Automatic Bayes Factors for Testing Equality- and Inequality-Constrained Hypotheses on Variances

In comparing characteristics of independent populations, researchers frequently expect a certain structure of the population variances. These expectations can be formulated as hypotheses with equality and/or inequality constraints on the variances. In this article, we consider the Bayes factor for testing such (in)equality-constrained hypotheses on variances. Application of Bayes factors requires specification of a prior under every hypothesis to be tested. However, specifying subjective priors for variances based on prior information is a difficult task. We therefore consider so-called automatic or default Bayes factors. These methods avoid the need for the user to specify priors by using information from the sample data. We present three automatic Bayes factors for testing variances. The first is a Bayes factor with equal priors on all variances, where the priors are specified automatically using a small share of the information in the sample data. The second is the fractional Bayes factor, where a fraction of the likelihood is used for automatic prior specification. The third is an adjustment of the fractional Bayes factor such that the parsimony of inequality-constrained hypotheses is properly taken into account. The Bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency. Based on this evaluation, it is concluded that the adjusted fractional Bayes factor is generally recommendable for testing equality- and inequality-constrained hypotheses on variances.     

Illegitimacy moderates the effects of power on approach

A wealth of research has found that power leads to behavioral approach and action. Four experiments demonstrate that this link between power and approach is broken when the power relationship is illegitimate. When power was primed to be legitimate or when power positions were assigned legitimately, the powerful demonstrated more approach than the powerless. However, when power was experienced as illegitimate, the powerless displayed as much approach as, or even more approach than, the powerful. This moderating effect of legitimacy occurred regardless of whether power and legitimacy were manipulated through experiential primes, semantic primes, or role manipulations. It held true for behavioral approach (Experiment 1) and two effects associated with it: the propensity to negotiate (Experiment 2) and risk preferences (Experiments 3 and 4). These findings demonstrate that how power is conceptualized, acquired, and wielded determines its psychological consequences and add insight into not only when but also why power leads to approach.     

Selfish or servant leadership? Evolutionary predictions on leadership personalities in coordination games

We study the personalities of emergent leaders in two coordination games in groups of four players each with monetary incentives. Our results support the evolutionary hypothesis that leadership is a social good for the group: leadership benefits followers but is potentially costly for the individual taking on the leader role. Across the two economic games leaders do less well - earn less money - on average than followers. Furthermore, social participants choose to lead more often than selfish participants and there is no relationship between leadership behavior and personal dominance. Our results support the idea that leadership can be servant rather than selfish and we note the implications of this finding.     

RELIGIONIS CAUSA

The claim is widespread that the preservation, or reintroduction, of Western traditions of holy war in the post‐Reformation period was due mostly to Protestantism, especially in its Calvinist variety. This paper makes a case for examining the thought of a much broader selection of minor intellectuals on just and holy war than is usually done, and to do so in other national contexts than exclusively the English Puritan one. To test the apparently widespread view that, historically, Calvinism has had a particular proclivity for holy war, the article treats theological justifications of war in seventeenth‐ and eighteenth‐century Dutch moral theology. Showing that a full‐blown concept of “holy war” was largely absent from Dutch theological thought, it falsifies the assumption that historical Calvinism (or Protestantism in general) is inherently belligerent. The paper demonstrates that justifications of violence religionis causa and ideological motives for war have always been contingent, not on religions, but on the historical contexts in which those religions operate.     

Model for a flexible motor memory based on a self-active recurrent neural network

Using recent recurrent network architecture based on the reservoir computing approach, we propose and numerically simulate a model that is focused on the aspects of a flexible motor memory for the storage of elementary movement patterns into the synaptic weights of a neural network, so that the patterns can be retrieved at any time by simple static commands. The resulting motor memory is flexible in that it is capable to continuously modulate the stored patterns. The modulation consists in an approximately linear inter- and extrapolation, generating a large space of possible movements that have not been learned before. A recurrent network of thousand neurons is trained in a manner that corresponds to a realistic exercising scenario, with experimentally measured muscular activations and with kinetic data representing proprioceptive feedback. The network is “self-active” in that it maintains recurrent flow of activation even in the absence of input, a feature that resembles the “resting-state activity” found in the human and animal brain. The model involves the concept of “neural outsourcing” which amounts to the permanent shifting of computational load from higher to lower-level neural structures, which might help to explain why humans are able to execute learned skills in a fluent and flexible manner without the need for attention to the details of the movement.     

Power increases infidelity among men and women

Data from a large survey of 1,561 professionals were used to examine the relationship between power and infidelity and the process underlying this relationship. Results showed that elevated power is positively associated with infidelity because power increases confidence in the ability to attract partners. This association was found for both actual infidelity and intentions to engage in infidelity in the future. Gender did not moderate these results: The relationship between power and infidelity was the same for women as for men, and for the same reason. These findings suggest that the common assumption (and often-found effect) that women are less likely than men to engage in infidelity is, at least partially, a reflection of traditional gender-based differences in power that exist in society.     

The role of liturgy in Apostolicae curae and Saepius officio

The aim of this article is to critically investigate the arguable role attributed to liturgy in two official documents issued by different ecclesial authorities in the late nineteenth century. Of these documents, Apostolicae curae is definitely the most commonly known, for, in it, Pope Leo XIII declared Anglican orders to be ‘absolutely null and utterly void’. In Saepius officio, their response to this declaration, the Archbishops of Canterbury and York developed a solid and detailed argumentation which directly addressed the issues involved. Strangely enough, however, their letter has scarcely received any scholarly attention, especially not from a liturgical perspective. Therefore, this article embarks on a comparative analysis of the liturgico-theological quality of both documents and endeavours to reopen discussions and reflections on the dignity and validity of Anglican orders at a time in which there seems to be little enthusiasm for that kind of enterprise.     

Bayes factors for testing inequality constrained hypotheses: Issues with prior specification

Several issues are discussed when testing inequality constrained hypotheses using a Bayesian approach. First, the complexity (or size) of the inequality constrained parameter spaces can be ignored. This is the case when using the posterior probability that the inequality constraints of a hypothesis hold, Bayes factors based on non‐informative improper priors, and partial Bayes factors based on posterior priors. Second, the Bayes factor may not be invariant for linear one‐to‐one transformations of the data. This can be observed when using balanced priors which are centred on the boundary of the constrained parameter space with a diagonal covariance structure. Third, the information paradox can be observed. When testing inequality constrained hypotheses, the information paradox occurs when the Bayes factor of an inequality constrained hypothesis against its complement converges to a constant as the evidence for the first hypothesis accumulates while keeping the sample size fixed. This paradox occurs when using Zellner's g prior as a result of too much prior shrinkage. Therefore, two new methods are proposed that avoid these issues. First, partial Bayes factors are proposed based on transformed minimal training samples. These training samples result in posterior priors that are centred on the boundary of the constrained parameter space with the same covariance structure as in the sample. Second, a g prior approach is proposed by letting g go to infinity. This is possible because the Jeffreys–Lindley paradox is not an issue when testing inequality constrained hypotheses. A simulation study indicated that the Bayes factor based on this g prior approach converges fastest to the true inequality constrained hypothesis.