A Frequentist Approach to Bayesian Regression

In this paper frequentist approaches to Bayesian regression are tested and compared to methods using ordinary least squares, pooling and Ridge estimation. We investigate how the prior parameters of the Bayesian regression could be established by means of a frequentist approach. The resulting estimates are evaluated based on their predictive performance. This paper focuses on the prediction of weekly sales of different types of orange juice incorporating explanatory variables of competing products including price and lagged sales. The data originates from the Dominick’s Finer Food chain in the greater Chicago area and is provided by The Kilts Center for Marketing at the Universtiy of Chicago’s Marketing Department. We introduce two Bayesian inspired shrinkage methods of which one outperforms all the other methods showing great promise to modeling cross-effects between competing products using limited data.