A bayesian model to predict saturation and logistic growth

Abstract

This paper formulates a Bayesian model to predict growth and eventual market saturation of a recently introduced (and possibly expensive) consumer-durable product. The mathematical model assumes that each new buyer buys only one item of the product, that the number of new buyers of the product in the next period of time is influenced by the current number of non-buyers and that the probability an individual will buy is the result of a diffusion of news among satisfied buyers. The solution of the prediction problem includes a two-stage Bayesian updating formula which first revises the prior distribution of market saturation based on the most recent number of new buyers and then, conditional on the saturation level, computes the predictive distribution of new buyers in future time-periods. © 1987 Operational Research Society Ltd.