Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.

Paternal inheritance of growth in fish pursuing alternative reproductive tactics

In species with indeterminate growth, age-related size variation of reproductive competitors within each sex is often high. This selects for divergence in reproductive tactics of same-sex competitors, particularly in males. Where alternative tactics are fixed for life, the causality of tactic choice is often unclear. In the African cichlid Lamprologus callipterus, large nest males collect and present empty snail shells to females that use these shells for egg deposition and brood care. Small dwarf males attempt to fertilize eggs by entering shells in which females are spawning. The bourgeois nest males exceed parasitic dwarf males in size by nearly two orders of magnitude, which is likely to result from greatly diverging growth patterns. Here, we ask whether growth patterns are heritable in this species, or whether and to which extent they are determined by environmental factors. Standardized breeding experiments using unrelated offspring and maternal half-sibs revealed highly divergent growth patterns of male young sired by nest or dwarf males, whereas the growth of female offspring of both male types did not differ. As expected, food had a significant modifying effect on growth, but neither the quantity of breeding substrate in the environment nor ambient temperature affected growth. None of the environmental factors tested influenced the choice of male life histories. We conclude that in L. callipterus growth rates of bourgeois and parasitic males are paternally inherited, and that male and female growth is phenotypically plastic to only a small degree.

Quantifying uncertainty in cost effectiveness analyses

This study compared four alternative approaches (Taylor, Fieller, percentile bootstrap, and bias-corrected bootstrap methods) to estimating confidence intervals (CIs) around cost-effectiveness (CE) ratio. The study consisted of two components: (1) Monte Carlo simulation was conducted to identify characteristics of hypothetical cost-effectiveness data sets which might lead one CI estimation technique to outperform another. These results were matched to the characteristics of an (2) extant data set derived from the National AIDS Demonstration Research (NADR) project. The methods were used to calculate (CIs) for data set. These results were then compared. The main performance criterion in the simulation study was the percentage of times the estimated (CIs) contained the “true” CE. A secondary criterion was the average width of the confidence intervals. For the bootstrap methods, bias was estimated. ^ Simulation results for Taylor and Fieller methods indicated that the CIs estimated using the Taylor series method contained the true CE more often than did those obtained using the Fieller method, but the opposite was true when the correlation was positive and the CV of effectiveness was high for each value of CV of costs. Similarly, the CIs obtained by applying the Taylor series method to the NADR data set were wider than those obtained using the Fieller method for positive correlation values and for values for which the CV of effectiveness were not equal to 30% for each value of the CV of costs. ^ The general trend for the bootstrap methods was that the percentage of times the true CE ratio was contained in CIs was higher for the percentile method for higher values of the CV of effectiveness, given the correlation between average costs and effects and the CV of effectiveness. The results for the data set indicated that the bias corrected CIs were wider than the percentile method CIs. This result was in accordance with the prediction derived from the simulation experiment. ^ Generally, the bootstrap methods are more favorable for parameter specifications investigated in this study. However, the Taylor method is preferred for low CV of effect, and the percentile method is more favorable for higher CV of effect. ^

AN EPIDEMIOLOGIC CASE-CONTROL ANALYSIS OF CHILDHOOD INTRACRANIAL AND SPINAL CORD TUMORS IN RELATION TO PATERNAL OCCUPATION AT BIRTH (BRAIN, CANCER)

Epidemiologic case-control studies of small groups of childhood nervous system tumor patients have suggested that parental employment in occupations with exposure to hydrocarbons is a risk factor for disease. The main focus of this case-control study was to assess the paternal occupation at the time of birth of offspring who later developed childhood intracranial and spinal tumors. All children under 15 years of age dying of such tumors in Texas, during the period 1964-1980, were selected as cases. Disease and demographic data were abstracted from death certificates. The birth certificate for each child of the final group of 499 cases was located and parental occupation information, as well as demographic and obstetric data, were collected. The comparison group consisted of a random sample from all Texas live births with the same birth year, race and sex distribution as the cases.^ The paternal occupations were categorized into broad classifications of those involving hydrocarbon exposure versus those that did not, based on the occupation criteria used in the previous studies. Odds ratios did not indicate any increased risk associated with general paternal hydrocarbon exposure in the workplace. In prior studies, increased risk estimates were detected with narrower groups of occupations involving exposure to hydrocarbon materials. The data from this study were classified according to these groups, and again, no increased risks were indicated except for a statistically insignificant but elevated odds ratio for fathers who were paper and pulp mill workers.^ Odds ratios were calculated for specific occupations and industries previously implicated as risk factors. Significantly associated odds ratios (OR) were detected for electricians (OR = 3.5), especially those working for construction companies (OR = 10.0), for employment in the printing occupations (OR = 4.5), particularly graphic arts workers (OR = 21.9), and in the electronics and electronic machinery industries (OR = 3.5). Analysis of the petroleum refining and chemical industries, which were not found in previous study populations, revealed significantly elevated odds ratios of 3.0 for occupations with probable heavy exposure to chemicals and petroleum compounds and 10.0 for salesmen of chemical products. ^

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of root s = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K-s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5 % for central isolated hadrons and 1-3 % for the final calorimeter jet energy scale.

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.