SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 53 Issue: 1

Non-informative Bayesian estimation in dispersion models

Ibrahim Sadok(University of Bechar Algeria)0000-0002-5366-5853
Mourad Zribi(Laboratoire d’Informatique Signal et Image de la Côte d’Opale)0000-0002-2622-901X
Afif Masmoudi(University of Sfax)0000-0003-1665-5354
Pages
—
Publication Date
2024-02-29
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We explore non-informative priors, such as uniform and Jeffrey's priors, and provide evidence of the effectiveness of our method through simulation studies.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The estimation of parameters for a distribution function is a significant and prominent field within statistical inference.
📊
Key Findings & Data:This particular problem holds great relevance in various domains, including industries, stock markets, image processing, and reliability studies.
💡
Conclusion & Impact:We explore non-informative priors, such as uniform and Jeffrey's priors, and provide evidence of the effectiveness of our method through simulation studies.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bayesian estimation · exponential dispersion distribution · non-informative prior

Abstract

The estimation of parameters for a distribution function is a significant and prominent field within statistical inference. This particular problem holds great relevance in various domains, including industries, stock markets, image processing, and reliability studies. There are two recognized approaches to estimation: point estimation and interval estimation, also known as confidence intervals. In this study, our primary focus lies in the point estimation of parameters associated with an exponential dispersion distribution function. In this process, we consider one of the parameters as a random variable that requires estimation. To tackle this, we adopt a Bayesian inference approach utilizing a one-parameter dispersion distribution. We explore non-informative priors, such as uniform and Jeffrey's priors, and provide evidence of the effectiveness of our method through simulation studies.

🔖

Cite This Article

Sadok, I., Zribi, M., Masmoudi, A. (2024). Non-informative Bayesian estimation in dispersion models. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 1. https://doi.org/10.15672/hujms.1053432

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (26)

  1. J.M. Bernardo and A.F.M. Smith, Bayesian Theory, Wiley, 1994.
  2. J. Bertrand, P. Bertrand and J.P. Ovarlez, The Transforms and Applications Handbook, CRC & IEEE Presses, 2000.
  3. G.E. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis, John Wiley & Sons, 2011.
  4. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
  5. G.S. Datta and M. Ghosh, Some remarks on noninformative priors, J. Amer. Statist. Assoc. 90 (432), 1357-1363, 1995.
  6. D.M. Eaves, On Bayesian nonlinear regression with an enzyme example, Biometrika 70 (2), 373-379, 1983.
  7. K. Fatima and S.P. Ahmad, Bayesian approach in estimation of shape parameter of the exponentiated moment exponential distribution, J. Stat. Theory Appl. 17 (2), 359-374, 2018.
  8. C.W. Garvan and M. Ghosh, On the property of posteriors for dispersion models, J. Statist. Plann. Inference 78 (1-2), 229-241, 1999.
  9. A. Gelman and J. Hill, Data Analysis using Regression and Multilevel/Hierarchical Models, Cambridge University Press, 2007.
  10. C.B. Guure, N.A. Ibrahim and M.B. Adam, Bayesian inference of the Weibull model based on interval-censored survival data, Comput. Math. Methods Med., Doi: 10.1155/2013/849520, 2013.
  11. J.A. Hartigan, Locally uniform prior distributions, Ann. Statist. 24 (1), 160-173, 1996.
  12. N.T. Hobbs and M.B. Hooten, Bayesian Models: A Statistical Primer for Ecologists, Princeton University Press, 2015.
  13. J.G. Ibrahim and P.W. Laud, On Bayesian analysis of generalized linear models using Jeffreys’s prior, J. Amer. Statist. Assoc. 86 (416), 981-986, 1991.
  14. H. Jeffreys, Theory of Probability, 3rd ed., Oxford University Press, 1961.
  15. B. Jorgensen, Exponential dispersion models, J. R. Stat. Soc. Ser. B. Stat. Methodol. 49 (2), 127-145, 1987.
  16. B. Jorgensen, The Theory of Dispersion Models, CRC Press, 1997.
  17. B. Jorgensen, J.R. Martinez and M. Tsao, Asymptotic behaviour of the variance function, Scand. J. Stat. 21 (3), 223-243, 1994.
  18. R. Kaas, M. Goovaerts, J. Dhaene and M. Denuit, Modern Actuarial Risk Theory, Springer, 2008.
  19. A.A. Khan, M. Aslam, Z. Hussain and M. Tahir, Comparison of loss functions for estimating the scale parameter of log-Normal distribution using non-informative priors, Hacet. J. Math. Stat. 45 (6), 1831-1845, 2015.
  20. N.P. Lemoine, Moving beyond noninformative priors: Why and how to choose weakly informative priors in Bayesian analyses, Oikos 128 (7), 912-928, 2019.
  21. P. McCullagh and J.A. Nelder, Generalized Linear Models, 2nd ed., Chapman & Hall, 1989.
  22. M.D. Nichols and W.J. Padgett, A bootstrap control chart for Weibull percentiles, Qual. Reliab. Eng. Int. 22 (2), 141-151, 2006.
  23. I. Sadok and A. Masmoudi, New parametrization of stochastic volatility models, Comm. Statist. Theory Methods 51 (7), 1936-1953, 2022.
  24. I. Sadok, A. Masmoudi and M. Zribi, Integrating the EM algorithm with particle filter for image restoration with exponential dispersion noise, Comm. Statist. Theory Methods 52 (2), 446-462, 2023.
  25. I. Sadok and M. Zribi, Image restoration using Weibull particle filters, 4th International Conference on Pattern Analysis and Intelligent Systems (PAIS), 12-13 October 2022, Algeria, 2022.
  26. S.K. Sinha, Bayes estimation of the reliability function and hazard rate of a Weibull failure time distribution, Trabajos de Estadistica 1 (2), 47-56, 1986.