Bayesian Methods for Media Mix Modelling with shape and funnel effects

In recent years, significant progress in generative AI has highlighted the important role of physics-inspired models that utilize advanced mathematical concepts based on fundamental physics principles to enhance artificial intelligence capabilities. Among these models, those based on diffusion equations have greatly improved image quality. This study aims to explore the potential uses of Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix Modelling (MMM) applications. We propose incorporating these equations into Hierarchical Bayesian models to analyse consumer behaviour in the context of advertising. These equation sets excel in accurately describing the random dynamics in complex systems like social interactions and consumer-advertising interactions.