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This paper proposes a bi-variate competition process to describe the spread of epidemics of SIS type through both horizontal and vertical transmission. The interest is in the exact reproduction number, , which is seen to be the stochastic version of the well-known basic reproduction number. We characterize the probability distribution function of by decomposing this number into two random contributions allowing us to distinguish between infectious person-to-person contacts and infections of newborns with infective parents. Numerical examples are presented to illustrate our analytical results.

This paper proposes a smooth copula-based Generalized Extreme Value (GEV) model to map and predict extreme rainfall in Central Eastern Canada. The considered data contains a large portion of missing values, and one observes several nonconcomitant record periods at different stations. The proposed two-step approach combines GEV parameters' smooth functions in space through the use of spatial covariates and a flexible hierarchical copula-based model to take into account dependence between the recording stations. The hierarchical copula structure is detected via a clustering algorithm implemented with an adapted version of the copula-based dissimilarity measure recently introduced in the literature. Finally, we compare the classical GEV parameter interpolation approaches with the proposed smooth copula-based GEV modeling approach.

Ordinary differential equation models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital, this is an extremely restrictive assumption as typically a hospital ward has a few dozen, or even fewer, patients. This work reframes a well-known model used in the study of the spread of antibiotic-resistant bacteria in hospitals, to consider the pathogen transmission dynamics in small populations. In this vein, this paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. We determine the probability law of the exact reproduction number , which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods. This guarantees the compatibility of the new, finite-population model, with large population models present in the literature and takes full advantage, in its mathematical analysis, of the intrinsic stochasticity.

To better manage the risks of destructive natural disasters, impact models can be fed with simulations of extreme scenarios to study the sensitivity to temporal and spatial variability. We propose a semi-parametric stochastic framework that enables simulations of realistic spatio-temporal extreme fields using a moderate number of observed extreme space-time episodes to generate an unlimited number of extreme scenarios of any magnitude. Our framework draws sound theoretical justification from extreme value theory, building on generalized Pareto limit processes arising as limits for event magnitudes exceeding a high threshold. Specifically, we exploit asymptotic stability properties by decomposing extreme event episodes into a scalar magnitude variable (that is resampled), and an empirical profile process representing space-time variability. For illustration on hourly gridded precipitation data in Mediterranean France, we calculate various risk measures using extreme event simulations for yet unobserved magnitudes, and we highlight contrasted behavior for different definitions of the magnitude variable.

The classic univariate risk measure in environmental sciences is the Return Period (RP). The RP is traditionally defined as “the average time elapsing between two successive realizations of a prescribed event”. The notion of design quantile related with RP is also of great importance. The design quantile represents the “value of the variable(s) characterizing the event associated with a given RP”. Since an individual risk may strongly be affected by the degree of dependence amongst all risks, the need for the provision of multivariate design quantiles has gained ground. In contrast to the univariate case, the design quantile definition in the multivariate setting presents certain difficulties. In particular, Salvadori, G., De Michele, C. and Durante F. define in the paper called “On the return period and design in a multivariate framework” (Hydrol Earth Syst Sci 15:3293–3305, 2011) the design realization as the vector that maximizes a weight function given that the risk vector belongs to a given critical layer of its joint multivariate distribution function. In this paper, we provide the explicit expression of the aforementioned multivariate risk measure in the Archimedean copula setting. Furthermore, this measure is estimated by using Extreme Value Theory techniques and the asymptotic normality of the proposed estimator is studied. The performance of our estimator is evaluated on simulated data. We conclude with an application on a real hydrological data-set.

Como consecuencia de que los reguladores necesitan gestionar el riesgo en los distintos sectores, se está extendiendo de forma rápida una metodología basada en el riesgo. En las últimas décadas, este problema ha sido tratado en su mayoría en una versión univariante. Sin embargo, los riesgos envuelven normalmente varias variables aleatorias que son a menudo dependientes. Por tanto, es crucial trabajar en un marco multivariante. Por otro lado, los fenómenos están caracterizados frecuentemente por eventos extremos. Esta tesis trata fundamentalmente dos problemas: la definición de medidas de riesgo en un marco multivariante y la estimatión de medidas de riesgo multivariantes teniendo en cuenta eventos extremos. El Capítulo 1 es un capítulo introductorio. Presentamos el estado del arte para la noción de medidas de riesgo multivariantes. También, recordamos los principales resultados en Teoría de Cópulas, Teoría de Valores Extremos y Órdenes Estocásticos que son útiles en este trabajo . Se introducen dos nuevas medidas de riesgo multivariantes en el Capítulo 2. Varias propiedades interesantes y, caracterizaciones bajo condiciones de cópulas Arquimedianas, se estudian para las medidas de riesgo propuestas. Además, se obtienen estimadores semiparamétricos para las nuevas medidas, y son ejempli_cados considerando datos simulados y un conjunto de datos real de seguros. El Capítulo 3 se centra en la estimación extrema no paramétrica de las medidas multivariantes propuestas en el Capítulo 2. Para este propósito, primero analizamos el comportamiento en la cola de las distribuciones condicionadas que de_nen dichas medidas. El principal resultado está constituido por el Teorema Central del Límite de los estimadores extremos. El rendimiento de los estimadores extremos se evalúa en datos simulados y para un conjunto de datos real de precipitaciones. El estudio de la medida de riesgo multivariante asociada con the Component-wise Excess(C.-E.) design realization dada por Salvadori et, As a consequence of the need for regulators to manage risk in various sectors, a riskbased methodology is undergoing a fast expansion. Over recent decades, this problem has been mostly addressed via a univariate approach. However, risks usually involve several random variables that are often non-independent. Therefore, it is crucial to work in a multivariate setting. On the other hand, phenomena are frequently characterized by extreme events. This thesis is fundamentally concerned with two problems: the de_nition of risk measures in a multivariate setting, and the estimation of multivariate risk measures by taking extreme events into account. Chapter 1 is an introductory chapter. We present the state-of-art of the notion of multivariate risk measures. The main results in Copula Theory, Extreme Value Theory, and Stochastic Orders, which are useful in this work, are also provided. Two new multivariate risk measures are introduced in Chapter 2. Several interesting properties and, characterizations under Archimedean copulas, are studied for the proposed risk measures. Furthermore, semi-parametric estimators for the new measures are obtained and are then exempli_ed considering simulated data and a real insurance data-set. Chapter 3 deals with the non-parametric extreme estimation procedure of the multivariate measures proposed in Chapter 2. For this purpose, we _rst analyse the tail behaviour of the conditional distributions that de_ne the aforementioned measures. The main result is given by the Central limit Theorem of the extreme estimators. The performance of the extreme estimators is evaluated in simulated data and for a real rainfall data-set. The multivariate risk measure associated with the Component-wise Excess (C.-E.) design realization given by Salvadori et al. (2011) is outlined in Chapter 4. The explicit expression of the measure for Archimedean copulas is obtained. In addition, an extreme estimation procedure for the C.-E. design realization is provided and

CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2011) able to measure a financial institution’s contribution to systemic risk and its contribution to the risk of other financial institutions. CoVaR stands for conditional Value-at-Risk, i.e. it indicates the Value at Risk for a financial institution that is conditional on a certain scenario. In this paper, two alternative extensions of the classic univariate Conditional Value-at-Risk are introduced in a multivariate setting. The two proposed multivariate CoVaRs are constructed from level sets of multivariate distribution functions (resp. of multivariate survival distribution functions). These vector-valued measures have the same dimension as the underlying risk portfolio. Several characterizations of these new risk measures are provided in terms of the copula structure and stochastic orderings of the marginal distributions. Interestingly, these results are consistent with existing properties on univariate risk measures. Furthermore, comparisons between existent risk measures and the proposed multivariate CoVaR are developed. Illustrations are given in the class of Archimedean copulas. Estimation procedure for the multivariate proposed CoVaRs is illustrated in simulated studies and insurance real data.

The school is becoming the focus of policies on sport at school age in their educational aspect, placing teachers as responsible not only for planning, but management of school resources. This study aims to determine the degree of satisfaction of teachers-managers of Escuelas Deportivas that educational centers develop, according to different ways of management (municipalities, utility companies or associations of parents of students). The research was conducted with the participation of 440 subjects who were administered a questionnaire designed specifically to know their satisfaction. The results show significant differences in indicators of Technical Staff (p = .004), with a better appreciation for the councils, and Monitoring and Control by the Administration (p = .017), reflecting greater satisfaction in those cases where management was performed by utility companies, El centro educativo se está convirtiendo en el eje de las políticas en materia de deporte en edad escolar en su vertiente educativa, situando a los docentes como encargados no solo de la planificación, sino de la gestión de los recursos del centro escolar. Con este estudio se persigue conocer el grado de satisfacción de los docentes-responsables del programa Escuelas Deportivas que se desarrolla en centros educativos, atendiendo a sus diferentes formas de gestión (ayuntamientos, empresas de servicios o asociaciones de madres y padres de alumnos). La investigación se llevó a cabo con la participación de 440 docentes a los que se aplicó un cuestionario diseñado específicamente para conocer su grado de satisfacción. Los resultados obtenidos presentan diferencias significativas en los indicadores de Personal Técnico (p= .004), con una mejor satisfacción por parte de los ayuntamientos, y de Seguimiento y Control por parte de la Administración (p= .017), reflejando una mayor satisfacción en el caso de la gestión a través de empresas

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article.