Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

Networks of Information Exchange Under Uncertainty: The Case of Unconventional Gas Development in the United Kingdom

Modern policy-making is increasingly influenced by different types of uncertainty. Political actors are supposed to behave differently under the context of uncertainty then in “usual” decision-making processes. Actors exchange information in order to convince other actors and decision-makers, to coordinate their lobbying activities and form coalitions, and to get information and learn on the substantive issue. The literature suggests that preference similarity, social trust, perceived power and functional interdependence are particularly important drivers of information exchange. We assume that social trust as well as being connected to scientific actors is more important under uncertainty than in a setting with less uncertainty. To investigate information exchange under uncertainty analyze the case of unconventional shale gas development in the UK from 2008 till 2014. Our study will rely on statistical analyses of survey data on a diverse set of actors dealing with shale gas development and regulation in the UK.

Policy Instrument Selection under Uncertainty: The Case of Micropollution Regulation

The paper addresses the question of which factors drive the formation of policy preferences when there are remaining uncertainties about the causes and effects of the problem at stake. To answer this question we examine policy preferences reducing aquatic micropollutants, a specific case of water protection policy and different actor groups (e.g. state, science, target groups). Here, we contrast two types of policy preferences: a) preventive or source-directed policies, which mitigate pollution in order to avoid contact with water; and b) reactive or end-of-pipe policies, which filter water already contaminated by pollutants. In a second step, we analyze the drivers for actors’ policy preferences by focusing on three sets of explanations, i.e. participation, affectedness and international collaborations. The analysis of our survey data, qualitative interviews and regression analysis of the Swiss political elite show that participation in the policy-making process leads to knowledge exchange and reduces uncertainties about the policy problem, which promotes preferences for preventive policies. Likewise, actors who are affected by the consequences of micropollutants, such as consumer or environmental associations, opt for anticipatory policies. Interestingly, we find that uncertainties about the effectiveness of preventive policies can promote preferences for end-of-pipe policies. While preventive measures often rely on (uncertain) behavioral changes of target groups, reactive policies are more reliable when it comes to fulfilling defined policy goals. Finally, we find that in a transboundary water management context, actors with international collaborations prefer policies that produce immediate and reliable outcomes.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Collaboration patterns, external shocks and uncertainty: Swiss nuclear energy politics before and after Fukushima

Energy shocks like the Fukushima accident can have important political consequences. This article examines their impact on collaboration patterns between collective actors in policy processes. It argues that external shocks create both behavioral uncertainty, meaning that actors do not know about other actors' preferences, and policy uncertainty on the choice and consequences of policy instruments. The context of uncertainty interacts with classical drivers of actor collaboration in policy processes. The analysis is based on a dataset comprising interview and survey data on political actors in two subsequent policy processes in Switzerland and Exponential Random Graph Models for network data. Results first show that under uncertainty, collaboration of actors in policy processes is less based on similar preferences than in stable contexts, but trust and knowledge of other actors are more important. Second, under uncertainty, scientific actors are not preferred collaboration partners.

The Value of Waiting: Foreign Direct Investment with Uncertainty and Imperfect Local Knowledge

This paper examines the role of uncertainty and imperfect local knowledge in foreign direct investment. The main idea comes from the literature on investment under uncertainty, such as Pindyck (1991) and Dixit and Pindyck (1994). We empirically test .the value of waiting. with a dataset on foreign direct investment (FDI). Many factors (e.g., political and economic regulations) as well as uncertainty and the risks due to imperfect local knowledge, determine the attractiveness of FDI. The uncertainty and irreversibility of FDI links the time interval between permission and actual execution of such FDI with explanatory variables, including information on foreign (home) countries and domestic industries. Common factors, such as regulatory change and external shocks, may affect the uncertainty when foreign investors make irreversible FDI decisions. We derive testable hypotheses from models of investment under uncertainty to determine those possible factors that induce delays in FDI, using Korean data over 1962 to 2001.

Uncertainty analysis of cost effectiveness in a tailored intervention to promote screening for colorectal cancer

Background. Screening for colorectal cancer (CRC) is considered cost effective but screening compliance in the US remains low. There have been very few studies on economic analyses of screening promotion strategies for colorectal cancer. The main aim of the current study is to conduct a cost effectiveness analysis (CEA) and examine the uncertainty involved in the results of the CEA of a tailored intervention to promote screening for CRC among patients of a multispeciality clinic in Houston, TX. ^ Methods. The two intervention arms received a PC based tailored program and web based educational information to promote CRC screening. The incremental cost of implementing a tailored PC based program was compared to the website based education and the status quo of no intervention for each unit of effect after 12 months of delivering the intervention. Uncertainty analysis in the point estimates of cost and effect was conducted using nonparametric bootstrapping. ^ Results. The cost of implementing a web based educational intervention was $36.00 per person and the cost of the tailored PC based interactive intervention was $43.00 per person. The additional cost per person screened for the web-based strategy was $2374 and the effect of the tailored intervention was negative. ^

Theory of uncertainty in illness in patients with cancer of unknown primary origin: Structure providers as antecedents of uncertainty in a population of cancer patients with an unknown primary diagnosis

Uncertainty has been found to be a major component of the cancer experience and can dramatically affect psychosocial adaptation and outcomes of a patient's disease state (McCormick, 2002). Patients with a diagnosis of Carcinoma of Unknown Primary (CUP) may experience higher levels of uncertainty due to the unpredictability of current and future symptoms, limited treatment options and an undetermined life expectancy. To date, only one study has touched upon uncertainty and its' effects on those with CUP but no information exists concerning the effects of uncertainty regarding diagnosis and treatment on the distress level and psychosocial adjustment of this population (Parker & Lenzi, 2003). ^ Mishel's Uncertainty in Illness Theory (1984) proposes that uncertainty is preceded by three variables, one of which being Structure Providers. Structure Providers include credible authority, the degree of trust and confidence the patient has with their doctor, education and social support. It was the goal of this study to examine the relationship between uncertainty and Structure Providers to support the following hypotheses: (1) There will be a negative association between credible authority and uncertainty, (2) There will be a negative association between education level and uncertainty, and (3) There will be a negative association between social support and uncertainty. ^ This cross-sectional analysis utilized data from 219 patients following their initial consultation with their oncologist. Data included the Mishel Uncertainty in Illness Scale (MUIS) which was used to determine patients' uncertainty levels, the Medical Outcomes Study-Social Support Scale (MOSS-SSS) to assess patients, levels of social support, the Patient Satisfaction Questionnaire (PSQ-18) and the Cancer Diagnostic Interview Scale (CDIS) to measure credible authority and general demographic information to assess age, education, marital status and ethnicity. ^ In this study we found that uncertainty levels were generally higher in this sample as compared to other types of cancer populations. And while our results seemed to support most of our hypothesis, we were only able to show significant associations between two. The analyses indicated that credible authority measured by both the CDIS and the PSQ was a significant predictor of uncertainty as was social support measured by the MOSS-SS. Education has shown to have an inconsistent pattern of effect in relation to uncertainty and in the current study there was not enough data to significantly support our hypothesis. ^ The results of this study generally support Mishel's Theory of Uncertainty in Illness and highlight the importance of taking into consideration patients, psychosocial factors as well as employing proper communication practices between physicians and their patients.^

Understanding and Characterizing Shared Decision-Making and Behavioral Intent in Medical Uncertainty

Applying Theoretical Constructs to Address Medical Uncertainty Situations involving medical reasoning usually include some level of medical uncertainty. Despite the identification of shared decision-making (SDM) as an effective technique, it has been observed that the likelihood of physicians and patients engaging in shared decision making is lower in those situations where it is most needed; specifically in circumstances of medical uncertainty. Having identified shared decision making as an effective, yet often a neglected approach to resolving a lack of information exchange in situations involving medical uncertainty, the next step is to determine the way(s) in which SDM can be integrated and the supplemental processes that may facilitate its integration. SDM involves unique types of communication and relationships between patients and physicians. Therefore, it is necessary to further understand and incorporate human behavioral elements - in particular, behavioral intent - in order to successfully identify and realize the potential benefits of SDM. This paper discusses the background and potential interaction between the theories of shared decision-making, medical uncertainty, and behavioral intent. Identifying Shared Decision-Making Elements in Medical Encounters Dealing with Uncertainty A recent summary of the state of medical knowledge in the U.S. reported that nearly half (47%) of all treatments were of unknown effectiveness, and an additional 7% involved an uncertain tradeoff between benefits and harms. Shared decision-making (SDM) was identified as an effective technique for managing uncertainty when two or more parties were involved. In order to understand which of the elements of SDM are used most frequently and effectively, it is necessary to identify these key elements, and understand how these elements related to each other and the SDM process. The elements identified through the course of the present research were selected from basic principles of the SDM model and the “Data, Information, Knowledge, Wisdom” (DIKW) Hierarchy. The goal of this ethnographic research was to identify which common elements of shared decision-making patients are most often observed applying in the medical encounter. The results of the present study facilitated the understanding of which elements patients were more likely to exhibit during a primary care medical encounter, as well as determining variables of interest leading to more successful shared decision-making practices between patients and their physicians. Understanding Behavioral Intent to Participate in Shared Decision-Making in Medically Uncertain Situations Objective: This article describes the process undertaken to identify and validate behavioral and normative beliefs and behavioral intent of men between the ages of 45-70 with regard to participating in shared decision-making in medically uncertain situations. This article also discusses the preliminary results of the aforementioned processes and explores potential future uses of this information which may facilitate greater understanding, efficiency and effectiveness of doctor-patient consultations.Design: Qualitative Study using deductive content analysisSetting: Individual semi-structure patient interviews were conducted until data saturation was reached. Researchers read the transcripts and developed a list of codes.Subjects: 25 subjects drawn from the Philadelphia community.Measurements: Qualitative indicators were developed to measure respondents’ experiences and beliefs related to behavioral intent to participate in shared decision-making during medical uncertainty. Subjects were also asked to complete the Krantz Health Opinion Survey as a method of triangulation.Results: Several factors were repeatedly described by respondents as being essential to participate in shared decision-making in medical uncertainty. These factors included past experience with medical uncertainty, an individual’s personality, and the relationship between the patient and his physician.Conclusions: The findings of this study led to the development of a category framework that helped understand an individual’s needs and motivational factors in their intent to participate in shared decision-making. The three main categories include 1) an individual’s representation of medically uncertainty, 2) how the individual copes with medical uncertainty, and 3) the individual’s behavioral intent to seek information and participate in shared decision-making during times of medically uncertain situations.

Global LAI uncertainty and relative uncertainty datasets derived from a Triple Collocation Error Model (TCEM)

Uncertainty information for global leaf area index (LAI) products is important for global modeling studies but usually difficult to systematically obtain at a global scale. Here, we present a new method that cross-validates existing global LAI products and produces consistent uncertainty information. The method is based on a triple collocation error model (TCEM) that assumes errors among LAI products are not correlated. Global monthly absolute and relative uncertainties, in 0.05° spatial resolutions, were generated for MODIS, CYCLOPES, and GLOBCARBON LAI products, with reasonable agreement in terms of spatial patterns and biome types. CYCLOPES shows the lowest absolute and relative uncertainties, followed by GLOBCARBON and MODIS. Grasses, crops, shrubs, and savannas usually have lower uncertainties than forests in association with the relatively larger forest LAI. With their densely vegetated canopies, tropical regions exhibit the highest absolute uncertainties but the lowest relative uncertainties, the latter of which tend to increase with higher latitudes. The estimated uncertainties of CYCLOPES generally meet the quality requirements (± 0.5) proposed by the Global Climate Observing System (GCOS), whereas for MODIS and GLOBCARBON only non-forest biome types have met the requirement. Nevertheless, none of the products seems to be within a relative uncertainty requirements of 20%. Further independent validation and comparative studies are expected to provide a fair assessment of uncertainties derived from TCEM. Overall, the proposed TCEM is straightforward and could be automated for the systematic processing of real time remote sensing observations to provide theoretical uncertainty information for a wider range of land products.