Integrating detection probabilities in species distribution models of amphibians breeding in Mediterranean temporary ponds

Aim  The imperfect detection of species may lead to erroneous conclusions about species-environment relationships. Accuracy in species detection usually requires temporal replication at sampling sites, a time-consuming and costly monitoring scheme. Here, we applied a lower-cost alternative based on a double-sampling approach to incorporate the reliability of species detection into regression-based species distribution modelling.Location  Doñana National Park (south-western Spain).Methods  Using species-specific monthly detection probabilities, we estimated the detection reliability as the probability of having detected the species given the species-specific survey time. Such reliability estimates were used to account explicitly for data uncertainty by weighting each absence. We illustrated how this novel framework can be used to evaluate four competing hypotheses as to what constitutes primary environmental control of amphibian distribution: breeding habitat, aestivating habitat, spatial distribution of surrounding habitats and/or major ecosystems zonation. The study was conducted on six pond-breeding amphibian species during a 4-year period.Results  Non-detections should not be considered equivalent to real absences, as their reliability varied considerably. The occurrence of Hyla meridionalis and Triturus pygmaeus was related to a particular major ecosystem of the study area, where suitable habitat for these species seemed to be widely available. Characteristics of the breeding habitat (area and hydroperiod) were of high importance for the occurrence of Pelobates cultripes and Pleurodeles waltl. Terrestrial characteristics were the most important predictors of the occurrence of Discoglossus galganoi and Lissotriton boscai, along with spatial distribution of breeding habitats for the last species.Main conclusions  We did not find a single best supported hypothesis valid for all species, which stresses the importance of multiscale and multifactor approaches. More importantly, this study shows that estimating the reliability of non-detection records, an exercise that had been previously seen as a naïve goal in species distribution modelling, is feasible and could be promoted in future studies, at least in comparable systems.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

On the efficient evaluation of ruin probabilities for completely monotone claim size distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Assigning and combining probabilities in single-case studies

There is currently a considerable diversity of quantitative measures available for summarizing the results in single-case studies. Given that the interpretation of some of them is difficult due to the lack of established benchmarks, the current paper proposes an approach for obtaining further numerical evidence on the importance of the results, complementing the substantive criteria, visual analysis, and primary summary measures. This additional evidence consists of obtaining the statistical significance of the outcome when referred to the corresponding sampling distribution. This sampling distribution is formed by the values of the outcomes (expressed as data nonoverlap, R-squared, etc.) in case the intervention is ineffective. The approach proposed here is intended to offer the outcome"s probability of being as extreme when there is no treatment effect without the need for some assumptions that cannot be checked with guarantees. Following this approach, researchers would compare their outcomes to reference values rather than constructing the sampling distributions themselves. The integration of single-case studies is problematic, when different metrics are used across primary studies and not all raw data are available. Via the approach for assigning p values it is possible to combine the results of similar studies regardless of the primary effect size indicator. The alternatives for combining probabilities are discussed in the context of single-case studies pointing out two potentially useful methods one based on a weighted average and the other on the binomial test.

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Assigning and combining probabilities in single-case designs: A second study

The present study builds on a previous proposal for assigning probabilities to the outcomes computed using different primary indicators in single-case studies. These probabilities are obtained comparing the outcome to previously tabulated reference values and reflect the likelihood of the results in case there was no intervention effect. The current study explores how well different metrics are translated into p values in the context of simulation data. Furthermore, two published multiple baseline data sets are used to illustrate how well the probabilities could reflect the intervention effectiveness as assessed by the original authors. Finally, the importance of which primary indicator is used in each data set to be integrated is explored; two ways of combining probabilities are used: a weighted average and a binomial test. The results indicate that the translation into p values works well for the two nonoverlap procedures, with the results for the regression-based procedure diverging due to some undesirable features of its performance. These p values, both when taken individually and when combined, were well-aligned with the effectiveness for the real-life data. The results suggest that assigning probabilities can be useful for translating the primary measure into the same metric, using these probabilities as additional evidence on the importance of behavioral change, complementing visual analysis and professional's judgments.

A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models

Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l'algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l'étude des processus de risque multivariés, qui peuvent être utiles dans l'étude des problèmes de la ruine des compagnies d'assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d'obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables.

Inclusive probabilities for the scattering system 16 MeV-S{^16+} on Ar

We performed ab initio calculations of many particle inclusive probabilities for the scattering system 16 MeV-S{^16+} on Ar. The solution of the time-dependent DIRAC-FOCK-SLATER-equation is achieved via a set of coupled-channel equations with energy eigenvalues and matrix elements which are given by static SCF molecular many electron calculations.