An important prerequisite for running a successful insurance business is to predict risk. By forecasting the future in as much detail as possible, competitive advantages are created in terms of price differentiation. This work aims at using spatial point processes to provide a proposal for how the geographical position of the customer can be used in developing risk differentiation tools. For spatial variation in claim frequency an approach is presented which is common in spatial epidemiology by considering a group of policyholders, with and without claims, as a realisation of a multivariate Poisson point process in two dimensions. Claim costs are then included by considering the claims as a realisation of a point process with continuous marks. To describe the spatial variation in relative risk, demographic and socio-economic information from Swedish agencies have been used. The insurance data that have been used come from the insurance company If Skadeförsäkring AB, where also the work has been carried out. The result demonstrates problems with parametric modelling of the intensity of policyholders, which makes it difficult to validate the spatial varying intensity of claim frequency. Therefore different proposals of non-parametric estimation are discussed. Further, there are no tendencies that the selected information is able to explain the variation in claim costs. / En viktig förutsättning för att kunna bedriva en framgångsrik försäkringsverksamhet är att prediktera risk. Genom att på en så detaljerad nivå som möjligt kunna förutse framtiden skapas konkurrensfördelar i form av prisdifferentiering. Målet med detta arbete är att med hjälp av spatiala punktprocesser ge ett förslag på hur kunders geografiska position kan utvecklas som riskdifferentieringsverktyg. För spatial variation i skadefrekvens presenteras ett tillvägagångssätt som är vanligt inom spatial epidemiologi genom att betrakta en grupp försäkringstagare, med och utan skador, som en realisering av en multivariat Poissonprocess i två dimensioner. Skadekostnaderna inkluderas sedan genom att betrakta skadorna som en punktprocess med kontinuerliga märken. För att beskriva spatial variation i relativ risk används demografisk och socioekonomisk information från svenska myndigheter. De försäkringsdata som använts kommer från If Skadeförsäkring AB, där också arbetet har utförts. Resultatet påvisar problem med att parametriskt modellera intensiteten för försäkringstagare, vilket medför svårigheter att validera den skattade spatiala variationen i skadefrekvens, varför olika ickeparametriska förslag diskuteras. Vidare upptäcktes inga tendenser till att variationen i skadekostnad kan förklaras med den utvalda informationen.

Functional Magnetic Resonance Imaging (fMRI) is a noninvasive imaging method that reflects local changes in brain activity. FMRI group studies involves the analysis of the functional images acquired for each of a group of subjects under the same experimental conditions. We propose a spatial marked point-process model for the activation patterns of the subjects in a group study. Each pattern is described as the sum of individual centres of activation. The marked point-process that we propose allows the researcher to enforce repulsion between all pairs of centres of an individual subject that are within a specified minimum distance of each other. It also allows the researcher to enforce attraction between similarly-located centres from different subjects. This attraction helps to compensate for the misalignment of corresponding functional areas across subjects and is a novel method of addressing the problem of imperfect inter-subject registration of functional images. We use a Bayesian framework and choose prior distributions according to current understanding of brain activity. Simulation studies and exploratory studies of our reference dataset are used to fine-tune the prior distributions. We perform inference via Markov chain Monte Carlo. The fitted model gives a summary of the activation in terms of its location, height and size. We use this summary both to identify brain regions that were activated in response to the stimuli under study and to quantify the discrepancies between the activation maps of subjects. Applied to our reference dataset, our measure is successful in separating out those subjects with activation patterns that do not agree with the overall group pattern. In addition, our measure is sensitive to subjects with a large number of activation centres relative to the other subjects in the group. The activation summary given by our model makes it possible to pursue a range of inferential questions that cannot be addressed with ease by current model-based approaches.

We study the minimum radius required for connectivity (CTR Critical Transmission Range) within homogeneous stationary Wireless Sensor Networks (WSN) topology control, considering different levels of attractivity within the sensors. Due to the complexity of dealing with this problem from a theoretical viewpoint, a Monte Carlo experience is devised for estimating the CTR distribution. With this information, we propose optimization procedures that, using as additional input a few known parameters (overall available budget, sensor cost, maximum available transmission radius, minimum probability of connectivity, environmental path loss and deployment cost) leads to the decision of the number and type of sensors to be acquired, their optimal communication radius and the ideal deployment strategy that maximize the WSN lifetime. As a previous result, the accuracy of several computational platforms for statistical computing was assessed, being the main conclusion that R (http://www.r-project.org) is the best choice / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresentamos a caracterização do raio de transmissão mínimo necessário para garantir conectividade, CTR (Critical Transmission Range), num cenário de controle de topologia em RSSF homogêneas e estacionárias. Dada a complexidade de se trabalhar com modelos analíticos, por meio de experiências Monte Carlo obtemos um estimador da distribuição do CTR sobre processos pontuais espaciais que descrevem o posicionamento dos nós sensores no ambiente para diferentes níveis de atratividade. Propomos modelos de otimização práticos que consideram diversos fatores conhecidos a priori pelo projetista como, por exemplo, os preços de diversos sensores, o raio de transmissão máximo disponível pelo sensor, os custos de posicionamento no ambiente (função da atratividade), o orçamento total do projeto, a probabilidade de conectividade mínima admissível e o exponente de path loss do ambiente. O modelo determina quais e quantos sensores devem ser comprados, com que raio de transmissão devem ser configurados e qual o preço conveniente a pagar pelo posicionamento (função da atratividade), para maximizar o tempo de vida de uma RSSF. Para guiar a escolha da plataforma de simulação e análise de dados, vários resultados a respeito de precisão numérica são apresentados, obtidos aplicando protocolos de avaliação já consolidados. Desta análise, determinamos que R (http://www.r-project.org) é a melhor escolha

Anonymous Call Detail Records (CDR’s) from mobile phone towers provide a unique opportunity to aggregate individual location data to overall human mobility patterns. Flowminder uses this data to improve the welfare of low- and middle-income countries. The movement patterns are studied through key measurements of mobility. This thesis seeks to evaluate the estimates of key measurements obtained with mobile phone towers through simulation of continuous human movement on a linear network. Simulation is made with an agent based approach. Spatial point processes are used to distribute continuous start points of the agents on the linear network. The start point is then equipped with a mark, a path with an end point dependent on the start point. A path from the start point to the end point of an agent is modeled with a Markov Decision Process. The simulated human movement can then be captured with different types of mobile phone tower distributions realized from spatial point processes. The thesis will initially consider homogeneous Poisson and Simple Sequential Inhibition (SSI) processes on a plane and then introduce local clusters (heterogeneity) with Matérn Cluster and SSI processes. The goal of the thesis is to investigate the effects of change in mobile phone tower distribution and call frequency on the estimates of key measurements of mobility. The effects of call frequency are unclear and invite more detailed study. The results suggest that a decrease in the total number of towers generally worsens the estimates and that introducing local clusters also has a negative effect on the estimates. The presented methodology provides a flexible and new way to model continuous human movement along a linear network.