Theorie des mehrfachen Würfelspiels

Multiple Dice Game Theory is an introduction to a novel approach to dice game and application to real data. The book presents a mathematical formulation of the Multiple Dice Rolling (MDR) game and develops an adaptive computational algorithm to simulate such game over time. This book uses the extended version of the well-known Chapman-Kolmogorov Equations to model the state transition of the probability mass function of each side of the dice during the game, and represents the time-dependent propensity of the game by a simple linear regression process which enable to capture the change in the expectation over time. Furthermore, we perform a statistical analysis of the outcomes of the game in a framework of Average Probability Value (APV) of each side of the dice over trials. The stochastic theory developed is book is successfully applied to real data from to the Ciona and Beer-Tavazoie dataset. The results established that the Ciona data (cell biometry) were relatively stable and the Beer-Tavazoie data (gene expression) were noisy in support of the well-known biologists' theory of molecular dogma.