Abstract

Abstract

Abstract
Predictive modelling is a process used in predictive analytics to create a statistical model of future behaviour. Predictive analytics is the area of data mining concerned with forecasting probabilities and trends. On the other hand, Artificial Intelligence (AI) concerns itself with intelligent behaviour, i.e. the things that make us seem intelligent. Following this process of thinking, in this work the main goal is the assessment of the impact of using AI based tools for the development of intelligent predictive models, in particular those that may be used to establish the conditions in which the levels of manganese and turbidity in water supply are high. Indeed, one of the main problems that the water treatment plant at Monte Novo (in Evora, Portugal) uncovers is the appearance of high levels of manganese and turbidity in treated water, which sometimes exceed the parametric values established in Portuguese Law, respectively 50 mu g dm(-3) and 4 NTU. In this study we tried to find answers to the above problem by building predictive models. The models we developed shall enable the prediction of manganese and turbidity levels in treated water, in order to ensure that the water supply does not affect public health in a negative way and obeys the current legislation. The software used in this study was the Clementine 11.1. The C5.0 Algorithm was also used as a means of introducing Decision Trees and the K-Means Algorithm was used to construct clustering models. The data in the database was collected from 2005 to 2006 and includes reservoir water quality data, treated water data and volumes of water stored in the reservoir.

Abstract
We present a new R&D investment function in a Cournot competition model inspired in the logistic equation. We do a full characterization of the associated game and study the short- and long-term economical effects derived from using this new R&D investment function. In particular, we find the existence of regions with multiple Nash investment equilibria. For low production costs, that can correspond to the production of old technologies, the long-term economical effects are not very sensitive to small changes in the efficiency of the R&D programmes neither to small changes in the market structure. However, for high production costs, that can correspond to the production of new technologies, the long-term economical effects are very sensitive to small changes in the efficiency of the R&D programmes and also to small changes in the market structure.

Abstract
The von Mises-Fisher distribution is widely used for modeling directional data. In this article, we derive the discriminant rules based on this distribution to assign objects into pre-existing classes. We determine a distance between two von Mises-Fisher populations and we calculate estimates of the misclassification probabilities. We also analyze the behavior of the distance between two von Mises-Fisher populations and of the estimates of the misclassification probabilities when we modify the parameters of the populations or the samples size or the dimension of the sphere. Finally, we present an example with real spherical data available in the literature.

Abstract
The Watson distribution is one of the most used distributions for modeling axial data. In some situations, it is important to investigate if several Watson populations differ significantly. In this paper, we develop likelihood ratio tests and the ANOVA for testing the hypothesis of the equality of the directional parameters of several Watson distributions with different concentrations. We also determine the empirical power of the ANOVA and LR tests for some dimensions of the sphere.