A Normal Approximation Method for Statistics in Knockouts

TL;DR

This paper introduces a normal approximation technique for Bayesian inference in arena models with paired comparisons, simplifying parameter estimation and prediction in knockout scenarios, demonstrated through simulations and FIFA World Cup data.

Contribution

The paper presents a novel normal approximation method for Bayesian inference in arena models, reducing computational complexity and enabling effective prediction in knockout competitions.

Findings

The approximation method is accurate and stable in simulations.

It effectively predicts individual strength and future outcomes.

Demonstrated successful application to FIFA World Cup data.

Abstract

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.