Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Estimating Heterogeneous Customer Arrivals to a Large Retail store : A Bayesian Poisson model perspective

대형할인매점의 요일별 고객 방문 수 분석 및 예측 : 베이지언 포아송 모델 응용을 중심으로

  • Received : 2015.01.30
  • Accepted : 2015.03.28
  • Published : 2015.06.30
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Abstract

This paper considers a Bayesian Poisson model for multivariate count data using multiplicative rates. More specifically we compose the parameter for overall arrival rates by the product of two parameters, a common effect and an individual effect. The common effect is composed of autoregressive evolution of the parameter, which allows for analysis on seasonal effects on all multivariate time series. In addition, analysis on individual effects allows the researcher to differentiate the time series by whatevercharacterization of their choice. This type of model allows the researcher to specifically analyze two different forms of effects separately and produce a more robust result. We illustrate a simple MCMC generation combined with a Gibbs sampler step in estimating the posterior joint distribution of all parameters in the model. On the whole, the model presented in this study is an intuitive model which may handle complicated problems, and we highlight the properties and possible applications of the model with an example, analyzing real time series data involving customer arrivals to a large retail store.

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References

  1. Aktekin, T. and R. Soyer, "Call center arrival modeling : A Bayesian state-space approach," Naval Research Logistics, Vol.58(2011), pp.28-42. https://doi.org/10.1002/nav.20436
  2. Aktekin, T., B. Kim, and R. Soyer, "Dynamic multivariate distributions for count data : A Bayesian approach," Institute for Integrating Statistics in Decision Sciences; The George Washington University, Technical Report(2014).
  3. Albert, J.H. and S. Chib, "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business and Economic Statistics, Vol.11(1993), pp.1-15.
  4. Arbous, A.G. and J.E. Kerrich, "Accident statistics and the concept of accident proneness," Biometrics, Vol.7(1951), pp.340-432. https://doi.org/10.2307/3001656
  5. Casella, G. and E.I. George, "Understanding the Gibbs Sampler," The American Statistician, Vol.46(1992), pp.167-174.
  6. Chib, S. and E. Greenberg, "Understanding the Metropolis-Hasting Algorithm," The American Statistician, Vol.49(1995), pp.327-335.
  7. Chib, S., E. Greenberg, and R. Winkelmann, "Posterior simulation and Bayes factors in panel count," Journal of Econometrics, Vol.86 (1998), pp.33-54. https://doi.org/10.1016/S0304-4076(97)00108-5
  8. Fruhwirth-Schnatter, S., "Data Augmentation and Dynamic Linear Models," Journal of Time Series Analysis, Vol.15(1994), pp.183-202. https://doi.org/10.1111/j.1467-9892.1994.tb00184.x
  9. Harvey, A.C. and C. Fernandes, "Time Series Models for Count or Qualitative Observations," Journal of Business and Economic Statistics, Vol.7(1989), pp.407-417.
  10. Manchanda, P. and P.K. Chintagunta, "Responsiveness of Physician Prescription Behavior to Salesforce Effort : An Individual Level Analysis," Marketing Letters, Vol.15(2004), pp.129-145. https://doi.org/10.1023/B:MARK.0000047389.93584.09
  11. McCabe, B.P.M. and G.M. Martin, "Bayesian predictions of low count time series," International Journal of Forecasting, Vol.21(2005), pp. 315-330. https://doi.org/10.1016/j.ijforecast.2004.11.001
  12. Smith, R.L. and J.E. Miller, "A Non-Gaussian State Space Model and Application to Prediction of Records," Journal of the Royal Statistical Society, Series B, Vol.48(1986), pp.79-88.
  13. Wedel, M., W.S. Desarbo, J.R. Bult, and V. Ramaswamy, "A latent class Poisson regression model for heterogeneous count data," Journal of Applied Econometrics, Vol.8(1993), pp.397-411. https://doi.org/10.1002/jae.3950080407
  14. Zeger, S.L., "A regression model for time series of counts," Biometrika, Vol.75(1988), pp.621-629. https://doi.org/10.1093/biomet/75.4.621