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Στις διακριτές κατανομές η εύρεση εκτιμητών μεγίστης πιθανοφάνειας παρουσιάζει δυσκολίες κυρίως όταν οι πιθανότητες δεν εκφράζονται με αναλυτικό τύπο και δίνονται αναγωγικά. Τέτοιες κλάσεις αποτελούν η συνέλιξη κατανομών και οι επιγενείς κατανομές. Στην παρούσα διπλωματική αντικείμενό μας είναι η παρουσίαση των ιδιοτήτων των εκτιμητών μεγίστης πιθανοφάνειας σε αυτές τις οικογένειες. Αποδεικνύεται ότι μια από τις εξισώσεις συμπίπτει με την εξίσωση που προέρχεται από τη μέθοδο των ροπών για τον δειγματικό μέσο. Έτσι σε περιπτώσεις κατανομών με δύο παραμέτρους, όπως η Charlier και η Neyman που παρουσιάζονται αναλυτικά, μόνο μια εξίσωση χρειάζεται να λυθεί επαναληπτικά για την εύρεση των εκτιμητών. Ο πληθυσμιακός μέσος επίσης αποτελεί τη βασική παράμετρο που μπορεί να χρησιμοποιηθεί σε ένα ορθογώνιο μετασχηματισμό των παραμέτρων της υπό μελέτη κατανομής. Η παραμετρικοποίηση αυτή εξαλείφει την υψηλή συσχέτιση μεταξύ των αρχικών παραμέτρων και επιτυγχάνει τη διάκριση όσον αφορά την πληροφορία που είναι σχετική με αυτές. Συγκεκριμένα παραδείγματα με τα οποία ασχοληθήκαμε είναι στις συνελίξεις δύο κατανομών η Delaporte καθώς και στις επιγενείς κατανομές η Hermite. / -

Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02-26Bitstream added on 2014-06-13T19:53:23Z : No. of bitstreams: 1 diniz_ec_me_rcla.pdf: 610866 bytes, checksum: 86834ae8acca4f4532e7d39107c9c8c7 (MD5) / Modelos de geração de precipitações são de extrema importância nos dias atuais, pois com o conhecimento do padrão de precipitação em certa área, pode-se planejar obras de forma a minimizar os efeitos das precipitações de grande intensidade. No presente trabalho, aplica-se o modelo de Neyman-Scott e, particularmente, o de Poisson na geração de precipitações de grande intensidade na região da Bacia do Tietê Superior, no Estado de São Paulo, Brasil. Essa região sofre anualmente com as enchentes devido às fortes precipitações e a alta densidade populacional nesta área. Para a aplicação dos modelos de distribuição espacial de precipitações Neyman-Scott e Poisson, foram considerados os dados coletados de 1980 a 1997 de uma rede pluviométrica constituída de treze pluviômetros. / Models related with precipitations generation have extremely importance nowadays because with the standard knowledge about an specific area, we can plan projects to minimize the effects caused by high intensity precipitations. At the present work, we applies Neyman-Scott s model and particularly the one from Poisson, in the precipitations generations with high intensity in the Superior Tietê Bays region, São Paulo state, Brazil. This region suffer annually with the floods due to the strong precipitations and the high human density. To use the Neyman-Scott and Poisson models related to spatial precipitations distribution, we have considered data collected during 1980 to 1997 from a pluviometric network consisted by thirteen rain gauges.

A search for vector-like quarks (VLQs) decaying to a Z boson using multi-stage machine learning was compared to a search using a standard square cuts search strategy. VLQs are predicted by several new theories beyond the Standard Model. The searches used 20.3 inverse femtobarns of proton-proton collisions at a center-of-mass energy of 8 TeV collected with the ATLAS detector in 2012 at the CERN Large Hadron Collider. CLs upper limits on production cross sections of vector-like top and bottom quarks were computed for VLQs produced singly or in pairs, Tsingle, Bsingle, Tpair, and Bpair. The two stage machine learning classification search strategy did not provide any improvement over the standard square cuts strategy, but for Tpair, Bpair, and Tsingle, a third stage of machine learning regression was able to lower the upper limits of high signal masses by as much as 50%. Additionally, new test statistics were developed for use in the Neyman construction of confidence regions in order to address deficiencies in current frequentist methods, such as the generation of empty set confidence intervals. A new method for treating nuisance parameters was also developed that may provide better coverage properties than current methods used in particle searches. Finally, significance ratio functions were derived that allow a more nuanced interpretation of the evidence provided by measurements than is given by confidence intervals alone.

We introduce the notion of diversity order as a performance measure for distributed radar systems. We define the diversity order of a radar network as the slope of the probability of detection (PD) versus SNR evaluated at PD =0.5. We prove that the communication bandwidth between the sensors and the fusion center does not affect the growth in diversity order. We also prove that the OR rule leads to the best performance and its diversity order grows as (log K). We then introduce the notion of a random radar network to study the effect of geometry on overall system performance. We approximate the distribution of the SINR at each sensor by an exponential distribution, and we derive the moments for a specific system model. We then analyze multistatic systems and prove that each sensor should be large enough to cancel the interference in order to exploit the available spatial diversity.

We introduce the notion of diversity order as a performance measure for distributed radar systems. We define the diversity order of a radar network as the slope of the probability of detection (PD) versus SNR evaluated at PD =0.5. We prove that the communication bandwidth between the sensors and the fusion center does not affect the growth in diversity order. We also prove that the OR rule leads to the best performance and its diversity order grows as (log K). We then introduce the notion of a random radar network to study the effect of geometry on overall system performance. We approximate the distribution of the SINR at each sensor by an exponential distribution, and we derive the moments for a specific system model. We then analyze multistatic systems and prove that each sensor should be large enough to cancel the interference in order to exploit the available spatial diversity.

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We consider the problem of extracting a specific feature from a noisy signal generated by a multi-channels Remote Field Eddy Current Sensor. The sensor is installed on a mobile robot whose mission is the detection of anomalous regions in metal pipelines. Given the presence of noise that characterizes the data series, anomaly signals could be masked by noise and therefore difficult to identify in some instances. In order to enhance signal peaks that potentially identify anomalies we consider an entropy filter built on a-posteriori probability density functions associated with data series. Thresholds based on the Neyman-Pearson criterion for hypothesis testing are derived. The algorithmic tool is applied to the analysis of data from a portion of pipeline with a set of anomalies introduced at predetermined locations. Critical areas identifying anomalies capture the set of damaged locations, demonstrating the effectiveness of the filter in detection with Remote Field Eddy Current Sensor.

Resumo: Modelos de geração de precipitações são de extrema importância nos dias atuais, pois com o conhecimento do padrão de precipitação em certa área, pode-se planejar obras de forma a minimizar os efeitos das precipitações de grande intensidade. No presente trabalho, aplica-se o modelo de Neyman-Scott e, particularmente, o de Poisson na geração de precipitações de grande intensidade na região da Bacia do Tietê Superior, no Estado de São Paulo, Brasil. Essa região sofre anualmente com as enchentes devido às fortes precipitações e a alta densidade populacional nesta área. Para a aplicação dos modelos de distribuição espacial de precipitações Neyman-Scott e Poisson, foram considerados os dados coletados de 1980 a 1997 de uma rede pluviométrica constituída de treze pluviômetros. / Abstract: Models related with precipitations generation have extremely importance nowadays because with the standard knowledge about an specific area, we can plan projects to minimize the effects caused by high intensity precipitations. At the present work, we applies Neyman-Scott’s model and particularly the one from Poisson, in the precipitations generations with high intensity in the Superior Tietê Bays’ region, São Paulo state, Brazil. This region suffer annually with the floods due to the strong precipitations and the high human density. To use the Neyman-Scott and Poisson models related to spatial precipitations distribution, we have considered data collected during 1980 to 1997 from a pluviometric network consisted by thirteen rain gauges. / Orientador: Roberto Naves Domingos / Coorientador: José Silvio Govone / Banca: José Manoel Balthazar / Banca: Marco Aurélio Sicchiroli Lavrador / Mestre

We consider the problem of extracting a specific feature from a noisy signal generated by a multi-channels Remote Field Eddy Current Sensor. The sensor is installed on a mobile robot whose mission is the detection of anomalous regions in metal pipelines. Given the presence of noise that characterizes the data series, anomaly signals could be masked by noise and therefore difficult to identify in some instances. In order to enhance signal peaks that potentially identify anomalies we consider an entropy filter built on a-posteriori probability density functions associated with data series. Thresholds based on the Neyman-Pearson criterion for hypothesis testing are derived. The algorithmic tool is applied to the analysis of data from a portion of pipeline with a set of anomalies introduced at predetermined locations. Critical areas identifying anomalies capture the set of damaged locations, demonstrating the effectiveness of the filter in detection with Remote Field Eddy Current Sensor.