A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Subsecond changes of global brain state in illusory multistable motion perception

This study explored transient changes in EEG microstates and spatial Omega complexity associated with changes in multistable perception. 21-channel EEG was recorded from 13 healthy subjects viewing an alternating dot pattern that induced illusory motion with ambiguous direction. Baseline epochs with stable motion direction were compared to epochs immediately preceding stimuli that were perceived with changed motion direction ('reference stimuli'). About 750 ms before reference stimuli, Omega complexity decreased as compared to baseline, and two of four classes of EEG microstates changed their probability of occurrence. About 300 ms before reference stimuli, Omega complexity increased and the previous deviations of EEG microstates were reversed. Given earlier results on Omega complexity and microstates, these sub-second EEG changes might parallel longer-lasting fluctuations in vigilance. Assumedly, the discontinuities of illusory motion thus occur during sub-second dips in arousal, and the following reconstruction of the illusion coincides with a state of relative over-arousal.

Magnitude and frequency: challenges for the assessment of vulnerability to geomorphic hazards

In natural hazard research, risk is defined as a function of (1) the probability of occurrence of a hazardous process, and (2) the assessment of the related extent of damage, defined by the value of elements at risk exposed and their physical vulnerability. Until now, various works have been undertaken to determine vulnerability values for objects exposed to geomorphic hazards such as mountain torrents. Yet, many studies only provide rough estimates for vulnerability values based on proxies for process intensities. However, the deduced vulnerability functions proposed in the literature show a wide range, in particular with respect to medium and high process magnitudes. In our study, we compare vulnerability functions for torrent processes derived from studies in test sites located in the Austrian Alps and in Taiwan. Based on this comparison we expose needs for future research in order to enhance mountain hazard risk management with a particular focus on the question of vulnerability on a catchment scale.

A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Detection histories for eight species of Amazona parrots in Venezuela during the NeoMaps bird surveys in 2010

Documenting changes in distribution is necessary for understanding species' response to environmental changes, but data on species distributions are heterogeneous in accuracy and resolution. Combining different data sources and methodological approaches can fill gaps in knowledge about the dynamic processes driving changes in species-rich, but data-poor regions. We combined recent bird survey data from the Neotropical Biodiversity Mapping Initiative (NeoMaps) with historical distribution records to estimate potential changes in the distribution of eight species of Amazon parrots in Venezuela. Using environmental covariates and presence-only data from museum collections and the literature, we first used maximum likelihood to fit a species distribution model (SDM) estimating a historical maximum probability of occurrence for each species. We then used recent, NeoMaps survey data to build single-season occupancy models (OM) with the same environmental covariates, as well as with time- and effort-dependent detectability, resulting in estimates of the current probability of occurrence. We finally calculated the disagreement between predictions as a matrix of probability of change in the state of occurrence. Our results suggested negative changes for the only restricted, threatened species, Amazona barbadensis, which has been independently confirmed with field studies. Two of the three remaining widespread species that were detected, Amazona amazonica, Amazona ochrocephala, also had a high probability of negative changes in northern Venezuela, but results were not conclusive for Amazona farinosa. The four remaining species were undetected in recent field surveys; three of these were most probably absent from the survey locations (Amazona autumnalis, Amazona mercenaria and Amazona festiva), while a fourth (Amazona dufresniana) requires more intensive targeted sampling to estimate its current status. Our approach is unique in taking full advantage of available, but limited data, and in detecting a high probability of change even for rare and patchily-distributed species. However, it is presently limited to species meeting the strong assumptions required for maximum-likelihood estimation with presence-only data, including very high detectability and representative sampling of its historical distribution.

Topsoil properties and abundance of Acari and Collembola species in northern Victoria Land, Antarctica

Soil fauna in the extreme conditions of Antarctica consists of a few microinvertebrate species patchily distributed at different spatial scales. Populations of the prostigmatic mite Stereotydeus belli and the collembolan Gressittacantha terranova from northern Victoria Land (Antarctica) were used as models to study the effect of soil properties on microarthropod distributions. In agreement with the general assumption that the development and distribution of life in these ecosystems is mainly controlled by abiotic factors, we found that the probability of occurrence of S. belli depends on soil moisture and texture and on the sampling period (which affects the general availability of water); surprisingly, none of the analysed variables were significantly related to the G. terranova distribution. Based on our results and literature data, we propose a theoretical model that introduces biotic interactions among the major factors driving the local distribution of collembolans in Antarctic terrestrial ecosystems.