Finite interval data, such as proportions, concentrations or rates, often exhibits asymmetryand heteroscedasticy in a regression setting, which can cause issues when tryingto model such data using common modelling approaches. Ferrari and Cribari-Neto, 2004 proposed a modeling approach similar to a generalized linear model, inwhich the response is assumed to be beta distributed, using an alternative parameterisationin terms of a mean and a precision parameter, and then modeled via a linkfunction depending on a linear predictor. The properties of the beta distributionthen accommodate for many of the issues inherent with interval data. This model,called beta regression, was later extended in Smithson and Verkuilen, 2006 to furtheraccount for heteroscedasticity, and then further and more formally developedin Simas, Barreto-Souza, and Rocha, 2010.In this thesis, an introduction to the beta regression model is given, and thena potential goodness of fit statistic for the beta regression model, based on nonparametric smoothing, is introduced, repurposed from a statistic in logistic regressiondeveloped in Cessie and Houwelingen, 1991. Then, through an extensive exploratorysimulation study, the behavior and performance of some of the availableinference tools for the beta regression model, such as point and interval estimators,is explored. Lastly, a simulated comparison study of the performance of the betaregression model to other alternatives is carried out.It is found that the goodness of fit statistic might have potential use, thoughit is suffering from low power. In some settings, point estimators of the dispersionparameter can exhibit considerable bias, resulting in confidence intervals of themean value parameters with below nominal coverage. This bias can in large part beavoided by the use of bias corrected estimators, though that in turn can introduceadditional, though less relevant problems in terms of coverage for the dispersionparameter. Comparing the beta regression model to other alternatives, it is found tohave as good or better performance, in terms of relative efficiency.

In this thesis we study the evolution of mass of asymptotically hyperbolic manifolds underRicci flow, following Balehowski and Woolgar [5]. Relying on Bahuaud [2] we assume shorttimeexistence of the flow, and derive the equations describing how the geometry of themanifold near infinity changes under the flow. In turn, we use these equations to findthe formula describing the evolution of the mass under the Ricci flow, in particular itsexponential decay in time. As an application, we discuss (again, following Balehowski andWoolgar [5]) how the Ricci flow technique can be used to prove the rigidity part of thepositive mass theorem for asymptotically hyperbolic manifolds.

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