Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling
Edwin Ng, Zhishi Wang and Athena Dai
Both Bayesian and varying coefficient models are very useful tools in practice as they can be used to model parameter heterogeneity in a generalizable way. Motivated by the need of enhancing Marketing Mix Modeling (MMM) at Uber, we propose a Bayesian Time Varying Coefficient (BTVC) model, equipped with a hierarchical Bayesian structure. This model is different from other time-varying coefficient models in the sense that the coefficients are weighted over a set of local latent variables following certain probabilistic distributions. Stochastic Variational Inference (SVI) is used to approximate the posteriors of latent variables and dynamic coefficients. The proposed model also helps address many challenges faced by traditional MMM approaches.We used simulations as well as real-world marketing datasets to demonstrate our model’s superior performance in terms of both accuracy and interpretability.