Densités de copules archimédiennes hiérarchiques

Les copulas archimédiennes hiérarchiques ont récemment gagné en intérêt puisqu’elles généralisent la famille de copules archimédiennes, car elles introduisent une asymétrie partielle. Des algorithmes d’échantillonnages et des méthodes ont largement été développés pour de telles copules. Néanmoins, concernant l’estimation par maximum de vraisemblance et les tests d’adéquations, il est important d’avoir à disposition la densité de ces variables aléatoires. Ce travail remplie ce manque. Après une courte introduction aux copules et aux copules archimédiennes hiérarchiques, une équation générale sur les dérivées des noeuds et générateurs internes apparaissant dans la densité des copules archimédiennes hiérarchique. sera dérivée. Il en suit une formule tractable pour la densité des copules archimédiennes hiérarchiques. Des exemples incluant les familles archimédiennes usuelles ainsi que leur transformations sont présentés. De plus, une méthode numérique efficiente pour évaluer le logarithme des densités est présentée.

Modèles de dépendance hiérarchique pour l’évaluation des passifs et la tarification en actuariat

Dans cette thèse on s’intéresse à la modélisation de la dépendance entre les risques en assurance non-vie, plus particulièrement dans le cadre des méthodes de provisionnement et en tarification. On expose le contexte actuel et les enjeux liés à la modélisation de la dépendance et l’importance d’une telle approche avec l’avènement des nouvelles normes et exigences des organismes réglementaires quant à la solvabilité des compagnies d’assurances générales. Récemment, Shi et Frees (2011) suggère d’incorporer la dépendance entre deux lignes d’affaires à travers une copule bivariée qui capture la dépendance entre deux cellules équivalentes de deux triangles de développement. Nous proposons deux approches différentes pour généraliser ce modèle. La première est basée sur les copules archimédiennes hiérarchiques, et la deuxième sur les effets aléatoires et la famille de distributions bivariées Sarmanov. Nous nous intéressons dans un premier temps, au Chapitre 2, à un modèle utilisant la classe des copules archimédiennes hiérarchiques, plus précisément la famille des copules partiellement imbriquées, afin d’inclure la dépendance à l’intérieur et entre deux lignes d’affaires à travers les effets calendaires. Par la suite, on considère un modèle alternatif, issu d’une autre classe de la famille des copules archimédiennes hiérarchiques, celle des copules totalement imbriquées, afin de modéliser la dépendance entre plus de deux lignes d’affaires. Une approche avec agrégation des risques basée sur un modèle formé d’une arborescence de copules bivariées y est également explorée. Une particularité importante de l’approche décrite au Chapitre 3 est que l’inférence au niveau de la dépendance se fait à travers les rangs des résidus, afin de pallier un éventuel risque de mauvaise spécification des lois marginales et de la copule régissant la dépendance. Comme deuxième approche, on s’intéresse également à la modélisation de la dépendance à travers des effets aléatoires. Pour ce faire, on considère la famille de distributions bivariées Sarmanov qui permet une modélisation flexible à l’intérieur et entre les lignes d’affaires, à travers les effets d’années de calendrier, années d’accident et périodes de développement. Des expressions fermées de la distribution jointe, ainsi qu’une illustration empirique avec des triangles de développement sont présentées au Chapitre 4. Aussi, nous proposons un modèle avec effets aléatoires dynamiques, où l’on donne plus de poids aux années les plus récentes, et utilisons l’information de la ligne corrélée afin d’effectuer une meilleure prédiction du risque. Cette dernière approche sera étudiée au Chapitre 5, à travers une application numérique sur les nombres de réclamations, illustrant l’utilité d’un tel modèle dans le cadre de la tarification. On conclut cette thèse par un rappel sur les contributions scientifiques de cette thèse, tout en proposant des angles d’ouvertures et des possibilités d’extension de ces travaux.

Explicit ruin formulas for models with dependence among risks

We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

Human Herpesvirus Infections Of The Central Nervous System: Laboratory Diagnosis Based On Dna Detection By Nested Pcr In Plasma And Cerebrospinal Fluid Samples.

Infections of the central nervous systems (CNS) present a diagnostic problem for which an accurate laboratory diagnosis is essential. Invasive practices, such as cerebral biopsy, have been replaced by obtaining a polymerase chain reaction (PCR) diagnosis using cerebral spinal fluid (CSF) as a reference method. Tests on DNA extracted from plasma are noninvasive, thus avoiding all of the collateral effects and patient risks associated with CSF collection. This study aimed to determine whether plasma can replace CSF in nested PCR analysis for the detection of CNS human herpesvirus (HHV) diseases by analysing the proportion of patients whose CSF nested PCR results were positive for CNS HHV who also had the same organism identified by plasma nested PCR. In this study, CSF DNA was used as the gold standard, and nested PCR was performed on both types of samples. Fifty-two patients with symptoms of nervous system infection were submitted to CSF and blood collection. For the eight HHV, one positive DNA result-in plasma and/or CSF nested PCR-was considered an active HHV infection, whereas the occurrence of two or more HHVs in the same sample was considered a coinfection. HHV infections were positively detected in 27/52 (51.9%) of the CSF and in 32/52 (61.5%) of the plasma, difference not significant, thus nested PCR can be performed on plasma instead of CSF. In conclusion, this findings suggest that plasma as a useful material for the diagnosis of cases where there is any difficulty to perform a CSF puncture.

Rapid detection of bovine coronavirus by a semi-nested RT-PCR

Bovine coronavirus (BCoV) is a member of the group 2 of the Coronavirus (Nidovirales: Coronaviridae) and the causative agent of enteritis in both calves and adult bovine, as well as respiratory disease in calves. The present study aimed to develop a semi-nested RT-PCR for the detection of BCoV based on representative up-to-date sequences of the nucleocapsid gene, a conserved region of coronavirus genome. Three primers were designed, the first round with a 463bp and the second (semi-nested) with a 306bp predicted fragment. The analytical sensitivity was determined by 10-fold serial dilutions of the BCoV Kakegawa strain (HA titre: 256) in DEPC treated ultra-pure water, in fetal bovine serum (FBS) and in a BCoV-free fecal suspension, when positive results were found up to the 10-2, 10-3 and 10-7 dilutions, respectively, which suggests that the total amount of RNA in the sample influence the precipitation of pellets by the method of extraction used. When fecal samples was used, a large quantity of total RNA serves as carrier of BCoV RNA, demonstrating a high analytical sensitivity and lack of possible substances inhibiting the PCR. The final semi-nested RT-PCR protocol was applied to 25 fecal samples from adult cows, previously tested by a nested RT-PCR RdRp used as a reference test, resulting in 20 and 17 positives for the first and second tests, respectively, and a substantial agreement was found by kappa statistics (0.694). The high sensitivity and specificity of the new proposed method and the fact that primers were designed based on current BCoV sequences give basis to a more accurate diagnosis of BCoV-caused diseases, as well as to further insights on protocols for the detection of other Coronavirus representatives of both Animal and Public Health importance.

Dual candidemia detected by nested polymerase chain reaction in two critically ill children

The use of improved microbiological procedures associated with molecular techniques has increased the identification of Candida bloodstream infections, even if the isolation of more than one species by culture methods remains uncommon. We report the cases of two children presenting with severe gastrointestinal disorders and other risk factors that contribute to Candida infections. In the first patient, C. albicans DNA was initially detected by a nested-amplification and C. tropicalis was found later during hospitalization, while blood cultures were persistently negative. In the second child, there was amplification of C. albicans and C. glabrata DNA in the same samples, but blood cultures yielded only C. albicans. Both patients received antifungal therapy but had unfavorable outcomes. These two cases illustrate that PCR was more successful than culture methods in detecting Candida in the bloodstream of high risk children, and was also able to detect the presence of more than one species in the same patient that might impact therapy when the fungi are resistant to azole compounds.

Multiplex semi-nested RT-PCR with exogenous internal control for simultaneous detection of bovine coronavirus and group A rotavirus

Neonatal calf diarrhea is a multi-etiology syndrome of cattle and direct detection of the two major agents of the syndrome, group A rotavirus and Bovine coronavirus (BCoV) is hampered by their fastidious growth in cell culture. This study aimed at developing a multiplex semi-nested RT-PCR for simultaneous detection of BCoV (N gene) and group A rotavirus (VP1 gene) with the addition of an internal control (mRNA ND5). The assay was tested in 75 bovine feces samples tested previously for rotavirus using PAGE and for BCoV using nested RT-PCR targeted to RdRp gene. Agreement with reference tests was optimal for BCoV (kappa = 0.833) and substantial for rotavirus detection (kappa = 0.648). the internal control, ND5 mRNA, was detected successfully in all reactions. Results demonstrated that this multiplex semi-nested RT-PCR was effective in the detection of BCoV and rotavirus, with high sensitivity and specificity for simultaneous detection of both viruses at a lower cost, providing an important tool for studies on the etiology of diarrhea in cattle. (C) 2010 Elsevier B.V. All rights reserved.

Development and validation of nested-PCR for the diagnosis of clinical and subclinical infectious laryngotracheitis

A standardised nested-PCR method that amplifies a region of the glycoprotein E gene of avian infectious laryngotracheitis virus (ILTV) has been developed for the diagnosis of infection by Gallid herpesvirus 1. The two sets of primers employed produced the expected ampIification products of 524bp(externa I primers) and 219bp (internal primers) in the presence of ILTV DNA, whereas no Such amplicons were obtained with other avian respiratory pathogens or with DNA extracted from the cells of uninfected chickens. The identity of the 219bp amplified product was con firmed by DNA sequencing. The standardised nested-PCR method detected ILTV DNA from trachea, lung, conjunctiva and trigeminal ganglia samples from flocks of birds with and without clinical signs. and showed hi.-h sensitivity (95.4%) and specificity (93.1%) when compared with the reference test involving virus isolation in specific-pathogen-free chicken embryos. The standardised nested-PCR method described may be used to detect clinical and latent ILTV infections, and will be of significant value for both diagnostic and epidemiological Studies. (c) 2008 Elsevier B.V. All rights reserved.

Algebraic structure for the crossing of balanced and stair nested designs

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Diagnosis of hepatitis C virus in Brazilian blood donors using a reverse transcriptase nested polymerase chain reaction: comparison with enzyme immunoassay and recombinant protein immunoblot assay

Screening blood donations for anti-HCV antibodies and alanine aminotransferase (ALT) serum levels generally prevents the transmission of hepatitis C virus (HCV) by transfusion. The aim of the present study was to evaluate the efficiency of the enzyme immunoassay (EIA) screening policy in identifying potentially infectious blood donors capable to transmit hepatitis C through blood transfusion. We have used a reverse transcriptase (RT)-nested polymerase chain reaction (PCR) to investigate the presence of HCV-RNA in blood donors. The prevalence of HCV-RNA positive individuals was compared with the recombinant immunoblot assay (RIBA-2) results in order to assess the usefulness of both tests as confirmatory assays. Both tests results were also compared with the EIA-2 OD/C ratio (optical densities of the samples divided by the cut off value). ALT results were expressed as the ALT quotient (qALT), calculated dividing the ALT value of the samples by the maximum normal value (53UI/l) for the method. Donors (n=178) were divided into five groups according to their EIA anti-HCV status and qALT: group A (EIA > or = 3, ALT<1), group B (EIA > or = 3, ALT>1), group C (1<=EIA<3, ALT<1), group D (1<=EIA<3, ALT>1) and group E (EIA<=0.7). HCV sequences were detected by RT-nested PCR, using primers for the most conserved region of viral genome. RIBA-2 was applied to the same samples. In group A (n=6), all samples were positive by RT-nested PCR and RIBA-2. Among 124 samples in group B, 120 (96.8%) were RIBA-2 positive and 4 (3.2%) were RIBA-2 indeterminate but were seropositive for antigen c22.3. In group B, 109 (87.9%) of the RIBA-2 positive samples were also RT-nested PCR positive, as well as were all RIBA-2 indeterminate samples. In group C, all samples (n=9) were RT-nested PCR negative: 4 (44.4%) were also RIBA-2 negative, 4 (44.4%) were RIBA-2 positive and 1 (11.1%) was RIBA-2 indeterminate. HCV-RNA was detected by RT-nested PCR in 3 (37.5%) out of 8 samples in group D. Only one of them was also RIBA-2 positive, all the others were RIBA-2 indeterminate. All of the group E samples (controls) were RT- nested PCR and RIBA-2 negative. Our study suggests a strong relation between anti-HCV EIA-2 ratio > or = 3 and detectable HCV-RNA by RT-nested PCR. We have also noted that blood donors with RIBA-2 indeterminate presented a high degree of detectable HCV-RNA using RT-nested PCR (75%), especially when the c22.3 band was detected.

Aplicação da Técnica de "Nested PCR" Durante o Período Pré-patente para Identificação de Schistosoma mansoni no Hospedeiro Intermediário Biomphalaria glabrata

Biomphalaria glabrata, molusco de água doce, desempenha um importante papel em Parasitologia Médica, por ser o hospedeiro intermediário de Schistosoma mansoni, tremátode digenético responsável pela schistosomose intestinal. A detecção de moluscos infectados pelo Schistosoma mansoni tem uma grande importância em Saúde pública, porque identifica focos de transmissão da schistosomose. As limitações dos métodos clássicos para o diagnóstico de infecções pré patentes fazem com que os métodos de biologia moleculares sejam vistos como possíveis alternativas através da detecção de ADN do S. mansoni em moluscos hospedeiros. A detecção de sequências específicas de ADN por reacção de polimerase em cadeia (PCR) tem-se verificado ser de extrema importância para a análise genética e diagnóstico de várias doenças infecciosas. Neste estudo foi aplicada a técnica de Nested-PCR, com o objectivo de identificar, no período pré-patente, S. mansoni em moluscos expostos a 1, 5 e 10 miracídios em diferentes períodos de tempo. Foram utilizados moluscos das estirpes albina e selvagem de B. glabrata. Para a realização das técnicas de PCR e de Nested–PCR (NPCR) foram utilizados dois pares de oligonucleótidos desenhados especificamente para detectar o ADN de S. mansoni . Verificou-se amplificação do fragmento de ADN do parasita em 80% das amostras analisadas, independentemente da dose de miracídios e do período de exposição. O método utilizado é altamente sensível, mostrando ser uma ferramenta útil na detecção de hospedeiros intermediários de S. mansoni, consequentemente na identificação de focos de schistosomose intestinal. Palavras-chave: Schistosoma mansoni, Biomphalaria glabrata, período pré-patente e Reacção em Cadeia de Polimerase.

A score test for non-nested hypotheses with applications to discrete data models

This paper suggests that a convenient score test against non-nested alternatives can be constructed from the linear combination of the likelihood functions of the competing models. It is shown that this procedure is essentially a test for the correct specification of the conditional distribution of the variable of interest.