Formula integrale di Poisson

Il tema centrale di questa tesi è lo studio del problema di Dirichlet per il Laplaciano in R^2 usando le serie di Fourier. Il problema di Dirichlet per il Laplaciano consiste nel determinare una funzione f armonica e regolare in un dominio limitato D quando sono noti i valori che f assume sul suo bordo. Ammette una sola soluzione, ma non esistono criteri generali per ricavarla. In questa tesi si mostra come la formula integrale di Poisson, sotto determinate condizioni, risolva il problema di Dirichlet in R^2 e in R^n.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Enamel loss and adhesive remnants following bracket removal and various clean-up procedures in vitro

This study evaluated the enamel loss and composite remnants after debonding and clean-up. The tested null hypothesis is that there are no differences between different polishing systems regarding removing composite remnants without damaging the tooth surface. Brackets were bonded to 75 extracted human molars and removed after a storage period of 100 hours. The adhesive remnant index (ARI) was evaluated. The clean-up was carried out with five different procedures: 1. carbide bur; 2. carbide bur and Brownie and Greenie silicone polishers; 3. carbide bur and Astropol polishers; 4. carbide bur and Renew polishers; and 5. carbide bur, Brownie, Greenie and PoGo polishers. Silicone impressions were made at baseline (T0) and after debonding (T1) and polishing (T2) to produce plaster replicas. The replicas were analysed with a three-dimensional laser scanner and measured with analytical software. Statistical analysis was performed with the Kruskal-Wallis test and pairwise Wilcoxon tests with Bonferroni-Holm adjustment (α = 0.05). Enamel breakouts after debonding were detectable in 27 per cent of all cases, with a mean volume loss of 0.02 mm(3) (±0.03 mm(3)) and depth of 44.9 μm (±48.3 μm). The overall ARI scores was 3 with a few scores of 1 and 2. The composite remnants after debonding had a mean volume of 2.48 mm(3) (±0.92 mm(3)). Mean volume loss due to polishing was 0.05 mm(3) (±0.26 mm(3)) and the composite remnants had a mean volume of 0.22 mm(3) (±0.32 mm(3)). There were no statistically significant differences in volumetric changes after polishing (P = 0.054) between the different clean-up methods. However, sufficient clean-up without enamel loss was difficult to achieve.

Comparative assessment of clinical performance of esthetic bracket materials

To compare the alterations in esthetic appearance and slot morphology/integrity of two main types of esthetic brackets caused after clinical use.

Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.