Les processus déterminantaux ont généré de l’intérêt dans des domaines très divers, tels que les matrices aléatoires, la théorie des processus ponctuels, ou les réseaux. Dans ce manuscrit, nous les considérons comme un type de processus ponctuel, c’est-à-dire comme un groupement de points aléatoires dans un espace très général. Ainsi, nous avons accès à une grande variété d’outils provenant de la théorie des processus ponctuels, ce qui permet une analyse précise d’un grand nombre de leur propriétés. Nous commençons par une analyse des processus déterminantaux d’un point de vue applicatif. Nous proposons ainsi différentes méthodes pour leur simulation dans un cadre général. Nous présentons une série de modèles dérivés du processus de Ginibre, et qui se trouvent être très utiles dans les applications. Troisièmement, nous introduisons un gradient différentiel sur l’espace des processus ponctuels. Grâce à des outils puissants de la théorie générale des formes de Dirichlet, nous montrons une formule d’intégration par parties pour un processus ponctuel général, et prouvons l’existence de diffusions correctement associées à ces processus. Nous sommes en mesure d’appliquer ces résultats aux processus déterminantaux, ce qui mènera à une caractérisation de ces diffusions en termes d’équations différentielles stochastiques. Enfin, nous nous intéressons au gradient différence. Dans un certain sens, nous définissons alors une intégrale de Skohorod qui satisfait une formule d'intégration par parties, c’est-à-dire que son adjoint est le gradient différence. Une application à l’étude d’une transformation aléatoire du processus ponctuel est présentée, dans laquelle nous caractérisons la distribution du processus ponctuel transformé sous certaines conditions. / Determinantal point processes have sparked interest in very diverse fields, such as random matrix theory, point process theory, and networking. In this manuscript, we consider them as random point processes, i.e. a stochastic collection of points in a general space. Hence, we are granted access to a wide variety of tools from point process theory, which allows for a precise study of many of their probabilistic properties. We begin with the study of determinantal point processes from an applicative point of view. To that end, we propose different methods for their simulation in a very general setting. Moreover, we bring to light a series of models derived from the well-known Ginibre point process, which are quite suited for applications. Thirdly, we introduce a differentiable gradient on the considered probability space. Thanks to some powerful tools from Dirichlet form theory, we discuss integration by parts for general point processes, and show the existence of the associated diffusion processes correctly associated to the point processes. We are able to apply these results to the specific case of determinantal point processes, which leads us to characterizing these diffusions in terms of stochastic differential equations. Lastly, we turn our attention to the difference gradient on the same space. In a certain sense, we define a Skohorod integral, which satisfies an integration by parts formula, i.e. its adjoint is the difference operator. An application to the study of a random transformation of the point process is given, wherein we characterize the distribution of the transformed point process under mild hypotheses.

This thesis covers non-homogeneous Poisson processes along with estimation of the intensity (rate) function and some selected simulation methods. In Chapter 1 the main properties of a non-homogeneous Poisson process are summarized. The main focus of Chapter 2 is the general maximum likelihood estimation procedure adjusted to a non-homogeneous Poisson process, together with some recommen- dations about calculation of the initial estimates of the intensity function param- eters. In Chapter 3 some general simulation methods as well as the methods designed specially for log linear and log quadratic rate functions are discussed. Chapter 4 contains the application of the described estimation and simulation methods on real data from non-life insurance. Furthermore, the considered sim- ulation methods are compared with respect to their time efficiency and accuracy of the simulations. 1

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Speech recognition threshold (SRT) is an important clinical measure that validates the pure-tone average (PTA), assists in diagnosis and prognosis of hearing and hearing impairment, and helps identify non-organic hearing impairment. Few published, recorded, and standardized materials exist in languages other than English, which results in audiologists testing individuals using materials developed in a non-native language. Research shows that this is problematic, as certain criterion for SRT testing are not met. Thus, performance may reflect test-language deficiency rather than hearing impairment. Currently, there are no known published materials for use in measuring the SRT in individuals whose native language is Tongan. The purpose of this project was to record and develop psychometrically equivalent words in Tongan for measuring the SRT. This study identified 28 trisyllabic words that were relatively homogenous in relation to audibility and psychometric function slope. The intensity of these 28 words was adjusted to equate 50% threshold performance for each word with the mean PTA (5.92 dB HL) for the twenty normally hearing participants. These materials were digitally recorded onto compact disc for distribution and use for SRT testing in Tongan.

No description available.

The speech recognition threshold (SRT) is an important measure, as it validates the pure-tone average (PTA), assists in the diagnosis and prognosis of hearing impairments, and aids in the identification of non-organic hearing impairments. Research has shown that in order for SRT testing to yield valid and reliable measures, testing needs to be performed in the patient's native language. There are currently no published materials for SRT testing in the Samoan language. As a result, audiologists are testing patients with English materials or other materials not of the patient's native language. Results produced from this manner of testing are confounded by the patient's vocabulary knowledge and may reflect a language deficit rather than a hearing loss. The present study is aimed at developing SRT materials for native speakers of Samoan to enable valid and reliable measures of SRT for the Samoan speaking population. This study selected 28 trisyllabic Samoan words that were found to be relatively homogeneous in regard to audibility and psychometric function slope. Data were gathered on 20 normal hearing native speakers of Samoan and the intensity of each selected word was adjusted to make the 50% performance threshold of each word equal to the mean PTA of the 20 research participants (5.33 dB HL). The final edited words were digitally recorded onto compact disc to allow for distribution and use for SRT testing in Samoan.

In addition to the use of pure-tones for testing hearing, speech signals are highly valuable diagnostic tools for identifying and evaluating hearing impairment. Speech audiometry involves the implementation of such signals in the measurement of hearing acuity. One aspect of speech audiometry involves assessment of the speech recognition threshold (SRT) which evaluates an individual's ability to hear and understand speech. While live speech has been used in the past to assess SRT, recorded materials are preferred and have been shown to be advantageous over live speech. High-quality digitally recorded speech audiometry materials have been available in English for some time, but assessment of individuals using speech materials from a language that they do not speak natively has been shown to be both inadequate and inaccurate. Speech audiometry materials have recently become available in many languages. Currently, however, there are no known published recordings for assessment of SRT in the Tagalog language. The goal of this study was to develop psychometrically equivalent speech audiometry materials for measuring speech recognition threshold in Tagalog. During this study Tagalog words were initially recorded by a native speaker selected for accent and vocal quality. The words were reduced down to 90 words to be evaluated in the study. Each of the 90 trisyllabic words were evaluated at 2 dB increments from -10 to 16 dB HL by 20 native Tagalog speakers, all having normal hearing. Based on the results, 34 trisyllabic Tagalog words were selected based on their familiarity to native listeners, relative homogeneity with regards to audibility and psychometric function slope. Each word was then adjusted to make the 50% performance threshold equal to the mean PTA of the 20 research participants (4.3 dB HL). The final edited words were then digitally recorded onto compact disc for distribution and for use in assessing SRT in native Tagalog speakers worldwide.

This dissertation aims to develop statistical methodologies for estimating the effects of time-fixed and time-varying factors in recurrent events modeling context. The research is motivated by the traffic safety research question of evaluating the influence of crash on driving risk and driver behavior. The methodologies developed, however, are general and can be applied to other fields. Four alternative approaches based on various data settings are elaborated and applied to 100-Car Naturalistic Driving Study in the following Chapters. Chapter 1 provides a general introduction and background of each method, with a sketch of 100-Car Naturalistic Driving Study. In Chapter 2, I assessed the impact of crash on driving behavior by comparing the frequency of distraction events in per-defined windows. A count-based approach based on mixed-effect binomial regression models was used. In Chapter 3, I introduced intensity-based recurrent event models by treating number of Safety Critical Incidents and Near Crash over time as a counting process. Recurrent event models fit the natural generation scheme of the data in this study. Four semi-parametric models are explored: Andersen-Gill model, Andersen-Gill model with stratified baseline functions, frailty model, and frailty model with stratified baseline functions. I derived model estimation procedure and and conducted model comparison via simulation and application. The recurrent event models in Chapter 3 are all based on proportional assumption, where effects are constant. However, the change of effects over time is often of primary interest. In Chapter 4, I developed time-varying coefficient model using penalized B-spline function to approximate varying coefficients. Shared frailty terms was used to incorporate correlation within subjects. Inference and statistical test are also provided. Frailty representation was proposed to link time-varying coefficient model with regular frailty model. In Chapter 5, I further extended framework to accommodate multi-type recurrent events with time-varying coefficient. Two types of recurrent-event models were developed. These models incorporate correlation among intensity functions from different type of events by correlated frailty terms. Chapter 6 gives a general review on the contributions of this dissertation and discussion of future research directions. / Ph. D.

La escasez de registros sísmicos de gran magnitud en algunas regiones del mundo limita la determinación de la respuesta sísmica de una edificación. En este sentido, los acelerogramas artificiales representan una alternativa para definir el evento sísmico porque consideran las condiciones específicas del sitio en estudio. Esta investigación analiza la respuesta sísmica de las estructuras para diversos registros sísmicos artificiales generados de espectros de diseño para distintas condiciones geotécnicas. El procedimiento de análisis empleado será el dinámico tiempo historia no lineal para obtener una mayor precisión en la respuesta sísmica. Los resultados obtenidos muestran que las derivas de entrepiso de las señales artificiales creadas con la función de intensidad de Liu se ajustan mejor a las derivas obtenidas del sismo real escalado. / The lack of large seismic records in some world regions limits the determination of the seismic response of a building. For that reason, artificial accelerograms represent an alternative to define the seismic event because they consider specific conditions of study site. This research analyses the structures seismic response for various artificial seismic records generated from design spectra and different geotechnical conditions. Dynamic nonlinear time history analyzing was used to obtain greater precision in the seismic response. The results obtained show that the mezzanine drifts of the artificial signals created with the Liu intensity function better fit the drifts obtained from the scaled real earthquake. / Trabajo de investigación