Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.     

Population monotonic path schemes for simple games

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.     

Living with unfairness: The limits of equal opportunity in a market economy

Equality of opportunity is often presented as a criterion which reconciles egalitarianism with principles of freedom and responsibility. This paper distinguishes between the principle of starting-line equality, which requires that everyones initial opportunities, assessed in relation to what is publicly known ex ante, are equal, and the principle that equal efforts should yield equal ex post rewards. It argues that the first principle is compatible with allocation of resources through markets but, because of the division of knowledge, the second is not. If we want the opportunities which markets give us, we have to accept ex post unfairness. Earlier versions of this paper were presented at a workshop on the measurement of freedom at the London School of Economics, and at a conference on non-welfarist issues in normative economics at the University of Caen. I thank participants at those meetings, and particularly Tania Burchardt, Marco Mariotti and Franz Prettenthaler, for comments. My work on this paper was supported by the Leverhulme Trust.     

When Passion Leads to Problematic Outcomes: A Look at Gambling

Vallerand et al. (2003) have proposed that individuals can have two distinct types of passion toward an activity. Harmonious passion, an internal force leading one to choose to engage in the activity, is proposed to be associated with positive consequences. Obsessive passion, an internal pressure forcing one to engage in an activity, is posited to be associated with negative consequences. The present study sought to determine the role of the two types of passion in various cognitive and affective states associated with dependence and problems with gambling. Participants (n = 412) were recruited at the Montréal Casino and given a questionnaire measuring passion toward gambling, as well as consequences associated with dependence and problem gambling. Results showed that obsessive passion for gambling predicted poorer vitality and concentration in daily tasks, as well as increased rumination, anxiety, negative mood, guilt, and problem gambling. These relations were not found for harmonious passion for gambling. Results are discussed in light of the motivational approach to passion (Vallerand et al., 2003).     

Multivariate forests with missing mixed outcomes

In this article, we propose a multivariate random forest method for multiple responses of mixed types with missing responses. Imputation is performed for each bootstrap sample used to build the individual trees that form the forest. The individual trees are built using a weighted splitting rule allowing downweighting of imputed observations. A simulation study shows the benefits of this approach over complete case analysis when missing responses are missing completely at random and missing at random (MAR). In particular, the gain in prediction accuracy of the proposed method is larger in the MAR case and also increases as the proportion of missing increases.     

Adolescent Electronic Media Use: Instead of Doing What?

Adolescents like to watch TV and listen to the radio, even on school days, but their day contains, like for all other people, only 24 hours. What do those who use electronic media frequently neglect? Data from 14- and 16-year-old adolescents from 12 European countries and from the USA (EURONET sample) were analyzed (N = 3,250). The correlations between time spent using electronic media (EM) and 15 other daily activities were all negative, which is not surprising given the fact that the sum of all activities is bound to be 24 hours. We, therefore, calculated correlations between electronic media use and the proportions of each other activity within the remaining time. A clear pattern emerged. The method allowed us to identify “mandatory” activities that always have high priority, such as sleeping and attending school, and “optional” activities that enter into competition with electronic media use, including engaging in sports, playing music, leisure reading, and being with friends without media use. As to the mandatory activities, the correlations between media-using time and the proportions of remaining time were positive; relative to the optional activities, the correlations between media-using time and the proportions of remaining time were negative. While one might expect school homework to be regarded as mandatory, the correlation patterns identified it as optional. As to the average electronic media-using times, there were marked differences not only between the individual participants, but also between the countries. While Bulgarian adolescents spent an average of 2.37 hours of a regular school day using electronic media, French adolescents averaged only 1.72 hours.     

Behavioral evidence for framing effects in the resolution of the doctrinal paradox

The aggregation of individual sets of judgments over interconnected propositions can yield inconsistent collective sets of judgments, even when the individual sets of judgments are themselves consistent. A doctrinal paradox occurs when majority voting on a compound proposition (such as a conjunction or disjunction) yields a different result than majority voting on each of the elements of the proposition. For example, when most individuals accept proposition X; most individuals accept proposition Y ; but only a minority of individuals accept the compound proposition ‘X and Y’. Conducting two elemental votes would lead to accept X and Y , but conducting one compound vote would lead to reject X and Y . In such a situation, do people manifest a stable preference as to which voting procedure should be applied? This research reports the results of two behavioral experiments using a within-participant design, which show that procedural preferences can be upturned by framing either positively or negatively the set of judgments to be aggregated. This shift in procedural preference leads to large swings in the final collective judgment endorsed by participants.