Estimadores bayesianos de la fiabilidad con muestreo censurado

El estudio de la fiabilidad de componentes y sistemas tiene gran importancia en diversos campos de la ingenieria, y muy concretamente en el de la informatica. Al analizar la duracion de los elementos de la muestra hay que tener en cuenta los elementos que no fallan en el tiempo que dure el experimento, o bien los que fallen por causas distintas a la que es objeto de estudio. Por ello surgen nuevos tipos de muestreo que contemplan estos casos. El mas general de ellos, el muestreo censurado, es el que consideramos en nuestro trabajo. En este muestreo tanto el tiempo hasta que falla el componente como el tiempo de censura son variables aleatorias. Con la hipotesis de que ambos tiempos se distribuyen exponencialmente, el profesor Hurt estudio el comportamiento asintotico del estimador de maxima verosimilitud de la funcion de fiabilidad. En principio parece interesante utilizar metodos Bayesianos en el estudio de la fiabilidad porque incorporan al analisis la informacion a priori de la que se dispone normalmente en problemas reales. Por ello hemos considerado dos estimadores Bayesianos de la fiabilidad de una distribucion exponencial que son la media y la moda de la distribucion a posteriori. Hemos calculado la expansion asint6tica de la media, varianza y error cuadratico medio de ambos estimadores cuando la distribuci6n de censura es exponencial. Hemos obtenido tambien la distribucion asintotica de los estimadores para el caso m3s general de que la distribucion de censura sea de Weibull. Dos tipos de intervalos de confianza para muestras grandes se han propuesto para cada estimador. Los resultados se han comparado con los del estimador de maxima verosimilitud, y con los de dos estimadores no parametricos: limite producto y Bayesiano, resultando un comportamiento superior por parte de uno de nuestros estimadores. Finalmente nemos comprobado mediante simulacion que nuestros estimadores son robustos frente a la supuesta distribuci6n de censura, y que uno de los intervalos de confianza propuestos es valido con muestras pequenas. Este estudio ha servido tambien para confirmar el mejor comportamiento de uno de nuestros estimadores. SETTING OUT AND SUMMARY OF THE THESIS When we study the lifetime of components it's necessary to take into account the elements that don't fail during the experiment, or those that fail by reasons which are desirable to exclude from consideration. The model of random censorship is very usefull for analysing these data. In this model the time to failure and the time censor are random variables. We obtain two Bayes estimators of the reliability function of an exponential distribution based on randomly censored data. We have calculated the asymptotic expansion of the mean, variance and mean square error of both estimators, when the censor's distribution is exponential. We have obtained also the asymptotic distribution of the estimators for the more general case of censor's Weibull distribution. Two large-sample confidence bands have been proposed for each estimator. The results have been compared with those of the maximum likelihood estimator, and with those of two non parametric estimators: Product-limit and Bayesian. One of our estimators has the best behaviour. Finally we have shown by simulation, that our estimators are robust against the assumed censor's distribution, and that one of our intervals does well in small sample situation.

Forward Stagewise Naive Bayes

The naïve Bayes approach is a simple but often satisfactory method for supervised classification. In this paper, we focus on the naïve Bayes model and propose the application of regularization techniques to learn a naïve Bayes classifier. The main contribution of the paper is a stagewise version of the selective naïve Bayes, which can be considered a regularized version of the naïve Bayes model. We call it forward stagewise naïve Bayes. For comparison’s sake, we also introduce an explicitly regularized formulation of the naïve Bayes model, where conditional independence (absence of arcs) is promoted via an L 1/L 2-group penalty on the parameters that define the conditional probability distributions. Although already published in the literature, this idea has only been applied for continuous predictors. We extend this formulation to discrete predictors and propose a modification that yields an adaptive penalization. We show that, whereas the L 1/L 2 group penalty formulation only discards irrelevant predictors, the forward stagewise naïve Bayes can discard both irrelevant and redundant predictors, which are known to be harmful for the naïve Bayes classifier. Both approaches, however, usually improve the classical naïve Bayes model’s accuracy.

Determination of suitable irrigation lengths and intervals using capacitance humidity sensors for a sandy soil

production, during the summer of 2010. This farm is integrated at the Spanish research network for the sugar beet development (AIMCRA) which regarding irrigation, focuses on maximizing water saving and cost reduction. According to AIMCRA 0 s perspective for promoting irrigation best practices, it is essential to understand soil response to irrigation i.e. maximum irrigation length for each soil infiltration capacity. The Use of Humidity Sensors provides foundations to address soil 0 s behavior at the irrigation events and, therefore, to establish the boundaries regarding irrigation length and irrigation interval. In order to understand to what extent farmer 0 s performance at Tordesillas farm could have been potentially improved, this study aims to address suitable irrigation length and intervals for the given soil properties and evapotranspiration rates. In this sense, several humidity sensors were installed: (1) A Frequency Domain Reflectometry (FDR) EnviroScan Probe taking readings at 10, 20, 40 and 60cm depth and (2) different Time Domain Reflectometry (TDR) Echo 2 and Cr200 probes buried in a 50cm x 30cm x 50cm pit and placed along the walls at 10, 20, 30 and 40 cm depth. Moreover, in order to define soil properties, a textural analysis at the Tordesillas Farm was conducted. Also, data from the Tordesillas meteorological station was utilized.