Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

The informal market of education in Egypt: Private tutoring and its implications /// Arbeitspapiere / Institut für Ethnologie und Afrikastudien ; 88

Education is generally perceived as a public good which should be provided by the state. In Egypt, free and equal access to education has been guaranteed to all citizens since President Nasser’s socialist reforms in the 1950s. However, due to high population growth rates and a lack of financial resources, the public education system has been struggling to accommodate rapidly increasing numbers of students. While enrolment rates have risen steadily, the quality of state-provided services has deteriorated. Teachers and students have to cope with high class densities, insufficient facilities, a rigid syllabus and a centralized examination system. Today, teaching is among the lowest-paying occupations in the public sector. One strategy to cope with this situation is the widespread practice of private tutoring, which usually takes place at students’ homes or in commercial tutoring centers. Based on research carried out in Cairo in 2004/05 and 2006, I use an actor-centered approach to analyze the motivations of Egyptian teachers and students for participating in private tutoring and the impact that this practice has on the relationship between teachers and students. Students of all socio-economic backgrounds resort to tutoring in order to succeed in a highly competitive and exam-oriented education system. However, the form and quality of tutoring that can be accessed depends on the financial means of the family. For teachers, tutoring provides a good opportunity not only to supplement their income, but also, in the case of renowned “star teachers”, to improve their professional status and autonomy. On the informal “market of education” that has developed in Egypt during the last decades, the educational responsibilities of the state are increasingly being taken over by private actors, i.e. the process of teaching and learning is dissociated from the direct control of the state and from school as an institution. At the same time, education is turned into a marketable commodity. Despite the government’s efforts to provide free education to all citizens, the quality of social services that can be accessed in Egypt, thus, depends mainly on the financial means of the individual or the family.