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A Normal Approximation Method for Statistics in Knockouts

The authors give an approximation method for Bayesian inference in arena model, which is focused on paired comparisons with eliminations and bifurcations. The approximation method simplifies the inference by reducing parameters and introducing normal distribution functions into the computation of posterior distribution, which is largely based on an important property of normal random variables. Maximum a posteriori probability (MAP) and Bayesian prediction are then used to mine the information from the past pairwise comparison data, such as an individual's strength or volatility and his possible future results. We conduct a simulation to show the accuracy and stability of the approximation method and demonstrate the algorithm on nonlinear parameter inference as well as prediction problem arising in the FIFA World Cup.