Abstract
We study the problem of online prediction with a set of candidate models using dynamic model averaging procedures. The standard assumptions of model averaging state that the set of admissible models contains the true one(s), and that these models are continuously updated by valid data. However, both these assumptions are often violated in practice. The models used for online tasks are often more or less misspecified and the data corrupted (which is, mathematically, a demonstration of the same problem). Both these factors negatively influence the Bayesian inference and the resulting predictions. In this paper, we propose to suppress these issues by extending the Bayesian update by a sort of likelihood tempering, moderating the impact of observed data to inference. The method is compared to the generic dynamic model averaging and to an alternative solution via sequential quasi-Bayesian mixture modeling.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Proposed in personal communication by Dr. Kárný (Institute of Information Theory and Automation, Czech Academy of Sciences).
- 2.
A thorough sensitivity analysis is postponed to further research.
References
Altekar, G., Dwarkadas, S., Huelsenbeck, J.P., Ronquist, F.: Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference. Bioinformatics 20(3), 407–415 (2004)
Aye, G., Gupta, R., Hammoudeh, S., Kim, W.J.: Forecasting the price of gold using dynamic model averaging. Int. Rev. Financ. Anal. 41, 257–266 (2015)
Bork, L., Møller, S.V.: Forecasting house prices in the 50 states using dynamic model averaging and dynamic model selection. Int. J. Forecast. 31(1), 63–78 (2015)
Bunke, O., Milhaud, X.: Asymptotic behavior of Bayes estimates under possibly incorrect models. Ann. Stat. 26(2), 617–644 (1998)
Dedecius, K., Nagy, I., Kárný, M.: Parameter tracking with partial forgetting method. Int. J. Adapt. Control Signal Process. 26(1), 1–12 (2012)
Del Negro, M., Hasegawa, R.B., Schorfheide, F.: Dynamic prediction pools: An investigation of financial frictions and forecasting performance. J. Econom. 192(2), 391–405 (2016)
Frühwirth-Schnatter, S.: Finite Mixture and Markov Switching Models. Springer, Heidelberg (2006)
Kárný, M., Kadlec, J., Sutanto, E.L.: Quasi-Bayes estimation applied to normal mixture. In: Proceedings of the 3rd European IEEE Workshop on Computer-Intensive Methods in Control and Data Processing, pp. 77–82. Praha (1998)
Koop, G., Korobilis, D.: Forecasting inflation using dynamic model averaging. Int. Econ. Rev. 53(3), 867–886 (2012)
Koop, G., Korobilis, D.: A new index of financial conditions. Eur. Econ. Rev. 71, 101–116 (2014)
Koop, G., Tole, L.: Forecasting the European carbon market. J. R. Stat. Soc. Ser. A (Stat. Soc.) 167(3), 723–741 (2013)
Leamer, E.E.: Specification Searches: Ad hoc Inference with Nonexperimental Data. Wiley, New York (1978)
McCormick, T., Raftery, A., Madigan, D., Burd, R.: Dynamic logistic regression and dynamic model averaging for binary classification. Biometrics 68(1), 23–30 (2012)
Miller, J.W., Dunson, D.B.: Robust Bayesian Inference via Coarsening pp. 1–31 (2015). http://arxiv.org/abs/1506.06101
Peterka, V.: Bayesian approach to system identification. In: Eykhoff, P. (ed.) Trends and Progress in System Identification, pp. 239–304. Pergamon Press, Oxford, U.K. (1981)
Raftery, A.E., Madigan, D., Hoeting, J.A.: Bayesian model averaging for linear regression models. JASA 92(437), 179–191 (1997)
Raftery, A.E., Kárný, M., Ettler, P.: Online prediction under model uncertainty via dynamic model averaging: Application to a cold rolling mill. Technometrics 52(1), 52–66 (2010)
Raiffa, H., Schlaifer, R.: Applied Statistical Decision Theory (Harvard Business School Publications). Harvard University Press, Cambridge (1961)
Titterington, D.M., Smith, A.F.M., Makov, U.E.: Statistical Analysis of Finite Mixture Distributions. Wiley, New York (1985)
Wang, X.: Approximating Bayesian inference by weighted likelihood. Cannadian J. Stat. 34(2), 279–298 (2006)
Acknowledgements
The project is supported by the Czech Science Foundation, project number 14–06678P. The authors thank to Dr. M. Kárný and Dr. L. Jirsa for the discussions about the model-based approach.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Reichl, J., Dedecius, K. (2017). Likelihood Tempering in Dynamic Model Averaging. In: Argiento, R., Lanzarone, E., Antoniano Villalobos, I., Mattei, A. (eds) Bayesian Statistics in Action. BAYSM 2016. Springer Proceedings in Mathematics & Statistics, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-319-54084-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-54084-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54083-2
Online ISBN: 978-3-319-54084-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)