Forecasting Olympic Medals: A Multivariate Negative Binomial Mixed-Effects Model with Bayesian Hierarchical Analysis

Abstract

This study established a predictive framework integrating a multivariate negative binomial mixed-effects model with a Bayesian hierarchical model to address the issues of overdispersion and uncertainty in discrete data prediction. Firstly, by organically coupling hierarchical regression with the negative binomial model, the study systematically explored the overdispersion characteristics and multi-level association mechanisms of the data, enabling precise prediction of count variables. For special samples with no historical data, the study employs a Bayesian hierarchical model: a similarity measurement system is constructed based on core indicators to match historical comparable data and infer the sample's result distribution; simultaneously, an average probability distribution is constructed using all historical data. Under the assumption of equal probabilities, the probability of the first occurrence of the target result in samples with no historical data is calculated using the binomial distribution. The framework demonstrates excellent generalisation capabilities while improving prediction accuracy through a multi-level design combining model integration and uncertainty quantification.