Bayesian Estimation of the Size of a Population

We consider the following problem: estimate the size of a population marked with serial numbers after only a sample of the serial numbers has been observed. Its simplicity in formulation and the inviting possibilities of application make this estimation well suited for an undergraduate level probability course. Our contribution consists in a Bayesian treatment of the problem. For an improper uniform prior distribution, we show that the posterior mean and variance have nice closed form expressions and we demonstrate how to compute highest posterior density intervals. Maple and R code is provided on the authors’ web-page to allow students to verify the theoretical results and experiment with data

A stochastic model for multivariate surveillance of infectious diseases

We describe a stochastic model based on a branching process for analyzing surveillance data of infectious diseases that allows to make forecasts of the future development of the epidemic. The model is based on a Poisson branching process with immigration with additional adjustment for possible overdispersion. An extension to a space-time model for the multivariate case is described. The model is estimated in a Bayesian context using Markov Chain Monte Carlo (MCMC) techniques. We illustrate the applicability of the model through analyses of simulated and real data

Statistical approaches to the surveillance of infectious diseases for veterinary public health

This technical report covers the aspect of using statistical methodology for the monitoring of routinely collected surveillance data in veterinary public health. An account of the Farrington algorithm and Poisson cumulative sum schemes for the detection of aberrations is given with special attention devoted to the occurrence of seasonality and spatial aggregation of the time series. Modelling approaches for retrospective analysis of surveillance counts are described. To illustrate the applicability of the methodology in veterinary public health, data from the surveillance of rabies among fox in Hesse, Germany, are analysed

Universality and predictability in molecular quantitative genetics

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology

Reliability of shoulder symptom recall after one year in a retrospective application of the oxford shoulder score

Includes abstract. Includes bibliographical references

Structure & Composition of a Climax Forest System in Boone County, Kentucky

The structure and composition of a 52 hectare mature mesic hardwood forest in Boone County, Kentucky was studied during 1973-74. Acer saccharum was the dominant tree species of the entire forest, with Fraxinus americana as the subdominant. In the understory vegetation, Acer and Fraxinus were among the dominant genera, thus this forest system can be described as being at the climax stage of development. A previously cleared area in the forest was also analyzed. It was found that the dominant tree species of the canopy were also dominant in the genera of the understory in the disturbed area, indicating a return to the stable maple-ash system of the entire forest. During the Spring of 1274, tornados moved across Boone County; one of these tornados damaged the forest that was under study. The effects of this wind storm were included in the collection of data. Tornado damage was not limited to any snecific species an.: in this study there was no apparent relationship beween root depth and soli type among uprooted trees

Probabilistically Safe Policy Transfer

Although learning-based methods have great potential for robotics, one concern is that a robot that updates its parameters might cause large amounts of damage before it learns the optimal policy. We formalize the idea of safe learning in a probabilistic sense by defining an optimization problem: we desire to maximize the expected return while keeping the expected damage below a given safety limit. We study this optimization for the case of a robot manipulator with safety-based torque limits. We would like to ensure that the damage constraint is maintained at every step of the optimization and not just at convergence. To achieve this aim, we introduce a novel method which predicts how modifying the torque limit, as well as how updating the policy parameters, might affect the robot's safety. We show through a number of experiments that our approach allows the robot to improve its performance while ensuring that the expected damage constraint is not violated during the learning process