Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods

In this work, we introduce a generalized rationale for local sensitivity analysis (SA) methods that allows to solve the problems connected with input constraints. Several models in use in the risk analysis field are characterized by the presence of deterministic relationships among the input parameters. However, SA issues related to the presence of constraints have been mainly dealt with in a heuristic fashion. We start with a systematic analysis of the effects of constraints. The findings can be summarized in the following three effects. (i) Constraints make it impossible to vary one parameter while keeping all others fixed. (ii) The model output becomes insensitive to a parameter if a constraint is solved for that parameter. (iii) Sensitivity analysis results depend on which parameter is selected as dependent. The explanation of these effects is found by proposing a result that leads to a natural extension of the local SA rationale introduced in Helton (1993) . We then extend the definitions of the Birnbaum, criticality, and the differential importance measures to the constrained case. In addition, a procedure is introduced that allows to obtain constrained sensitivity results at the same cost as in the absence of constraints. The application to a nonbinary event tree concludes the article, providing a numerical illustration of the above findings.     

Care earnings in the United States and 24 European countries: The role of social policy and labour market institutions

Care occupations are gendered and remain relatively poorly paid, particularly in the United States. Prior research on the ‘care penalty’ primarily points to individual, relational, and market-valuation factors in explaining the relative earnings of care workers. This study integrates these explanations with a comparative institutional perspective. Using higher-quality data and methods than previous comparative research in the field—that is, harmonized micro-data from the Current Population Survey and EU-SILC from 2005 to 2016, country and year fixed effects models, and a counterfactual analysis—we find that national variance in labour market and welfare state institutions explains most of the difference in the relative earnings of reproductive care workers between the United States and European countries. Higher rates of collective bargaining coverage, stronger employment protection and welfare state spending contribute to higher relative earnings for reproductive care occupations, and lower relative earnings for high-status nurturant care occupations. Differences in the relative earnings of care workers appear to be mostly a construct of social policy and labour market institutions rather than individual, relational, and market-valuation factors.     

Unemployment Protection and Family Policy at the Turn of the 21st Century: A Dynamic Approach to Welfare Regime Theory

This article contributes to the welfare state regime literature from a substantive and methodological perspective. At a very abstract level we confirm the relevance of the welfare state regime theory and stability for the period from 1971 to the end of the 1990s. However, by analyzing family policy and unemployment protection, we observe a dual transformation of the welfare state, consisting of a trend towards a ‘socialization’ of family policies and a retrenchment in unemployment insurance benefits. Our Multiple Correspondence Analysis (MCA) of the two policy domains captures the multi‐dimensionality of the decommodification and defamilialization concepts and visualizes welfare state developments over time in a Cartesian space. This dynamic analysis provides us with a nuanced understanding of welfare state regime stability and change.     

The Stock Market Reaction to Investment Decisions: Evidence from Italy

Based on a study of new investment announcements from 1989 to 1995 by Italian firms listed on the Milan Stock Exchange, we find a positive stock price reaction to new investment decisions. The stock price reaction is larger for joint venture announcements. The market response is also larger for non-state owned companies and when the announcement is released in a period of rising stock prices. The announced investment has no impact on the non-voting shares but increases the voting shares' market price through a significant revaluation of their vote-segment. We find some evidence that new investments lead to management's private benefits rather than towards firm value. This is consistent with the typical Italian corporate governance structure, where a majority shareholder safely controls a listed company while having only a fractional claim on the firm's cash flows.     

A Methodology for Determining Interactions in Probabilistic Safety Assessment Models by Varying One Parameter at a Time

In risk analysis problems, the decision‐making process is supported by the utilization of quantitative models. Assessing the relevance of interactions is an essential information in the interpretation of model results. By such knowledge, analysts and decisionmakers are able to understand whether risk is apportioned by individual factor contributions or by their joint action. However, models are oftentimes large, requiring a high number of input parameters, and complex, with individual model runs being time consuming. Computational complexity leads analysts to utilize one‐parameter‐at‐a‐time sensitivity methods, which prevent one from assessing interactions. In this work, we illustrate a methodology to quantify interactions in probabilistic safety assessment (PSA) models by varying one parameter at a time. The method is based on a property of the functional ANOVA decomposition of a finite change that allows to exactly determine the relevance of factors when considered individually or together with their interactions with all other factors. A set of test cases illustrates the technique. We apply the methodology to the analysis of the core damage frequency of the large loss of coolant accident of a nuclear reactor. Numerical results reveal the nonadditive model structure, allow to quantify the relevance of interactions, and to identify the direction of change (increase or decrease in risk) implied by individual factor variations and by their cooperation.     

Epistemic Uncertainty in the Ranking and Categorization of Probabilistic Safety Assessment Model Elements: Issues and Findings

In this work, we study the effect of epistemic uncertainty in the ranking and categorization of elements of probabilistic safety assessment (PSA) models. We show that, while in a deterministic setting a PSA element belongs to a given category univocally, in the presence of epistemic uncertainty, a PSA element belongs to a given category only with a certain probability. We propose an approach to estimate these probabilities, showing that their knowledge allows to appreciate " the sensitivity of component categorizations to uncertainties in the parameter values " (U.S. NRC Regulatory Guide 1.174). We investigate the meaning and utilization of an assignment method based on the expected value of importance measures. We discuss the problem of evaluating changes in quality assurance, maintenance activities prioritization, etc. in the presence of epistemic uncertainty. We show that the inclusion of epistemic uncertainly in the evaluation makes it necessary to evaluate changes through their effect on PSA model parameters. We propose a categorization of parameters based on the Fussell-Vesely and differential importance (DIM) measures. In addition, issues in the calculation of the expected value of the joint importance measure are present when evaluating changes affecting groups of components. We illustrate that the problem can be solved using DIM. A numerical application to a case study concludes the work.     

Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches

Uncertainty importance measures are quantitative tools aiming at identifying the contribution of uncertain inputs to output uncertainty. Their application ranges from food safety (Frey & Patil (2002)) to hurricane losses (Iman et al. (2005a, 2005b)). Results and indications an analyst derives depend on the method selected for the study. In this work, we investigate the assumptions at the basis of various indicator families to discuss the information they convey to the analyst/decisionmaker. We start with nonparametric techniques, and then present variance-based methods. By means of an example we show that output variance does not always reflect a decisionmaker state of knowledge of the inputs. We then examine the use of moment-independent approaches to global sensitivity analysis, i.e., techniques that look at the entire output distribution without a specific reference to its moments. Numerical results demonstrate that both moment-independent and variance-based indicators agree in identifying noninfluential parameters. However, differences in the ranking of the most relevant factors show that inputs that influence variance the most are not necessarily the ones that influence the output uncertainty distribution the most.     

A Common Rationale for Global Sensitivity Measures and Their Estimation

Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double‐loop form. Recently, a more efficient single‐loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single‐loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.