Email this article A Comparative Study of Loss Functions for Bayesian Control in Mixture Models
Abstract
Berliner (1987) discussed the issue of controlling the output (response) towards the specified value by choosing the values for independent variables in a regression mixture model, taking it as a Bayesian Decision Problem. The quantification of the potential loss was done with the help of quadratic loss function, which was a symmetric loss function. We have tried to quantify this loss with the help of Precautionary Loss Function and Modified Squared Error Loss Function, in linear Scheffé mixture model and comparison is established between these loss function. Results are improved as compared to Berliner (1987).
References
Ali, S., Aslam, M., Kundu, D. and Kazmi, S.M.A. (2012), Mixture of Generalized Exponential Distribution: a versatile lifetime model in Industrial Engineering Processes. Journal of the Chinese Institute of Industrial Engineers, Vol. 29, No. 4, 246–269.
Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis (2nd ed), New York: Springer-Verlag.
Berliner, L. M. (1987). Bayesian Control in Mixture Models. Technometrics, Vol. 29, No. 4, pp. 455-460.
Castillo .E.D. (2007).Process optimization: A statistical Approach, (1st ed), New York: Springer-Verlag.
Norstram, J. G. (1996). The use of Precautionary Loss function in Risk Analysis. IEEE Transaction On Reliability, Vol. 45, No. 3, pp. 400-403.
Scheffé, H (1958). Experiments with Mixtures Journal of Royal Statistical Society, B, Vol. 20, pp. 344-360.
Scheffé, H. (1963). Simplex-Centroid Designs for Experiments with Mixtures. Journal of Royal Statistical Society, B, Vol. 25, pp. 235–263.
Snee, R. D. (1981). Developing Blending Models for Gasoline and Other Blends. Technometrics, Vol. 23, pp. 119-130.
Uhlich, S. and Yang, B. (2012), Bayesian estimation for nonstandard loss functions using a parametric family of estimators, IEEE Transitions on Signal Processing, Vol. 60 (3), pp. 1022-1031.
Full Text: pdf
