On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Dynamic fault tree analysis with PEWMA modeling of event rates and Bayesian updating of material balance parameters using MCMC

This research explores Bayesian updating as a tool for estimating parameters probabilistically by dynamic analysis of data sequences. Two distinct Bayesian updating methodologies are assessed. The first approach focuses on Bayesian updating of failure rates for primary events in fault trees. A Poisson Exponentially Moving Average (PEWMA) model is implemnented to carry out Bayesian updating of failure rates for individual primary events in the fault tree. To provide a basis for testing of the PEWMA model, a fault tree is developed based on the Texas City Refinery incident which occurred in 2005. A qualitative fault tree analysis is then carried out to obtain a logical expression for the top event. A dynamic Fault Tree analysis is carried out by evaluating the top event probability at each Bayesian updating step by Monte Carlo sampling from posterior failure rate distributions. It is demonstrated that PEWMA modeling is advantageous over conventional conjugate Poisson-Gamma updating techniques when failure data is collected over long time spans. The second approach focuses on Bayesian updating of parameters in non-linear forward models. Specifically, the technique is applied to the hydrocarbon material balance equation. In order to test the accuracy of the implemented Bayesian updating models, a synthetic data set is developed using the Eclipse reservoir simulator. Both structured grid and MCMC sampling based solution techniques are implemented and are shown to model the synthetic data set with good accuracy. Furthermore, a graphical analysis shows that the implemented MCMC model displays good convergence properties. A case study demonstrates that Likelihood variance affects the rate at which the posterior assimilates information from the measured data sequence. Error in the measured data significantly affects the accuracy of the posterior parameter distributions. Increasing the likelihood variance mitigates random measurement errors, but casuses the overall variance of the posterior to increase. Bayesian updating is shown to be advantageous over deterministic regression techniques as it allows for incorporation of prior belief and full modeling uncertainty over the parameter ranges. As such, the Bayesian approach to estimation of parameters in the material balance equation shows utility for incorporation into reservoir engineering workflows.

Multi-View Weighted Network

Extensive investigation has been conducted on network data, especially weighted network in the form of symmetric matrices with discrete count entries. Motivated by statistical inference on multi-view weighted network structure, this paper proposes a Poisson-Gamma latent factor model, not only separating view-shared and view-specific spaces but also achieving reduced dimensionality. A multiplicative gamma process shrinkage prior is implemented to avoid over parameterization and efficient full conditional conjugate posterior for Gibbs sampling is accomplished. By the accommodating of view-shared and view-specific parameters, flexible adaptability is provided according to the extents of similarity across view-specific space. Accuracy and efficiency are tested by simulated experiment. An application on real soccer network data is also proposed to illustrate the model.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different ofrailtyo models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

Pipkiiα Is Widely Expressed In Hematopoietic-derived Cells And May Play A Role In The Expression Of Alpha- And Gamma-globins In K562 Cells.

Characterized for the first time in erythrocytes, phosphatidylinositol phosphate kinases (PIP kinases) belong to a family of enzymes that generate various lipid messengers and participate in several cellular processes, including gene expression regulation. Recently, the PIPKIIα gene was found to be differentially expressed in reticulocytes from two siblings with hemoglobin H disease, suggesting a possible relationship between PIPKIIα and the production of globins. Here, we investigated PIPKIIα gene and protein expression and protein localization in hematopoietic-derived cells during their differentiation, and the effects of PIPKIIα silencing on K562 cells. PIPKIIα silencing resulted in an increase in α and γ globins and a decrease in the proliferation of K562 cells without affecting cell cycle progression and apoptosis. In conclusion, using a cell line model, we showed that PIPKIIα is widely expressed in hematopoietic-derived cells, is localized in their cytoplasm and nucleus, and is upregulated during erythroid differentiation. We also showed that PIPKIIα silencing can induce α and γ globin expression and decrease cell proliferation in K562 cells.

Leishmania spp. parasite isolation through inoculation of patient biopsy macerates in interferon gamma knockout mice

Isolation of Leishmania parasite and species identification are important for confirmation and to help define the epidemiology of the leishmaniasis. Mice are often used to isolate pathogens, but the most common mouse strains are resistant to infection with parasites from the Leishmania (Viannia) subgenus. In this study we tested the inoculation of interferon gamma knockout (IFNγ KO) mice with biopsy macerates from Leishmania-infected patients to increase the possibility of isolating parasites. Biopsies from twenty five patients with clinical signs of leishmaniasis were taken and tested for the presence of parasites. Immunohistochemical assay (IHC) and conventional histopathology detected the parasite in 88% and 83% of the patients, respectively. Leishmania sp. were isolated in biopsy macerates from 52% of the patients by culture in Grace's insect medium, but 13% of isolates were lost due to contamination. Inoculation of macerates in IFNγ KO mice provides isolation of parasites in 31.8% of the biopsies. Most isolates belong to L. (Viannia) subgenus, as confirmed by PCR, except one that belongs to L. (Leishmania) subgenus. Our preliminary results support the use of IFNγ KO mice to improve the possibility to isolate New World Leishmania species.

High-Density Lipoprotein Inhibits the Uptake of Modified Low-Density Lipoprotein and the Expression of CD36 and Fc gamma RI

Aim: Modified low-density lipoprotein (mLDL), mainly upon oxidative and enzymatic modification, is the major atherogenic lipoprotein. Conversely, high-density lipoprotein (HDL) is considered anti-atherogenic because of its ability to remove cholesterol. The aim of this work was to analyze both the influence of HDL on the uptake of mLDL and the expression of CD36 and Fc gamma I receptors on monocytic cell lines during cell differentiation. Methods: Uptake of fluorescein isothiocyanate (FITC)-conjugated LDL and FITC-conjugated mLDL, i.e., copper-oxidized LDL (oxLDL) or trypsin enzyme modified LDL (enzLDL), was analyzed, as well as the expression of CD36 and Fc gamma RI in THP-1 and U937 cells, using flow cytometry. Results: HDL inhibited the uptake of mLDL, which varied in degree depending on the cell line or type of mLDL. Further, HDL rapidly decreased CD36 and Fc gamma RI involved in the uptake of mLDL. Conclusions: We demonstrate that modified LDL promotes specific LDL receptor-independent uptake by monocytic cell lines, and that the uptake of LDL and enzLDL is less than that of oxLDL. In this process, HDL diminishes the uptake of LDL or mLDL, which may involve the down-regulation of receptors (CD36 and Fc gamma I). This regulatory process represents another way by which HDL can be anti-atherogenic and it depends on the type of modification of LDL and the stage of differentiation of monocytes to macrophages.

Maternal immunization with ovalbumin prevents neonatal allergy development and up-regulates inhibitory receptor Fc gamma RIIB expression on B cells

Background: Preconception allergen immunization prevents neonatal allergen sensitization in mice by a complex interaction between regulatory cells/factors and antibodies. The present study assessed the influence of maternal immunization with ovalbumin (OVA) on the immune response of 3 day-old and 3 week-old offspring immunized or non-immunized with OVA and evaluated the effect of IgG treatment during fetal development or neonatal period. Results: Maternal immunization with OVA showed increased levels of Fc gamma RIIb expression in splenic B cells of neonates, which were maintained for up to 3 weeks and not affected by additional postnatal OVA immunization. Maternal immunization also exerted a down-modulatory effect on both IL-4 and IFN-gamma-secreting T cells and IL-4 and IL-12-secreting B cells. Furthermore, immunized neonates from immunized mothers showed a marked inhibition of antigen-specifc IgE Ab production and lowered Th2/Th1 cytokine levels, whereas displaying enhanced Fc gamma RIIb expression on B cells. These offspring also showed reduced antigen-specific proliferative response and lowered B cell responsiveness. Moreover, in vitro evaluation revealed an impairment of B cell activation upon engagement of B cell antigen receptor by IgG from OVA-immunized mice. Finally, in vivo IgG transference during pregnancy or breastfeeding revealed that maternal Ab transference was able to increase regulatory cytokines, such as IL-10, in the prenatal stage; yet only the postnatal treatment prevented neonatal sensitization. None of the IgG treatments induced immunological changes in the offspring, as it was observed for those from OVA-immunized mothers. Conclusion: Maternal immunization upregulates the inhibitory Fc gamma RIIb expression on offspring B cells, avoiding skewed Th2 response and development of allergy. These findings contribute to the advancement of prophylactic strategies to prevent allergic diseases in early life.