Overview of Bounded Support Distributions and Methods for Bayesian Treatment of Industrial Data
Kamil Dedecius, Pavel Ettler
2013
Abstract
Statistical analysis and modelling of various phenomena are well established in nowadays industrial practice. However, the traditional approaches neglecting the true properties of the phenomena still dominate. Among others, this includes also the cases when a variable with bounded range is analyzed using probabilistic distributions with unbounded domain. Since many of those variables nearly fulfill the basic conditions imposed by the chosen distribution, the properties of used statistical models are violated rather rarely. Still, there are numerous cases, when inference with distributions with unbounded domain may lead to absurd conclusions. This paper addresses this issue from the Bayesian viewpoint. It briefly discusses suitable distributions and inferential methods overcoming the emerging computational issues.
References
- Bayes, C. L., Bazán, J. L., and García, C. (2012). A new robust regression model for proportions. Bayesian Analysis, 7(4):841-866.
- Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
- Branscum, A. J., Johnson, W. O., and Thurmond, M. C. (2007). Bayesian beta regression: Applications to household expenditure data and genetic distance between foot-and-mouth disease viruses. Australian & New Zealand Journal of Statistics, 49(3):287-301.
- Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39(1):1-38.
- Ferrari, S. and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7):799-815.
- Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2003). Bayesian Data Analysis, Second Edition (Chapman & Hall/CRC Texts in Statistical Science). Chapman and Hall/CRC, 2 edition.
- Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell., 6:721-741.
- Hahn, E. (2008). Mixture densities for project management activity times: A robust approach to PERT. European Journal of Operational Research, 188(2):450-459.
- Jaakkola, T. and Jordan, M. (2000). Bayesian parameter estimation via variational methods. Statistics and Computing, 10(1):25-37.
- Jordan, M. I. (1999). An introduction to variational methods for graphical models. In Machine Learning, pages 183-233.
- Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1):79-86.
- Ma, Z. and Leijon, A. (2011). Bayesian estimation of beta mixture models with variational inference. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 33(11):2160-2173.
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087-1092.
- Minka, T. P. (2001). Expectation propagation for approximate Bayesian inference. In UAI 7801: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, pages 362-369, San Francisco, CA, USA. Morgan Kaufmann Publishers Inc.
- Ospina, R. and Ferrari, S. (2010). Inflated beta distributions. Statistical Papers, 51:111-126. 10.1007/s00362-008- 0125-4.
- Rigby, R. A. and Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3):507-554.
Paper Citation
in Harvard Style
Dedecius K. and Ettler P. (2013). Overview of Bounded Support Distributions and Methods for Bayesian Treatment of Industrial Data . In Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-70-9, pages 380-387. DOI: 10.5220/0004439003800387
in Bibtex Style
@conference{icinco13,
author={Kamil Dedecius and Pavel Ettler},
title={Overview of Bounded Support Distributions and Methods for Bayesian Treatment of Industrial Data},
booktitle={Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2013},
pages={380-387},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004439003800387},
isbn={978-989-8565-70-9},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Overview of Bounded Support Distributions and Methods for Bayesian Treatment of Industrial Data
SN - 978-989-8565-70-9
AU - Dedecius K.
AU - Ettler P.
PY - 2013
SP - 380
EP - 387
DO - 10.5220/0004439003800387