Bayesian Nonparametric Dynamic Methods: Applications to Linear and Nonlinear Advertising Models

Abstract

Bayesian methods for dynamic models in marketing have so far been parametric. For instance, it is invariably assumed that model errors emerge from normal distributions. Yet using arbitrary distributional assumptions can result in false inference, which in turn misleads managers. The author therefore presents a set of flexible Bayesian nonparametric (NP) dynamic models that treat error densities as unknown but assume that they emerge from Dirichlet process mixtures. Although the methods address misspecification in dynamic linear models, the main innovation is a particle filter algorithm for nonlinear state-space models. The author used two advertising studies to confirm the benefits of the methods when strict error assumptions are untenable. In both studies, NP models markedly outperformed benchmarks in terms of fit and forecast results. In the first study, the benchmarks understated the effects of competitive advertising on own brand awareness. In the second study, the benchmark inflated ad quality, and consequently, the effects of past advertising appeared 36% higher than that predicted by the NP model. In general, these methods should be valuable wherever state-space models appear (e.g., brand and advertising dynamics, diffusion of innovation, dynamic discrete choice).