Hannover, Univ., Diss., 2001. / Computerdatei im Fernzugriff.

Kaiserslautern, Techn. University, Diss., 2005.

Bochum, Universiẗat, Diss., 2004.

Hannover, University, Diss., 2001.

This work is devoted to simultaneously estimating the parameters of the distributions of several independent Poisson random variables. In particular, we explore the possibility of finding estimators of the Poisson parameters which have better performance than the maximum likelihood estimator (MLE). We first approach the problem from a fre-quentist point of view, employing a generally scaled loss function, called the k-normalized squared error loss function L[sub k] (λ, [sup ^]λ) = [sup P] ∑ [sub i=1] (λ[sub i] – [sup ^]λ[sub i])²/ λ[sup k][sub i], where k is a non-negative integer. The case k=0' is the squared error loss case, in which we propose a large class of estimators including those proposed by Peng [1975] as special cases. Estimators pulling the MLE towards a point other than zero as well as a point determined by the data itself are proposed, and it is shown that these estimators dominate the MLE uniformly. Under L[sub k] with k ≥ 1, we obtain a class of estimators dominating the MLE which includes the estimators proposed by Clevenson and Zidek [1975]. We next approach the problem from a Bayesian point, of view; a two-stage prior distribution is adopted and results for a large class of prior distributions are derived. Substantial savings in terms of mean squared error loss of the Bayes point estimators over the MLE are expected, especially when the Poisson parameters fall into a relatively narrow range. An empirical Bayes approach to the problem is carried out along the line suggested by Clevenson and Zidek [1975]. Some results are obtained which parallel those of Efron and Morris [1973], who work under the assumption that the random variables are normally distributed. We report the results of our computer simulation to quantitatively examine the performance of some of our proposed estimators. In most cases, the savings, under the appropriate loss functions, are an increasing function of the number of Poisson parameters. The simulation results indicate that our estimators are very promising. The savings of the Bayes estimators depend on the choice of prior hyperparameters, and hence proper choice leads to substantial improvement over the MLE. Although most of the results in this work are derived under the assumption that only one observation is taken from each Poisson distribution, we extend some results to the case where possibly more than one observation is taken. We conclude with suggestions for further work. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.

The need to model the quantum effects in semiconductor devices such as resonance tunneling diodes and quantum dots has lead to an intense study of the Wigner-Poisson (WP) and Schroedinger-Poisson (SP) systems. In this work we present the mathematical analysis of several related models for these systems. These include: a time-dependent model of dissipation in (SP), a quasi-linear (SP) system, a study of the stationary (WP)-(SP) problem with a discussion of the quantum analogue of classical BGK modes and a proof of existence of eigenfunctions for (SP) with periodic boundary conditions, and an examination of the stationary Wigner equations with inflow" boundary conditions. Finally, a proposed numerical scheme for the stationary (SP) system with Boltzmann distribution functions is shown along with its corresponding Bloch equation. / Ph. D.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

The key task for a search engine advertising system is, for each query that the search engine receives, to choose what advertisement should be displayed, and in what order. This ranking order has a strong impact on the revenue the search engine receives from the ads. Meanwhile, showing the user an advertisement that they prefer to click on improves user satisfaction. Therefore, it is reasonable to set up click-through rate (CTR) as a weighted ranking criteria. In this project, we aim to develop a model capable of accurately predicting CTR of ads in the system. For ads that have been displayed repeatedly, this is empirically measurable, but for new ads, other means must be used. Combining logistic regression model with L1 regularization we are able to predict CTR for new ads based on self-defined features. The ultimate goal is to improve the convergence and performance of our advertising system, consequently increasing both revenue and user satisfaction. Second part of this report is about a study on poisson factorization recommender evaluation. As recommender systems become more and more popular, many approaches have been suggested to evaluate the performance of traditional recommenders based on Gaussian distribution. However, few evaluating approaches were designed for poisson factorization recommender. This study checked some most common evaluation methods and discussed about their appropriateness in poisson factorization recommender evaluation. / text