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.

Copula-Based Modeling of TMI Brightness Temperature With Rainfall Type

Overland rain retrieval using spaceborne microwave radiometer offers a myriad of complications as land presents itself as a radiometrically warm and highly variable background. Hence, land rainfall algorithms of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) have traditionally incorporated empirical relations of microwave brightness temperature (Tb) with rain rate, rather than relying on physically based radiative transfer modeling of rainfall (as implemented in the TMI ocean algorithm). In this paper, sensitivity analysis is conducted using the Spearman rank correlation coefficient as benchmark, to estimate the best combination of TMI low-frequency channels that are highly sensitive to the near surface rainfall rate from the TRMM Precipitation Radar (PR). Results indicate that the TMI channel combinations not only contain information about rainfall wherein liquid water drops are the dominant hydrometeors but also aid in surface noise reduction over a predominantly vegetative land surface background. Furthermore, the variations of rainfall signature in these channel combinations are not understood properly due to their inherent uncertainties and highly nonlinear relationship with rainfall. Copula theory is a powerful tool to characterize the dependence between complex hydrological variables as well as aid in uncertainty modeling by ensemble generation. Hence, this paper proposes a regional model using Archimedean copulas, to study the dependence of TMI channel combinations with respect to precipitation, over the land regions of Mahanadi basin, India, using version 7 orbital data from the passive and active sensors on board TRMM, namely, TMI and PR. Studies conducted for different rainfall regimes over the study area show the suitability of Clayton and Gumbel copulas for modeling convective and stratiform rainfall types for the majority of the intraseasonal months. Furthermore, large ensembles of TMI Tb (from the most sensitive TMI channel combination) were generated conditional on various quantiles (25th, 50th, 75th, and 95th) of the convective and the stratiform rainfall. Comparatively greater ambiguity was observed to model extreme values of the convective rain type. Finally, the efficiency of the proposed model was tested by comparing the results with traditionally employed linear and quadratic models. Results reveal the superior performance of the proposed copula-based technique.

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.

A nested real-time PCR assay has an increased sensitivity suitable for detection of viruses in aerosol studies

Aims: Influenza is commonly spread by infectious aerosols; however, detection of viruses in aerosols is not sensitive enough to confirm the characteristics of virus aerosols. The aim of this study was to develop an assay for respiratory viruses sufficiently sensitive to be used in epidemiological studies. Method: A two-step, nested real-time PCR assay was developed for MS2 bacteriophage, and for influenza A and B, parainfluenza 1 and human respiratory syncytial virus. Outer primer pairs were designed to nest each existing real-time PCR assay. The sensitivities of the nested real-time PCR assays were compared to those of existing real-time PCR assays. Both assays were applied in an aerosol study to compare their detection limits in air samples. Conclusions: The nested real-time PCR assays were found to be several logs more sensitive than the real-time PCR assays, with lower levels of virus detected at lower Ct values. The nested real-time PCR assay successfully detected MS2 in air samples, whereas the real-time assay did not. Significance and Impact of the Study: The sensitive assays for respiratory viruses will permit further research using air samples from naturally generated virus aerosols. This will inform current knowledge regarding the risks associated with the spread of viruses through aerosol transmission.

Design and implementation of wideband baluns for Archimedean spiral antennas

The demand for high-speed data services for portable device has become a driving force for development of advanced broadband access technologies. Despite recent advances in broadband wireless technologies, there remain a number of critical issues to be resolved. One of the major concerns is the implementation of compact antennas that can operate in a wide frequency band. Spiral antenna has been used extensively for broadband applications due to its planar structure, wide bandwidth characteristics and circular polarisation. However, the practical implementation of spiral antennas is challenged by its high input characteristic impedance, relatively low gain and the need for balanced feeding structures. Further development of wideband balanced feeding structures for spiral antennas with matching impedance capabilities remain a need. This thesis proposes three wideband feeding systems for spiral antennas which are compatible with wideband array antenna geometries. First, a novel tapered geometry is proposed for a symmetric coplanar waveguide (CPW) to coplanar strip line (CPS) wideband balun. This balun can achieve the unbalanced to balanced transformation while matching the high input impedance of the antenna to a reference impedance of 50 . The discontinuity between CPW and CPS is accommodated by using a radial stub and bond wires. The bandwidth of the balun is improved by appropriately tapering the CPW line instead of using a stepped impedance transformer. Next, the tapered design is applied to an asymmetric CPW to propose a novel asymmetric CPW to CPS wideband balun. The use of asymmetric CPW does away with the discontinuities between CPW and CPS without having to use a radial stub or bond wires. Finally, a tapered microstrip line to parallel striplines balun is proposed. The balun consists of two sections. One section is the parallel striplines which are connected to the antenna, with the impedance of balanced line equal to the antenna input impedance. The other section consists of a microstrip line where the width of the ground plane is gradually reduced to eventually resemble a parallel stripline. The taper accomplishes the mode and impedance transformation. This balun has significantly improved bandwidth characteristics. Characteristics of proposed feeding structures are measured in a back-to-back configuration and compared to simulated results. The simulated and measured results show the tapered microstrip to parallel striplines balun to have more than three octaves of bandwidth. The tapered microstrip line to parallel striplines balun is integrated with a single Archimedean spiral antenna and with an array of spiral antennas. The performance of the integrated structures is simulated with the aid of electromagnetic simulation software, and results are compared to measurements. The back-to-back microstrip to parallel strip balun has a return loss of better than 10 dB over a wide bandwidth from 1.75 to 15 GHz. The performance of the microstrip to parallel strip balun was validated with the spiral antennas. The results show the balun to be an effective mean of feeding network with a low profile and wide bandwidth (2.5 to 15 GHz) for balanced spiral antennas.

Comparison of PCR, nested PCR, and random amplified polymorphic DNA PCR for detection and typing of Ureaplasma urealyticum in specimens from pregnant women

A PCR assay, using three primer pairs, was developed for the detection of Ureaplasma urealyticum, parvo biovar, mba types 1, 3, and 6, in cultured clinical specimens. The primer pairs were designed by using the polymorphic base positions within a 310- to 311-bp fragment of the 5* end and upstream control region of the mba gene. The specificity of the assay was confirmed with reference serovars 1, 3, 6, and 14 and by the amplified-fragment sizes (81 bp for mba 1, 262 bp for mba 3, and 193 bp for mba 6). A more sensitive nested PCR was also developed. This involved a first-step PCR, using the primers UMS-125 and UMA226, followed by the nested mba-type PCR described above. This nested PCR enabled the detection and typing of small numbers of U. urealyticum cells, including mixtures, directly in original clinical specimens. By using random amplified polymorphic DNA (RAPD) PCR with seven arbitrary primers, we were also able to differentiate the two biovars of U. urealyticum and to identify 13 RAPD-PCR subtypes. By applying these subtyping techniques to clinical samples collected from pregnant women, we established that (i) U. urealyticum is often a persistent colonizer of the lower genital tract from early midtrimester until the third trimester of pregnancy, (ii) mba type 6 was isolated significantly more often (P 5 0.048) from women who delivered preterm than from women who delivered at term, (iii) no particular ureaplasma subtype(s) was associated with placental infections and/or adverse pregnancy outcomes, and (iv) the ureaplasma subtypes most frequently isolated from women were the same subtypes most often isolated from infected placentas.

The ‘Russian doll’ approach : developing nested case-studies to support international comparative research in education

International comparison is complicated by the use of different terms, classification methods, policy frameworks and system structures, not to mention different languages and terminology. Multi-case studies can assist in the understanding of the influence wielded by cultural, social, economic, historical and political forces upon educational decisions, policy construction and changes over time. But case studies alone are not enough. In this paper, we argue for an ecological or scaled approach that travels through macro, meso and micro levels to build nested case-studies to allow for more comprehensive analysis of the external and internal factors that shape policy-making and education systems. Such an approach allows for deeper understanding of the relationship between globalizing trends and policy developments.

Hybrid chalcogenide nanoparticles : 2D-WS2 nanocrystals inside nested WS2 fullerenes

The MOCVD assisted formation of nested WS2 inorganic fullerenes (IF-WS2) was performed by enhancing surface diffusion with iodine, and fullerene growth was monitored by taking TEM snapshots of intermediate products. The internal structure of the core-shell nanoparticles was studied using scanning electron microscopy (SEM) after cross-cutting with a focused ion beam (FIB). Lamellar reaction intermediates were found occluded in the fullerene particles. In contrast to carbon fullerenes, layered metal chalcogenides prefer the formation of planar, plate-like structures where the dangling bonds at the edges are stabilized by excess S atoms. The effects of the reaction and annealing temperatures on the composition and morphology of the final product were investigated, and the strength of the WS2 shell was measured by intermittent contact-mode AFM. The encapsulated lamellar structures inside the hollow spheres may lead to enhanced tribological activities.

Effectiveness of an emergency nurse practitioner service for adults presenting to rural hospitals with chest pain : Protocol for a multicentre, longitudinal nested cohort study

Introduction Chest pain is common in emergency department (ED) patients and represents a considerable burden for rural health services. Health services reforms to improve access to care need appropriately skilled and supported clinicians in the delivery of safe and effective care, including the use of emergency nurse practitioners (ENPs). Despite increasing use of ENPs, little is known about the safety and quality of the service in the rural ED context. The aims of this study are (1) to examine the safety and quality of the ENP service model in the provision of care in the rural environment and (2) to evaluate the effectiveness of the service in the management of patients presenting with undifferentiated chest pain. Methods and analysis This is the protocol for a prospective longitudinal nested cohort study to compare the effectiveness of ENP service with that of standard care. Adults presenting to three rural EDs in Queensland, Australia with a primary presenting complaint of atraumatic chest pain will be eligible for enrolment. We will measure (1) clinician's use of evidence-based guidelines (2) diagnostic accuracy of ECG interpretation for the management of patients with suspected or confirmed ACS (3) service indicators of waiting times, length-of-stay and did-not-wait rates and (4) clinician's diagnostic accuracy as measured by rates of unplanned representation within 7 days (5) satisfaction with care, (6) quality-of-life and (7) functional status. To assess these outcomes we will use a combination of measures collected from routinely collected data, medical record review and questionnaires (with 30-day follow-up). Ethics and dissemination Queensland Health Human Research Ethics Committee (HREC) has approved this protocol. The results will be published in peer-reviewed scientific journals and presented at one or more scientific conferences.

Optimal adaptive sequential spatial sampling of soil using pair-copulas

A spatial sampling design that uses pair-copulas is presented that aims to reduce prediction uncertainty by selecting additional sampling locations based on both the spatial configuration of existing locations and the values of the observations at those locations. The novelty of the approach arises in the use of pair-copulas to estimate uncertainty at unsampled locations. Spatial pair-copulas are able to more accurately capture spatial dependence compared to other types of spatial copula models. Additionally, unlike traditional kriging variance, uncertainty estimates from the pair-copula account for influence from measurement values and not just the configuration of observations. This feature is beneficial, for example, for more accurate identification of soil contamination zones where high contamination measurements are located near measurements of varying contamination. The proposed design methodology is applied to a soil contamination example from the Swiss Jura region. A partial redesign of the original sampling configuration demonstrates the potential of the proposed methodology.

An approximate algorithm for the minimal vertex nested polygon problem

Given two simple polygons, the Minimal Vertex Nested Polygon Problem is one of finding a polygon nested between the given polygons having the minimum number of vertices. In this paper, we suggest efficient approximate algorithms for interesting special cases of the above using the shortest-path finding graph algorithms.