An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Inter-informant agreement and prevalence estimates for substance use disorders: direct interview versus family history method.

OBJECTIVES: Family studies typically use multiple sources of information on each individual including direct interviews and family history information. The aims of the present study were to: (1) assess agreement for diagnoses of specific substance use disorders between direct interviews and the family history method; (2) compare prevalence estimates according to the two methods; (3) test strategies to approximate prevalence estimates according to family history reports to those based on direct interviews; (4) determine covariates of inter-informant agreement; and (5) identify covariates that affect the likelihood of reporting disorders by informants. METHODS: Analyses were based on family study data which included 1621 distinct informant (first-degree relatives and spouses) - index subject pairs. RESULTS: Our main findings were: (1) inter-informant agreement was fair to good for all substance disorders, except for alcohol abuse; (2) the family history method underestimated the prevalence of drug but not alcohol use disorders; (3) lowering diagnostic thresholds for drug disorders and combining multiple family histories increased the accuracy of prevalence estimates for these disorders according to the family history method; (4) female sex of index subjects was associated with higher agreement for nearly all disorders; and (5) informants who themselves had a history of the same substance use disorder were more likely to report this disorder in their relatives, which entails the risk of overestimation of the size of familial aggregation. CONCLUSION: Our findings have important implications for the best-estimate procedure applied in family studies.

Decision-theoretic analysis of forensic sampling criteria using Bayesian decision networks

Sampling issues represent a topic of ongoing interest to the forensic science community essentially because of their crucial role in laboratory planning and working protocols. For this purpose, forensic literature described thorough (Bayesian) probabilistic sampling approaches. These are now widely implemented in practice. They allow, for instance, to obtain probability statements that parameters of interest (e.g., the proportion of a seizure of items that present particular features, such as an illegal substance) satisfy particular criteria (e.g., a threshold or an otherwise limiting value). Currently, there are many approaches that allow one to derive probability statements relating to a population proportion, but questions on how a forensic decision maker - typically a client of a forensic examination or a scientist acting on behalf of a client - ought actually to decide about a proportion or a sample size, remained largely unexplored to date. The research presented here intends to address methodology from decision theory that may help to cope usefully with the wide range of sampling issues typically encountered in forensic science applications. The procedures explored in this paper enable scientists to address a variety of concepts such as the (net) value of sample information, the (expected) value of sample information or the (expected) decision loss. All of these aspects directly relate to questions that are regularly encountered in casework. Besides probability theory and Bayesian inference, the proposed approach requires some additional elements from decision theory that may increase the efforts needed for practical implementation. In view of this challenge, the present paper will emphasise the merits of graphical modelling concepts, such as decision trees and Bayesian decision networks. These can support forensic scientists in applying the methodology in practice. How this may be achieved is illustrated with several examples. The graphical devices invoked here also serve the purpose of supporting the discussion of the similarities, differences and complementary aspects of existing Bayesian probabilistic sampling criteria and the decision-theoretic approach proposed throughout this paper.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Bayesian classification criterion for forensic multivariate data

This study presents a classification criteria for two-class Cannabis seedlings. As the cultivation of drug type cannabis is forbidden in Switzerland, law enforcement authorities regularly ask laboratories to determine cannabis plant's chemotype from seized material in order to ascertain that the plantation is legal or not. In this study, the classification analysis is based on data obtained from the relative proportion of three major leaf compounds measured by gas-chromatography interfaced with mass spectrometry (GC-MS). The aim is to discriminate between drug type (illegal) and fiber type (legal) cannabis at an early stage of the growth. A Bayesian procedure is proposed: a Bayes factor is computed and classification is performed on the basis of the decision maker specifications (i.e. prior probability distributions on cannabis type and consequences of classification measured by losses). Classification rates are computed with two statistical models and results are compared. Sensitivity analysis is then performed to analyze the robustness of classification criteria.

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

Detection of nandrolone metabolites in urine after a football game in professional and amateur players: a Bayesian comparison.

Nandrolone (19-nortestosterone) is a widely used anabolic steroid in sports where strength plays an essential role. Once nandrolone has been metabolised, two major metabolites are excreted in urine, 19-norandrosterone (NA) and 19-noretiocholanolone (NE). In 1997, in France, quite a few sportsmen had concentrations of 19-norandrosterone very close to the IOC cut off limit (2ng/ml). At that time, a debate took place about the capability of the human male body to produce by itself these metabolites without any intake of nandrolone or related compounds. The International Football Federation (FIFA) was very concerned with this problematic, especially because the World Cup was about to start in France. In this respect, a statistical study was held with all football players from the first and second divisions of the Swiss Football National League. All players gave a urine sample after effort and around 6% of them showed traces of 19-norandrosterone. These results were compared with amateur football players (control group) and around 6% of them had very small amounts of 19-norandrosterone and/or 19-noretiocholanolone in urine after effort, whereas none of them had detectable traces of one or the other metabolite before effort. The origin of these compounds in urine after a strenuous physical activity is still unknown, but three hypotheses can be put forward. First, an endogenous production of nandrolone metabolites takes place. Second, nandrolone metabolites are released from the fatty tissues after an intake of nandrolone, some related compounds or some contaminated nutritive supplements. Finally, the sportsmen may have taken something during or just before the football game.

Agar dilution method for susceptibility testing of Neisseria gonorrhoeae

The antibiotic susceptibilities of Neisseria gonorrhoeae isolates obtained from patients attending a clinic for sexually transmitted diseases in Tucumán, Argentina, were determined by the agar dilution method (MIC). 3.5% of the isolates produced ²-lactamase. A total of 96.5% of ²-lactamase negative isolates tested were susceptible to penicillin (MIC < 2 µgml-1); 14.03% of the tested isolates were resistant to tetracycline (MIC < 2 µgml-1), and 98% of the tested isolates were susceptible to spectinomycin (MIC < 64 µgml-1). The MICs for 95% of the isolates, tested for other drugs were: < 2 µgml-1 for cefoxitin, < 0.06 µgml-1 for cefotaxime, < 0.25 µgml-1 for norfloxacin, < 10 µgml-1 for cephaloridine, < 10 µgml-1 for cephalexin, and < 50 µgml-1 for kanamycin. Antibiotic resistance among N. gonorrhoeae isolates from Tucumán, Argentina, appeared to be primarily limited to penicillin and tetracycline, which has been a general use against gonorrhoeae in Tucumán since 1960. Periodic monitoring of the underlying susceptibility profiles of the N. gonorrhoeae strains prevalent in areas of frequent transmission may provide clues regarding treatment options and emerging of drug resistance.

Detection of Rotavirus in Sewage and Creek Water: Efficiency of the Concentration Method

Simian rotavirus SA-11, experimentally seeded, was recovered from raw domestic sewage by a two-step concentration procedure, using filtration through a positively charged microporous filter (Zeta Plus 60 S) followed by ultracentrifugation, effecting an 8,000-fold concentration. By this method, a mean recovery of 81% ± 7.5 of the SA-11 virus, was achieved