Bayesian forecasting of an inhomogeneous poisson process with applications to call center data

Journal of the American Statistical Association

Volumn 102, Issue 480, 2007, Pages 1185-1198

  Weinberg, Jonathan ^a   Brown, Lawrence D ^a   Stroud, Jonathan R ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Autoregressive models; Bayesian forecasting; Call center; Cubic smoothing spline; Inhomogeneous poisson process; Markov chain Monte Carlo; Multiplicative model; Sequential Monte Carlo; State space model

Indexed keywords

EID: 38349052063     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000001455     Document Type: Article

References (26)

1. Andrews, B. H., and Cunningham, S. M. (1995), "L.L. Bean Improves Call-Center Forecasting," Interfaces, 25, 1-13.
2. Avramidis, A. N., Deslauriers, A., and L'Ecuyer, P. (2004), "Modeling Daily Arrivals to a Telephone Call Center," Management Science, 50, 896-908.
3. Bianchi, L., Jarrett, J., and Choudary Hanumara, R. (1993), "Forecasting Incoming Calls to Telemarketing Centers," Journal of Business Forecasting Methods and Systems, 12, 3-12.
4. Brown, L. D., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S., and Zhao, L. H. (2005), "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, 100, 36-50.
5. Brown, L. D., Zhang, R., and Zhao, L. (2001), "Root-Unroot Methodology for Non-Parametric Density Estimation," technical report, University of Pennsylvania, Dept. of Statistics.
6. Carter, C. K., and Kohn, R. (1994), "On Gibbs Sampling for State-Space Models," Biometrika, 81, 541-553.
7. Chen, R., and Fomby, T. (1999), "Forecasting With Stable Seasonal Pattern Models With an Application of Hawaiian Tourist Data," Journal of Business & Economic Statistics, 17, 497-504.
8. Chen, R., and Liu, J. S. (2000), "Mixture Kalman Filters," Journal of the Royal Statistical Society, Ser. B, 62, 493-508.
9. Diebold, F. X., Gunther, T., and Tay, A. (1998), "Evaluating Density Forecasts, With Applications to Financial Risk Management," International Economic Review, 39, 863-883.
10. Frühwirth-Schnatter, S. (1994), "Data Augmentation and Dynamic Linear Models," Journal of Time Series Analysis, 15, 183-202.
11. Gamerman, D. (1998), "Markov Chain Monte Carlo for Dynamic Generalized Linear Models," Biometrika, 85, 215-227.
12. Gans, N., Koole, G., and Mandelbaum, A. (2003), "Telephone Call Centers: Tutorial, Review and Research Prospects," Manufacturing and Service Operations Management, 5, 79-141.
13. Gel, Y., Raftery, A. E., and Gneiting, T. (2004), "Calibrated Probabilistic Mesoscale Weather Field Forecasting: The Geostatistical Output Perturbation (GOP) Method," Journal of the American Statistical Association, 99, 575-583.
14. Jongbloed, G., and Koole, G. (2001), "Managing Uncertainty in Call Centers Using Poisson Mixtures," Applied Stochastic Models in Business and Industry, 17, 307-318.
15. Kohn, R., and Ansley, C. F. (1987), "A New Algorithm for Spline Smoothing Based on Smoothing a Stochastic Process," Journal of Scientific and Statistical Computing, 8, 33-48.
16. Lindley, D. V., and Smith, A. F. M. (1972), "Bayes Estimates for the Linear Model," Journal of the Royal Statistical Society, Ser. B, 34, 1-41.
17. Little, J. (1961), "A Proof of the Theorem L = λW," Operations Research, 9, 383-387.
18. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953), "Equation of State Calculations by Fast Computing Machines," Journal of Chemical Physics, 21, 1087-1092.
19. Robert, C. P., and Casella, G. (2004), Monte Carlo Statistical Methods, New York: Springer-Verlag.
20. Rosenblatt, M. (1952), "Remarks on a Multivariate Transformation," The Annals of Mathematical Statistics, 23, 470-472.
21. Shephard, N. (1994), "Partial Non-Gaussian State Space," Biometrika, 81, 115-131.
22. Shephard, N., and Pitt, M. K. (1997), "Likelihood Analysis of Non-Gaussian Measurement Time Series," Biometrika, 84, 653-667.
23. Soyer, R., and Tarimcilar, M. (2006), "Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach," Management Science, to appear.
24. Stein, C. M. (1981), "Estimating the Mean of a Multivariate Normal Distribution," The Annals of Statistics, 9, 1135-1151.
25. Trofimov, V., Feigin, P., Mandelbaum, A., and Ishay, E. (2005), "DATAMOCCA, Data Model for Call Center Analysis," computer software.
26. Wahba, G. (1983), "Bayesian 'Confidence Intervals' for the Cross-Validated Smoothing Spline," Journal of the Royal Statistical Society, Ser. B, 45, 133-150.