In research there is often a need to choose between multiple competing models. Two popular criteria for model selection are the AIC and BIC. The AIC excels in estimating the best model for the unknown data generating process. The BIC on the other hand is consistent in finding the true model. It is clear that for model selection these two information criterion give answers to different selection criteria. The question that arises is whether it is possible to construct a model selection criterion which combines the strengths of both AIC and BIC. In this study we will show that it is impossible to construct a model selection criterion which shares the above mentioned two strenghts by revisiting the proof of \cite{yang2005can} : That is, any consistent model selection criterion must be sub-optimal in the minimax convergence rate for regression estimation compared to the AIC.

In de statistiek zijn er verschillende methodes voor het uitvoeren van model selectie. Het verschil in deze methodes komt voort uit het verschil in stromingen. Voor niet-geneste model selectie zijn de meest ganbare stromingen de Bayes Factor en de likelihood ratio. D. M. Ommen en C. P. Saunders presenteerden theoretische resultaten voor de relatie tussen de Bayes Factor en de likelihood ratio, waardoor de resultaten van beide paradigma's met elkaar kunnen worden vergeleken [5]. De Bayes Factor wordt uitgedrukt in de verwachting van likelihoodratio functie met betrekking tot de posterior verdeling van de parameters. In de bewijzen van deze theoriën ontbraken een aantal belangrijke aspecten. Om deze resultaten volledig te kunnen bewijzen, wordt in dit verslag aangetoond dat eerdere theoretische resultaten moeten worden uitgebreid met extra aannames of volledig moeten worden aangepast. Aan de hand van deze aannames en aanpassingen worden de theoretische resultaten bewezen. De theoretische resultaten zijn belangrijk in de toepassing van niet-geneste model selectie, omdat er nu gecommuniceerd kan worden tussen experts vanuit een ander paradigma.

Danieli Corus supplies tailor-made solutions for the global steel industry. Cameras are used in tuyeres of blast furnaces to detect physical aspects and irregularities. No operator could monitor those videos all day, which is why video analyses are needed. A program is written to analyse a test video and give information about the temperature, the injection of pulverized coal and the movement of rocks. The mathematical background of these calculations is presented, which depend on the transport of light from the blast furnace to the camera through the tuyere. Also the implementation of the calculations can be found. The results are interpreted and discussed and further improvements are suggested.

In this thesis, we consider levelling the number of required beds at the holding and recovery department. Due to the decreased number of available nurses, the workload for the nurses at hospitals has increased. For this reason, it is important to level the number of required beds at the holding and recovery department. By doing so, the workload can be reduced, beds will be available for emergency surgeries, less surgeries will be cancelled due to the lack of beds and less staff will be needed.
The thesis starts with introducing an analytic calculation of the number of required beds at the holding and recovery department. These calculations consider a stochastic length of stay (LOS) distribution for each surgery type. Making use of the analytic calculation and the stochastic length of stay, several solution methods are developed. The first solution method includes a formulation of the problem as an Integer Linear Program (ILP). The exact calculation of the number of required beds is not linear, so the objective function is simplified. The ILP minimises the number of expected beds.
The other solution methods uses the start and end times of each surgery. These start and end times are spread using two algorithms called Fixed Goal Values and Flexible Goal Values.
Data from an Academic Medical Centre in the Netherlands is used to determine the LOS distributions and to find solutions for the ILP and the algorithms. This thesis shows that the number of required bed at the holding and recovery department can be reduced.

Over time, the width-averaged depth of estuaries changes due to a complex interaction of hydrodynamics and suspended sediment transport. In many estuaries one specic location with a suspended sediment concentration (SSC) higher than in the sea or in the upstream river, is found, which is called sediment
trapping. The location of the maximum SSC is called the estuary turbidity maximum (ETM). Understanding the dynamics is important to maintain a healthy ecosystem while making anthropogenic changes. To investigate such changes, a two-dimensional model is developed, considering the Ems estuary as a case study. The model equations consist of the width-averaged shallow water equations and a SSC equation. Assuming a morphodynamic equilibrium, these equations are solved mostly analytically by making a regular expansion of each physical variable in a relatively small parameter. Using this method, we are able to gain insight into the fundamental physical processes resulting in sediment trapping in an estuary by studying the influence of various forcings separately. One of the hydrodynamic forces is vertical mixing. This force has been assumed to be constant over time in previous studies [1]. In this thesis vertical mixing as a function that varies on the tidal timescale has been added to the model and is analysed. As a result of the salinity gradient in the estuary the mixing is stronger during flood and weaker during ebb. Using the model it is found that time variations in vertical mixing result in tidally averaged non-zero, and therefore contributing, transports. They cause a narrowing of the location where sediment is trapped. If vertical mixing is exactly maximal when the flood is maximal and minimal when ebb is maximal, the ETM shifts downstream. But if the vertical mixing is lagging the tidal stream, which is more plausible, the ETM will stay or shift upstream.