In a regression context, the aim is to analyse a response variable of interest conditional to a set of covariates. In many applications the response variable is discrete. Examples include the event of surviving a heart attack, the number of hospitalisation days, the number of times that individuals benefit of a health service, and so on. This thesis advances the methodology and the application of regression models with discrete response. First, we present a difference-in-differences approach to model a binary response in a health policy evaluation framework. In particular, generalized linear mixed methods are employed to model multiple dependent outcomes in order to quantify the effect of an adopted pay-for-performance program while accounting for the heterogeneity of the data at the multiple nested levels. The results show how the policy had a positive effect on the hospitals' quality in terms of those outcomes that can be more influenced by a managerial activity. Next, we focus on regression models for count response variables. In a parametric framework, Poisson regression is the simplest model for count data though it is often found not adequate in real applications, particularly in the presence of excessive zeros and in the case of dispersion, i.e. when the conditional mean is different to the conditional variance. Negative Binomial regression is the standard model for over-dispersed data, but it fails in the presence of under-dispersion. Poisson-Inverse Gaussian regression can be used in the case of over-dispersed data, Generalised-Poisson regression can be employed in the case of under-dispersed data, and Conway-Maxwell Poisson regression can be employed in both cases of over- or under-dispersed data, though the interpretability of these models is ot straightforward and they are often found computationally demanding. While Jittering is the default non-parametric approach for count data, inference has to be made for each individual quantile, separate quantiles may cross and the underlying uniform random sampling can generate instability in the estimation. These features motivate the development of a novel parametric regression model for counts via a Discrete Weibull distribution. This distribution is able to adapt to different types of dispersion relative to Poisson, and it also has the advantage of having a closed form expression for the quantiles. As well as the standard regression model, generalized linear mixed models and generalized additive models are presented via this distribution. Simulated and real data applications with different type of dispersion show a good performance of Discrete Weibull-based regression models compared with existing regression approaches for count data.

Diplomová práce představuje vytvoření softwarového 2D MKP modelu přehrady Slezská Harta v České Republice za pomoci softwaru PLAXIS 2D. V úvodu práce je analýza vodní nádrže, vytvořené jako zásobárna vody a protipovodňové dílo. Analýza sleduje geomorfologii, geologii, konstrukci tělesa hráze, použité materiály a metody, a stávající monitorovací zařízení. Pro pochopení tvorby 2D MKP modelu jsou předloženy a definované metody použitých analýz - metoda konečných prvků, analýza prosakování, materiálové modely, citlivostná analýza. Následně byla definována tvorba struktury modelu - určení posloupnosti použitých analýz, definování vstupních dat a mezních podmínek a tvorba kalibračního segmentu. V závěrečné části práce je analýza dosažených výstupů rozsáhlého testování modelu, jejich korelace s reálnými naměřenými hodnotami a celkové shrnutí přínosu vytvořeného modelu pro jeho využití při předpovídání chování přehrady v extrémních případech.