Bayesian inverse problems with Gaussian priors

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case credible sets are of the correct order of magnitude. The results are numerically illustrated by the problem of recovering a function from observation of a noisy version of its primitive.Comment: Published in at http://dx.doi.org/10.1214/11-AOS920 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Engaged but exhausted: Work-related wellbeing profiles of South African employees

Organizations and colleagues alike benefit from dedicated employees who are immersed in their work and energetically pursue their tasks. Unfortunately, this may come at a price for employees who may burn out. Organizations are, therefore, confronted with a responsibility to assist employees in striking a balance between eagerly engaging in their tasks and taking care of their wellbeing. Before designing and implementing interventions, it is valuable to identify how engagement and burnout components cluster within individuals and whether these different combinations have different implications for employees. The study aimed to explore whether burnout and work engagement combine within individuals to form different burnout-engagement profiles. The study also aimed to examine the implications of different profiles for employees’ psychological distress, affective commitment, and turnover intention. Among 1048 South African employees, latent profile analysis highlighted five distinct burnout-engagement profiles: Burned-out, Risky, Moderately balanced, Stars, and Workaholics. The Burned-out reported higher levels of psychological distress than the Risky. Still, both reported higher levels than the Moderately balanced, who also reported higher levels of psychological distress than the Stars. The Burned out and the Workaholics reported equal levels of psychological distress. The Stars reported the highest levels of affective commitment, followed by the Workaholics, the Moderately balanced, and the Risky, with the lowest levels reported by the Burned-out. The Burned-out reported the highest levels of turnover intention, followed by the Risky, the Workaholics, and the Moderately balanced, with the lowest levels reported by the Stars. Limitations, recommendations for future research and practical implications are discussed

Social value orientation, organizational goal concerns and interdepartmental problem-solving behavior

In a study in 11 organizations among 120 manufacturing, planning and sales employees, support was found for the hypothesis that a prosocial value orientation – as a personality trait -increases the likelihood that employees show a high concern for the goals of other departments. This concern, combined with a high concern for own goals, furthermore appeared to increase the likelihood of problem-solving behavior during interdepartmental negotiations. Measures of goal concerns were attained, firstly, by asking employees how important they found six specific organizational goals and, secondly, by assessing which goals were found most important by members of which department. The results of this study suggest that problem solving can be induced by selecting or developing prosocial employees, because a prosocial value orientation increases the likelihood of having broad role orientations, in which employees not only care for goals characteristic of their own department, but also for goals of other departments

Three-Dimensional Time-Resolved Trajectories from Laboratory Insect Swarms

Aggregations of animals display complex and dynamic behaviour, both at the individual level and on the level of the group as a whole. Often, this behaviour is collective, so that the group exhibits properties that are distinct from those of the individuals. In insect swarms, the motion of individuals is typically convoluted, and swarms display neither net polarization nor correlation. The swarms themselves, however, remain nearly stationary and maintain their cohesion even in noisy natural environments. This behaviour stands in contrast with other forms of collective animal behaviour, such as flocking, schooling, or herding, where the motion of individuals is more coordinated, and thus swarms provide a powerful way to study the underpinnings of collective behaviour as distinct from global order. Here, we provide a data set of three-dimensional, time-resolved trajectories, including positions, velocities, and accelerations, of individual insects in laboratory insect swarms. The data can be used to study the collective as a whole as well as the dynamics and behaviour of individuals within the swarm

Environmental Perturbations Induce Correlations in Midge Swarms

Although collectively behaving animal groups often show large-scale order (such as in bird flocks), they need not always (such as in insect swarms). It has been suggested that the signature of collective behavior in disordered groups is a residual long-range correlation. However, results in the literature have reported contradictory results as to the presence of long-range correlation in insect swarms, with swarms in the wild displaying correlation but those in a controlled laboratory environment not. We resolve these apparently incompatible results by showing the external perturbations generically induce the emergence of correlations. We apply a range of different external stimuli to laboratory swarms of the non-biting midge Chironomus riparius, and show that in all cases correlations appear when perturbations are introduced. We confirm the generic nature of these results by showing that they can be reproduced in a stochastic model of swarms. Given that swarms in the wild will always have to contend with environmental stimuli, our results thus harmonize previous findings

Bayesian recovery of the initial condition for the heat equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This version differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1103.269

A matrix interpolation between classical and free max operations: I. The univariate case

Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings.Comment: 14 page