A BAYESIAN HERMITE REGRESSION MODEL WITH CLASSES OF PRIOR DISTRIBUTIONS APPLIED TO RIDE-HAILING PLATFORM USAGE

Abstract

Econometric and applied statistical modelling frequently encounter 
nonlinear datasets characterised by heavy tails, skewness, and volatility clustering.  Classical regression methods, including ordinary least squares, often perform poorly under such conditions, while conventional polynomial regression may be unstable in the presence of extreme observations. To address these limitations, this study 
develops a Bayesian Hermite Regression Model (BHRM) that integrates truncated Hermite polynomial expansions within a coherent Bayesian framework. The model enables flexible nonlinear approximation while incorporating structured regularisation through alternative classes of prior distributions. Four prior categories—conjugate, noninformative, shrinkage, and heavy-tailed, are systematically examined to assess their influence on posterior inference and predictive behaviour. Posterior estimation is conducted using Markov Chain Monte Carlo methods, and model adequacy is evaluated using predictive and information
theoretic criteria. The results demonstrate that prior specification materially affects regularisation strength, predictive stability, and robustness to extreme demand fluctuations. Shrinkage and heavy-tailed priors enhance generalisation performance relative to standard specifications. These findings establish Bayesian Hermite regression as a scalable and principled framework for modelling nonlinear and volatile datasets such as ride-hailing demand.