtained from the Monte Carlo propagation of distributions concur with the results obtained from the propagation of uncertainty to within 3% in all three considered scenarios, validating the assumption of normality. The overall skin dose relative uncertainty has been found to range from 13 to 61%, emphasizing the importance of adequate analysis and control of all relevant uncertainty sources.

Attribute‐scale selection for hybrid data with test cost constraint: The approach and uncertainty measures

Recently several novel cost-sensitive attribute-scale selection approaches have been proposed based on measurement errors. They are significant because they can simultaneously select attributes and scale combination to minimize the cost consumed in data processing. However, these approaches cannot deal with hybrid data with test cost constraint, and most of them do not consider the scale diversity between different attributes; and these approaches do not touch the uncertainty measurement, all of which are important issues in real applications. To address this situation, in this paper an effective cost-sensitive attribute-scale selection approach is presented based on the rough set theory, and multiple relevant uncertainty measures are developed. The main contributions of the paper are threefold. First, a generalized confidence level vector-based neighborhood rough set model is constructed. It takes into account the scale diversity between different attributes of hybrid data. Then, multiple uncertainty measures are developed. They consider both attributes and scales, thus are more general than existing ones which consider only attributes or only scales. Finally, an efficient heuristic attribute-scale selection algorithm is designed, which can select attributes and their respective scales to minimize the consumed total cost of hybrid data under any rational value of test cost upper bound. Detailed experiments thoroughly confirm the effectiveness of the proposed cost-sensitive attribute-scale selection approach. The experiments also reveal the influences of different test cost upper bounds to the attribute-scale selection and some related quantities including the uncertainty measures. This study would enrich the rough set theory to some extent, and provide an effective support for some test cost-constrained decision makings.

Using cross‐impact analysis for probabilistic risk assessment

AbstractCross‐impact analysis is widely employed to inform management and policy decisions based on the formulation of scenarios, defined as combinations of outcomes of relevant uncertainty factors. In this paper, we argue that the use of nonprobabilistic variants of cross‐impact analysis is problematic in the context of risk assessment where the usual aim is to produce conservative risk estimates which may exceed but are not smaller than the actual risk level. Then, building on the characterization of probabilistic dependencies, we develop an approach to probabilistic cross‐impact analysis which (i) admits several kinds of probabilistic statements about the outcomes of relevant uncertainty factors and their dependencies; (ii) maps such statements into constraints on the joint probability distribution over all possible scenarios; (iii) provides support for preserving the consistency of elicited statements; and (iv) uses mathematical optimization to compute lower and upper bounds on the overall risk level. This approach—which is illustrated with an example from the context of nuclear waste repositories—is useful in that it retains the informativeness of cross‐impact statements while ensuring that these statements are interpreted within the coherent framework of probability theory.

Flight Mechanics Feasibility Assessment for Co-Delivery of Direct-Entry Probe and Aerocapture Orbiter

The co-delivery of a direct-entry probe and an aerocapture orbiter from a single atmospheric entry state is a novel way to include ride-along probes or orbiters on interplanetary missions. This is made possible through combining two technologies: low-cost small satellites and aerocapture. This study investigates the feasibility of this co-delivery method from a flight-mechanics perspective. The availability of direct-entry and aerocapture trajectories from a single entry flight-path angle is assessed for a large range of feasible ballistic coefficients at Earth, Mars, Venus, Titan, and Neptune. Apoapsis altitude, peak heat flux, total heat load, and peak g-load are also quantified across this trade space. A representative scenario implementing closed-loop guidance is presented for a proof of concept, and the trajectory dispersions due to relevant uncertainties are quantified in a Monte Carlo analysis. Passive ballistic impactor or penetrator probes as a secondary mission with a primary lift-modulated aerocapture orbiter is identified as the most promising configuration.

Procedure for the Accurate Modelling of Ring Induction Motors

This paper proposes a procedure for the accurate modelling of the ring induction motors (RIMs), based on the Monte Carlo (MC) method and the relations presented in the relevant metrology guidelines. Modelling was carried out based on the measured data for the torque-slip characteristic (TSC) and using the equivalent circuit for the RIM. The parameters included an extended Kloss equation (EKE) and the associated uncertainties were determined using the MC method. The polynomial procedure was applied as a numerical tool to complement the MC method to determine the power losses in the stator iron and the relevant uncertainty. This is in line with international standards for the theory of uncertainty application in the field of engineering. The novelty of this paper refers to the accurate modelling of the RIMs obtained by determining the corresponding uncertainties. The procedure presented in this paper was developed based on the assumption that the parameters of the equivalent circuit are independent of the temperature, influence of core saturation, and the phenomenon of current displacement. Our procedure can be successfully used for both the theoretical calculations related to the modelling of the RIMs, and in practical applications involving detailed measurements and the corresponding uncertainties. The use of the MC method allowed for significant improvement in the modelling results, in terms of both the TSC and EKE.

Information search in times of market uncertainty: an examination of aggregate and disaggregate uncertainty

PurposeThis study explores the association between individual investor information demand and two measures of market uncertainty – aggregate market uncertainty and disaggregate industry-specific market uncertainty. It extends the literature by being the first to empirically examine investor information demand and disaggregate market uncertainty.Design/methodology/approachThis paper constructs a measure of information search by using the Google Search Volume Index and computes measures of aggregate and disaggregate market uncertainty using institutional investors' trading data from Ancerno Ltd. The relation between market uncertainty, as measured by trading disagreements among institutional investors, and information search is analyzed using an OLS (Ordinary Least Squares) regression model.FindingsThis paper finds that individual investor information demand is significantly and positively correlated with aggregate market uncertainty but not associated with disaggregated industry uncertainty. The findings suggest that individual investors may not fully incorporate all relevant uncertainty information and that ambiguity-related market pricing anomalies may be more associated with disaggregate market uncertainty.Research limitations/implicationsThis study presents an examination of aggregate and disaggregate measures of market uncertainty and individual investor demand for information, shedding light on the efficiency of the market in incorporating information. A limitation of our study is that our data for market uncertainty is based on investor trading disagreement from Ancerno, Ltd. which is only available till 2011. However, we believe the implications are generalizable to the current time period.Practical implicationsThis study provides the first concurrent empirical assessment of investor information search and aggregate and disaggregate market uncertainty. Prior research has separately examined information demand in these two types of market uncertainty. Thus, this study provides information to investors regarding the importance of assessing disaggregate component measures of the market.Originality/valueThis paper is the first to empirically examine investor information search and disaggregate market uncertainty. It also employs a unique data set and method to determine disaggregate, and aggregate, market uncertainty.

Integrating macroseismic intensity distributions with a probabilistic approach: an application in Italy

Abstract. The geographic distribution of earthquake effects quantified in terms of macroseismic intensities, the so-called macroseismic field, provides basic information for several applications including source characterization of pre-instrumental earthquakes and risk analysis. Macroseismic fields of past earthquakes as inferred from historical documentation may present spatial gaps, due to the incompleteness of the available information. We present a probabilistic approach aimed at integrating incomplete intensity distributions by considering the Bayesian combination of estimates provided by intensity prediction equations (IPEs) and data documented at nearby localities, accounting for the relevant uncertainties and the discrete and ordinal nature of intensity values. The performance of the proposed methodology is tested at 28 Italian localities with long and rich seismic histories and for two well-known strong earthquakes (i.e., 1980 southern Italy and 2009 central Italy events). A possible application of the approach is also illustrated relative to a 16th-century earthquake in the northern Apennines.

Divergent, plausible, and relevant climate futures for near- and long-term resource planning

Scenario planning has emerged as a widely used planning process for resource management in situations of consequential, irreducible uncertainty. Because it explicitly incorporates uncertainty, scenario planning is regularly employed in climate change adaptation. An early and essential step in developing scenarios is identifying “climate futures”—descriptions of the physical attributes of plausible future climates that could occur at a specific place and time. Divergent climate futures that describe the broadest possible range of plausible conditions support information needs of decision makers, including understanding the spectrum of potential resource responses to climate change, developing strategies robust to that range, avoiding highly consequential surprises, and averting maladaptation. Here, we discuss three approaches for generating climate futures: a Representative Concentration Pathway (RCP)-ensemble, a quadrant-average, and an individual-projection approach. All are designed to capture relevant uncertainty, but they differ in utility for different applications, complexity, and effort required to implement. Using an application from Big Bend National Park as an example of numerous similar efforts to develop climate futures for National Park Service applications over the past decade, we compare these approaches, focusing on their ability to capture among-projection divergence during early-, mid-, and late-twenty-first century periods to align with near-, mid-, and long-term planning efforts. The quadrant-average approach and especially the individual-projection approach captured a broader range of plausible future conditions than the RCP-ensemble approach, particularly in the near term. Therefore, the individual-projection approach supports decision makers seeking to understand the broadest potential characterization of future conditions. We discuss tradeoffs associated with different climate future approaches and highlight suitable applications.

Uncertainty, Possibility, and Causal Power in QCA

Uncertainty undermines causal claims; however, the nature of causal claims decides what counts as relevant uncertainty. Empirical robustness is imperative in regularity theories of causality. Regularity theory features strongly in QCA, making its case sensitivity a weakness. Following qualitative comparative analysis (QCA) founder Charles Ragin’s emphasis on ontological realism, this article suggests causality as a power and thus breaks with the ontological determinism of regularity theories. Exercising causal powers makes it possible for human agents to achieve an outcome but does not determine that they will. The article explains how QCA’s truth table analysis “models” possibilistic uncertainty and how crisp sets do this better than fuzzy sets. Causal power is at the heart of critical realist philosophy of science. Like Ragin, critical realism suggests empirical analysis as merely describing underlying causal relationships. Empirical statements must be substantively interpreted into causal claims. The article is critical of “empiricist” QCA that infers causality from the robustness of set relationships.

The current state of uncertainty reporting in ecosystem studies: a systematic evaluation of peer‐reviewed literature

AbstractTransparency in reporting is essential to scientific progress. No report should be considered complete without a full account of uncertainties, including those due to natural variation and measurement and model error and those incurred by handling problematic data, such as outliers. We randomly selected 132 papers published in 2019 from a list of 100 scientific journals to characterize the current state of uncertainty reporting in ecosystem studies. Each paper was evaluated for the extent to which it reported measures of uncertainty in any of four topic areas common to ecosystem studies: vegetation, soils, precipitation, and surface water. We found that most papers reported a minority of the uncertainty sources we deemed relevant. Papers on surface water reported the highest fraction of uncertainty sources (averaging 47% ± 5%), followed by soils (45% ± 4%), vegetation (32% ± 4%), and precipitation (21% ± 8%). A greater fraction of relevant uncertainty sources were reported when the topics were the primary focus of the paper (44% ± 3%) than when they were not (32% ± 4%). Sampling error—the uncertainty in replicate measurements—was the source most commonly reported in studies of vegetation (84%), soil mass (56%), and surface water (76% of papers). The source of measurement error most often reported was chemical analysis, with 41% of papers on surface water and 75% of papers on precipitation reporting this source, if applicable. In contrast, only 1 of 12 papers reporting chemistry of vegetation provided information on analytical uncertainty. Fewer papers reported what methods were used for handling missing or unusable data and observations below detection limits, but it was difficult to judge whether these sources were relevant if they were not mentioned. Finally, we found that a minority of the papers made all (21%) or some (an additional 21%) of their data available in online repositories, after correcting for a failure rate of 13% of the links. Clearly, there is room for improving the completeness and transparency of scientific reporting in ecosystem studies.

Incorporating data‐based estimates of temporal variation into projections for newly monitored populations

AbstractThe importance of accounting for temporal variation in vital rates when modelling population dynamics is well recognized. However, long‐term (usually >5 years) datasets are needed to estimate this variation. Consequently, models for newly monitored populations typically assume no temporal variation or use default values provided in software programmes, both of which can give misleading inferences about population dynamics. The goal of this study is to improve estimation of dynamics in the initial years of conservation programmes by incorporating data‐based estimates of temporal variation from other populations with longer‐term data available. We show how data‐derived priors can be generated using estimates of temporal variation in vital rates from other populations, providing information about expected variation until sufficient population‐specific data are available. We specifically evaluated whether data‐derived priors improved our ability to estimate temporal variation for a reintroduced population monitored for 3 years postrelease. We first predicted population growth and probability of extinction assuming no temporal variation in vital rates, then compared projections to those obtained when temporal variation was estimated with uniform priors or with the data‐derived priors. Both types of priors were constrained to plausible ranges, and we also assessed sensitivity of model outputs to widening those ranges. Median projected population size was similar under all three models, but extinction probability was higher with inclusion of temporal variability, reiterating the importance of incorporating this source of uncertainty. Projections with temporal variation were similar irrespective of whether data‐derived priors or uniform priors were used. However, the data‐derived priors generated more precise estimates of annual variation that were less sensitive to relaxation of prior constraints. The approach we present can facilitate management decisions at the outset of conservation programmes when risk assessments that account for all relevant uncertainties can be crucial for determining optimal management strategies.

Dynamic Bayesian Networks for Evaluation of Granger Causal Relationships in Climate Reanalyses

AbstractWe apply a Bayesian structure learning approach to study interactions between global climate modes, so illustrating its use as a framework for developing process‐based diagnostics with which to evaluate climate models. Homogeneous dynamic Bayesian network models are constructed for time series of empirical indices diagnosing the activity of major tropical, Northern and Southern Hemisphere modes of climate variability in the NCEP/NCAR and JRA‐55 reanalyses. The resulting probabilistic graphical models are comparable to Granger causal analyses that have recently been advocated. Reversible jump Markov Chain Monte Carlo is employed to provide a quantification of the uncertainty associated with the selection of a single network structure. In general, the models fitted from the NCEP/NCAR reanalysis and the JRA‐55 reanalysis are found to exhibit broad agreement in terms of associations for which there is high posterior confidence. Differences between the two reanalyses are found that involve modes for which known biases are present or that may be attributed to seasonal effects, as well as for features that, while present in point estimates, have low overall posterior mass. We argue that the ability to incorporate such measures of confidence in structural features is a significant advantage provided by the Bayesian approach, as point estimates alone may understate the relevant uncertainties and yield less informative measures of differences between products when network‐based approaches are used for model evaluation.

A Multistage Dynamic Emergency Decision-Making Method considering the Satisfaction under Uncertainty Information

Emergency decision-making (EDM) is of paramount importance, especially when the emergency occurs. The evolution nature of the emergency, such as multistage, uncertainty, dynamic, and information updating, has been playing a key role in the dynamic emergency decision-making process. However, most existing studies ignored the aforementioned nature. Our approach accounts for the dynamics inherent to a real emergency decision-making process and presents a multistage dynamic emergency decision-making (MSDEDM) procedure of a dynamic programming model based on decision-makers’ psychological reference satisfactory degree. Firstly, interval-valued trapezoidal intuitionistic fuzzy numbers (IVTrIFNs) are used to depict the relevant fuzziness and uncertainty of information. Secondly, by considering the dynamic evolution process of emergency and the decision-makers’ psychological reference expectation effect, the principle of MSDEDM approach is presented. Based on the analysis, the dynamic model on the new psychological reference satisfactory parameter formula is presented to obtain the optimal satisfaction and weight of each stage. Then, the value utility function based on the DMs’ risk attitude is proposed to obtain the comprehensive value of each emergency alternative for each stage and achieve the ranking results of each stage. Furthermore, a case study involving the transportation emergency decision-making problem demonstrates that the proposed method can achieve selection of the optimal alternatives for each stage, as well as adjustment of the alternatives for neighbouring stages. Finally, the comparative analysis and sensitivity analysis for the results are used to further verify the feasibility and practicability of the proposed method.