Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .

Experimental plant communities develop phylogenetically overdispersed abundance distributions during assembly

The importance of competition between similar species in driving community assembly is much debated. Recently, phylogenetic patterns in species composition have been investigated to help resolve this question: phylogenetic clustering is taken to imply environmental filtering, and phylogenetic overdispersion to indicate limiting similarity between species. We used experimental plant communities with random species compositions and initially even abundance distributions to examine the development of phylogenetic pattern in species abundance distributions. Where composition was held constant by weeding, abundance distributions became overdispersed through time, but only in communities that contained distantly related clades, some with several species (i.e., a mix of closely and distantly related species). Phylogenetic pattern in composition therefore constrained the development of overdispersed abundance distributions, and this might indicate limiting similarity between close relatives and facilitation/complementarity between distant relatives. Comparing the phylogenetic patterns in these communities with those expected from the monoculture abundances of the constituent species revealed that interspecific competition caused the phylogenetic patterns. Opening experimental communities to colonization by all species in the species pool led to convergence in phylogenetic diversity. At convergence, communities were composed of several distantly related but species-rich clades and had overdispersed abundance distributions. This suggests that limiting similarity processes determine which species dominate a community but not which species occur in a community. Crucially, as our study was carried out in experimental communities, we could rule out local evolutionary or dispersal explanations for the patterns and identify ecological processes as the driving force, underlining the advantages of studying these processes in experimental communities. Our results show that phylogenetic relations between species provide a good guide to understanding community structure and add a new perspective to the evidence that niche complementarity is critical in driving community assembly.

Optical quantum random number generator

A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters’ noise, dead-time and after pulses.

Bioavailability of pharmaceuticals in waters close to wastewater treatment plants: use of fish bile for exposure assessment

Pharmaceuticals are ubiquitous in surface waters as a consequence of discharges from municipal wastewater treatment plants. However, few studies have assessed the bioavailability of pharmaceuticals to fish in natural waters. In the present study, passive samplers and rainbow trout were experimentally deployed next to three municipal wastewater treatment plants in Finland to evaluate the degree of animal exposure. Pharmaceuticals from several therapeutic classes (in total 15) were analyzed by liquid chromatography-tandem mass spectrometry in extracts of passive samplers and in bile and blood plasma of rainbow trout held at polluted sites for 10 d. Each approach indicated the highest exposure near wastewater treatment plant A and the lowest near that of plant C. Diclofenac, naproxen, and ibuprofen were found in rainbow trout, and their concentrations in bile were 10 to 400 times higher than in plasma. The phase I metabolite hydroxydiclofenac was also detected in bile. Hence, bile proved to be an excellent sample matrix for the exposure assessment of fish. Most of the monitored pharmaceuticals were found in passive samplers, implying that they may overestimate the actual exposure of fish in receiving waters. Two biomarkers, hepatic vitellogenin and cytochrome P4501A, did not reveal clear effects on fish, although a small induction of vitellogenin mRNA was observed in trout caged near wastewater treatment plants B and C.

Efficiency of risk-based vs . random sampling for the monitoring of tetracycline residues in slaughtered calves in Switzerland

In all European Union countries, chemical residues are required to be routinely monitored in meat. Good farming and veterinary practice can prevent the contamination of meat with pharmaceutical substances, resulting in a low detection of drug residues through random sampling. An alternative approach is to target-monitor farms suspected of treating their animals with antimicrobials. The objective of this project was to assess, using a stochastic model, the efficiency of these two sampling strategies. The model integrated data on Swiss livestock as well as expert opinion and results from studies conducted in Switzerland. Risk-based sampling showed an increase in detection efficiency of up to 100% depending on the prevalence of contaminated herds. Sensitivity analysis of this model showed the importance of the accuracy of prior assumptions for conducting risk-based sampling. The resources gained by changing from random to risk-based sampling should be transferred to improving the quality of prior information.

Choosing a random distribution with prescribed risks

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating rather general random probability distributions on the unit interval. A new algorithm based on the simulation of a weighted barycentres array is suggested to generate random probability distributions with a given value of the spectral risk measure.

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Stereological Modelling of Random Particles

Stochastic models for three-dimensional particles have many applications in applied sciences. Lévy–based particle models are a flexible approach to particle modelling. The structure of the random particles is given by a kernel smoothing of a Lévy basis. The models are easy to simulate but statistical inference procedures have not yet received much attention in the literature. The kernel is not always identifiable and we suggest one approach to remedy this problem. We propose a method to draw inference about the kernel from data often used in local stereology and study the performance of our approach in a simulation study.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.