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 .

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.

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.

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.

Robust Proximal Femur Segmentation in Conventional X-Ray Images via Random Forest Regression on Multi-resolution Gradient Features

In this paper, we propose a fully automatic, robust approach for segmenting proximal femur in conventional X-ray images. Our method is based on hierarchical landmark detection by random forest regression, where the detection results of 22 global landmarks are used to do the spatial normalization, and the detection results of the 59 local landmarks serve as the image cue for instantiation of a statistical shape model of the proximal femur. To detect landmarks in both levels, we use multi-resolution HoG (Histogram of Oriented Gradients) as features which can achieve better accuracy and robustness. The efficacy of the present method is demonstrated by experiments conducted on 150 clinical x-ray images. It was found that the present method could achieve an average point-to-curve error of 2.0 mm and that the present method was robust to low image contrast, noise and occlusions caused by implants.