Análisis reflexivo de la práctica docente

The mesh in our experiment is a 10µm thin gold foil with small holes of 5µm diameter which are arranged in a rectangular grid pattern with spacings equal to or a multiple of the CCD structure e.g. 150µm in x and y direction for a CCD with 75_×75µm2 _pixels.

The mesh is placed directly in front of the CCD and blocks the homogenous illumination with X-rays from entering the CCD except for the given holes. A slight rotation of the mesh with respect to the CCD structure leads to different placements of the holes over the respective pixels as shown in figure 2.39. Under the assumption that all pixels behave equally the holes sample thus the whole area of a pixel and define isolated incident positions for photons.

Figure 2.39: The mesh-experiment: A small rotation of the mesh structure with respect to the pixel structure places the holes over different parts of the individual pixels.

The main target of the mesh-experiment is to understand the detector behaviour. The charge splitting is caused by diffusion and electrostatic repulsion of the charge carriers during their drift time. The charge splitting thus also depends on the electric field which affects the electrons as they drift to the front side into the potential minimum. Knowing how the electron cloud is split among different pixels due to the electric fields for each specific incident position will help to understand the detector behaviour.

An interesting byproduct of the mesh-experiment is the possibility to generate training data for the reconstruction of the incident position. Real experimental data could then replace the data coming from Monte Carlo simulations. As will be discussed in section 3.10 the usage of experimental data should of course be preferred. To have training data means to know the correct incident position for each event. This information is then used to teach a reconstruction method. The mesh experiment offers this unique possibility: to see real events in the detector and to know in addition where they come from because the position of the respective mesh hole is known (appendix B.2 will show how the position and angle of the mesh relative to the CCD can be determined).

Chapter 3

Statistical Learning for Physics

Experiments

In this chapter the basic concepts and properties of statistical learning will be explained. The emphasis is put on the motivation why and in which case statistical learning methods should be used and on the way they are applied correctly. Most of the mathematical background is skipped here and will be dealt with in the next chapter.

The terminology and all the examples are closely related to the application of statistical learning to physics experiments. Nevertheless all comments and advices apply also to other fields of application.

The next few sections (3.1 to 3.6) start with an introduction to statistical learning and present the most basic concepts and notions. Afterwards (sections 3.7 to 3.10) the classi- cal alternatives to statistical learning and the most common motivations to use statistical learning methods will be discussed. In the following sections (3.11 to 3.13) the correct handling and control of statistical learning methods during the training and in the perfor- mance evaluation will be explained including the calculation of statistical und systematic uncertainties. This chapter ends with a description of the data mining capabilities of sta- tistical learning methods (section 3.14) and with a guide to compare learning methods in a statistically correct way (section 3.15).

3.1

Statistical Learning in the World of Artificial In-

telligence

Historically the development of artificial neural networks as simplified models of the human brain was one of the fundamental starting points of artificial intelligence and signified the desire to make machines “intelligent”, similar to humans. Other starting points made use of knowledge databases or tried to induce logical rules. Whereas the structure of neural networks was derived from the first insights into the structure of the brain (mainly of animals but also of humans), the idea behind the neural network training is clearly induced by psychology. Supervised learning, the interaction between a flexible learner and a precise teacher, is still one of the most fundamental and successful paradigms of today’s artificial intelligence (AI). Although the focus of current AI research shifted to agent-based systems, distributed learning and parallel systems, statistical learning – the principle of learning by examples – remains a very important building block [31].

42 3. Statistical Learning for Physics Experiments A common problem with statistical learning methods is the need for a teacher (compare the introduction in section 3.3) who gives a feedback for every single decision which is made by the method. In real world applications we often have only a global reinforcement which means that the feedback is given after a time-dependent series of decisions. A major focus of current AI research is to break down the global feedback to the local decisions. Unfortunately the methods which generate the local from the global feedback are mostly application dependent (see for example [32]).

General overviews of the relation between machine learning, artificial intelligence and statistical learning can for example be found in [33, 34, 35, 36, 37].