Calibration scores for discrete random variables

During this bachelorproject, more research is done to investigate the properties of the Hanea’s and Nane’s calibration score and to look at slight adjustment of Hanea’s and Nane’s calibration score. Both simulated data and real data will be used to investigate the behaviour of these calibration scores.

Effects of Fitness on Generative Graph Models with Preferential Attachment

Preferential Attachment models offer an explanation for why power laws are so common in real-world data. In these models, we start out with an initial network and add nodes one at a time. For each new node, we make m connections to existing nodes and if we define the attachment probability of attaching to a vertex to be proportional to its...

The "Number Hides Game" on a Tree: A bachelor thesis in game theory

The "Number Hides Game" (NHG) is 2-player game played on a board that consists of a row of p consecutive coins. Player I and player II simultaneously choose subsets of m and n consecutive coins respectively. Player II pays the number of coins that lie in the intersection of the subsets to player I. This thesis introduces basic knowledge from the...

Duality in interacting particle systems out of equilibrium

In this thesis we study a class of interacting particle systems sharing a duality property. This class includes the Symmetric Inclusion Process (SIP(2k)), the Symmetric Exclusion Process (SEP(2j)) and the Independent Random Walkers (IRW). When these systems are in equilibrium (namely they are isolated from the exterior) they admit stationary...

Three Way Duels: Infinite Games on the Unit Square

With the growing wealth and economy of a country, there are an increasing amount of small and big businesses. Every company has its own marketing strategy that it uses in order to lure customers away from their competition and increase their sales. Choosing the perfect time to advertise or discount several products is of essence for a company to...

Avalanche distribution on the Abelian sandpile model: Avalanche distribution on the Abelian sandpile model

[ not the actual abstract] In this thesis, the sandpile models distributions are analysed on the finite and infinite bethe lattice. To do so, the recursive property of the lattice is used.