Forecasting from others’ experience: Bayesian estimation of the generalized Bass model

Abstract We propose a Bayesian estimation procedure for the generalized Bass model that is used in product diffusion models. Our method forecasts product sales early based on previous similar markets; that is, we obtain pre-launch forecasts by analogy. We compare our forecasting proposal to traditional estimation approaches, and alternative new product diffusion specifications. We perform several simulation exercises, and use our method to forecast the sales of room air conditioners, BlackBerry handheld devices, and compressed natural gas. The results show that our Bayesian proposal provides better predictive performances than competing alternatives when little or no historical data are available, which is when sales projections are the most useful.

[1]  Malcolm J. Wright,et al.  Forecasting new product trial with analogous series , 2015 .

[2]  Jungsik Hong,et al.  Easy, reliable method for mid-term demand forecasting based on the Bass model: A hybrid approach of NLS and OLS , 2016, Eur. J. Oper. Res..

[3]  Ambar G. Rao,et al.  Bayesian Estimation and Control of Detailing Effort in a Repeat Purchase Diffusion Environment , 1981 .

[4]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[5]  P. K. Kannan,et al.  Using online search data to forecast new product sales , 2012, Decis. Support Syst..

[6]  Peter E. Rossi,et al.  The Value of Purchase History Data in Target Marketing , 1996 .

[7]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[8]  Taegu Kim,et al.  Forecasting diffusion of innovative technology at pre-launch: A survey-based method , 2013, Ind. Manag. Data Syst..

[9]  L. Pericchi,et al.  The Scaled Beta2 Distribution as a Robust Prior for Scales , 2017 .

[10]  Zhengrui Jiang,et al.  Virtual Bass Model and the Left-Hand Data-Truncation Bias in Diffusion of Innovation Studies , 2006 .

[11]  Ashish Sood,et al.  Functional Regression: A New Model for Predicting Market Penetration of New Products , 2009, Mark. Sci..

[12]  Mariangela Guidolin,et al.  Modelling a dynamic market potential: A class of automata networks for diffusion of innovations , 2009 .

[13]  Dennis Fok,et al.  Forecasting cross-population innovation diffusion: A Bayesian approach , 2005 .

[14]  Wagner A. Kamakura,et al.  A Bayesian Model for Prelaunch Sales Forecasting of Recorded Music , 2003, Manag. Sci..

[15]  Donald R. Lehmann,et al.  A Meta-Analysis of Applications of Diffusion Models , 1990 .

[16]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[17]  E. Rogers.  Diffusion of Innovations , 1962 .

[18]  P. Goodwin,et al.  The challenges of pre-launch forecasting of adoption time series for new durable products , 2014 .

[19]  Anne T. Coughlan,et al.  New technology adoption in an innovative marketplace: Micro- and macro-level decision making models , 1991 .

[20]  A. D. Hall,et al.  The PORT Mathematical Subroutine Library , 1978, TOMS.

[21]  Sataya D. Dubey,et al.  Compound gamma, beta and F distributions , 1970 .

[22]  Philip M. Parker,et al.  Aggregate diffusion forecasting models in marketing: A critical review , 1994 .

[23]  Ambar G. Rao,et al.  New Models from Old: Forecasting Product Adoption by Hierarchical Bayes Procedures , 1990 .

[24]  Hermann Simon,et al.  ADPULS: An Advertising Model with Wearout and Pulsation , 1982 .

[25]  G. Lilien,et al.  Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models , 1997 .

[26]  V.V.N. Kishore,et al.  A review of technology diffusion models with special reference to renewable energy technologies , 2010 .

[27]  Wallace J. Hopp,et al.  Ten Most Influential Papers of Management Science's First Fifty Years , 2004, Manag. Sci..

[28]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[29]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[30]  Dipak C. Jain,et al.  Optimal Dynamic Advertising Policy for New Products , 2006, Manag. Sci..

[31]  Vijay Mahajan,et al.  Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance , 1982 .

[32]  Taegu Kim,et al.  Bass model with integration constant and its applications on initial demand and left-truncated data , 2015 .

[33]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[34]  M. Plummer,et al.  CODA: convergence diagnosis and output analysis for MCMC , 2006 .

[35]  L. Pericchi,et al.  An alternative to the Inverted Gamma for the variances to modelling outliers and structural breaks in dynamic models , 2014 .

[36]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[37]  N. Meade,et al.  Modelling and forecasting the diffusion of innovation – A 25-year review , 2006 .

[38]  Cinzia Mortarino,et al.  Pre-launch forecasting of a pharmaceutical drug , 2017 .

[39]  Dipak C. Jain,et al.  Why the Bass Model Fits without Decision Variables , 1994 .

[40]  Peter E. Rossi,et al.  Bayesian Statistics and Marketing , 2005 .

[41]  Frank M. Bass,et al.  Comments on "A New Product Growth for Model Consumer Durables The Bass Model" , 2004, Manag. Sci..

[42]  Vijay Mahajan,et al.  New Product Diffusion Models in Marketing: A Review and Directions for Research: , 1990 .

[43]  V. Mahajan,et al.  Innovation diffusion and new product growth models: A critical review and research directions , 2010 .

[44]  A. Valle,et al.  Forecasting accuracy of wind power technology diffusion models across countries , 2011 .

[45]  Karima Dyussekeneva,et al.  The use of analogies in forecasting the annual sales of new electronics products , 2013 .

[46]  G. Tellis,et al.  Will It Ever Fly? Modeling the Takeoff of Really New Consumer Durables , 1997 .

[47]  Dani Gamerman,et al.  Generalized exponential growth models a bayesian approach , 1993 .

[48]  Barry L. Bayus,et al.  High-definition television: assessing demand forecasts for a next generation consumer durable , 1993 .

[49]  F. Bass.  A new product growth model for consumer durables , 1976 .

[50]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[51]  Nigel Meade,et al.  Prediction intervals for growth curve forecasts , 1995 .

[52]  Gerard J. Tellis,et al.  A Critical Review of Marketing Research on Diffusion of New Products , 2007 .

[53]  Frank M. Bass,et al.  DIRECTV: Forecasting Diffusion of a New Technology Prior to Product Launch , 2001 .

[54]  N. Meade.  Forecasting Using Growth Curves—An Adaptive Approach , 1985 .

[55]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[56]  Shlomo Yitzhaki,et al.  The Diffusion of Innovations: A Methodological Reappraisal , 1982 .

[57]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..