Take a look at the hierarchical Bayesian estimation of parameters from several different angles

References

• Ali, S. 2015. On the Bayesian estimation of the weighted Lindley distribution. Journal of Statistical Computation and Simulation 85 (5):855–80. doi: 10.1080/00949655.2013.847442.
   Web of Science ®Google Scholar
• Ali, S., M. Aslam, and S. M. A. Kazmi. 2013. A study of the effect of the loss function on Bayes estimate, posterior risk and hazard function for Lindley distribution. Applied Mathematical Modelling 37 (8):6068–78. doi: 10.1016/j.apm.2012.12.008.
   Web of Science ®Google Scholar
• Ando, T, and A. Zellner. 2010. Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques. Bayesian Analysis 5 (1):65–96. doi: 10.1214/10-BA503.
   Web of Science ®Google Scholar
• Athirakrishnan, R. B, and E. I. Abdul-Sathar. 2022. E-Bayesian and hierarchical Bayesian estimation of inverse Rayleigh distribution. American Journal of Mathematical and Management Sciences 41 (1):70–87. doi: 10.1080/01966324.2021.1914250.
   Google Scholar
• Berger, J. O. 1985. Statistical decision theory and Bayesian analysis. 2nd ed. New York: Springer-Verlag.
   Google Scholar
• Gonzalez-Lopez, V. A., R. Gholizadeh, and C. E. Galarza. 2017. E-Bayesian estimation for system reliability and availability analysis based on exponential distribution. Communications in Statistics-Simulation and Computation 46 (8):6221–41. doi: 10.1080/03610918.2016.1202269.
   Web of Science ®Google Scholar
• Hamada, M. S. A. G. Wilson, C. S. Reese, and H. F. Martz. 2008. Bayesian reliability. New York: Springer.
   Google Scholar
• Han, M. 1997. The Structure of hierarchical prior distribution and its applications. Chinese Operations Research and Management Science 6 (3):31–40.
   Google Scholar
• Han, M. 2007. E-Bayesian estimation of failure probability and its application. Mathematical and Computer Modelling 45 (9–10):1272–9. doi: 10.1016/j.mcm.2006.11.007.
   Google Scholar
• Han, M. 2009. E-Bayesian estimation and hierarchical Bayesian estimation of failure rate. Applied Mathematical Modelling 33 (4):1915–22. doi: 10.1016/j.apm.2008.03.019.
   Web of Science ®Google Scholar
• Han, M. 2017. The E-Bayesian and hierarchical Bayesian estimations of Pareto distribution parameter under different loss functions. Journal of Statistical Computation and Simulation 87 (3):577–93. doi: 10.1080/00949655.2016.1221408.
   Web of Science ®Google Scholar
• Han, M. 2021. A study on the effect of the loss function on Bayesian estimation and posterior risk of binomial distribution. Communications in Statistics-Theory and Methods 50 (18):4386–99. doi: 10.1080/03610926.2020.1719160.
   Web of Science ®Google Scholar
• Jaheen, Z. F, and H. M. Okasha. 2011. E-Bayesian estimation for the Burr type XII model based on type-2 censoring. Applied Mathematical Modelling 35 (10):4730–7. doi: 10.1016/j.apm.2011.03.055.
   Web of Science ®Google Scholar
• Karimnezhad, A, and F. Moradi. 2016. Bayes, E-Bayes and robust Bayes prediction of a future observation under precautionary prediction loss functions with applications. Applied Mathematical Modelling 40 (15-16):7051–61. doi: 10.1016/j.apm.2016.02.040.
   Web of Science ®Google Scholar
• Kazmi, A. M. S., M. Aslam, and S. Ali. 2012. Preference of prior for the class of life-time distribution under different loss functions. Pakistan Journal of Statistics 28 (4):467–84.
   Web of Science ®Google Scholar
• Kiapour, A. 2018. Bayes, E-Bayes and robust Bayes premium estimation and prediction under the squared log error loss function. Journal of the Iranian Statistical Society 17 (1):33–47.
   Google Scholar
• Kizilaslan, F. 2017. The E-Bayesian and hierarchical Bayesian estimations for the proportional reversed hazard rate model based on record values. Journal of Statistical Computation and Simulation 87:2253–73.
   Web of Science ®Google Scholar
• Kizilaslan, F. 2019. E-Bayesian estimation for the proportional hazard rate model based on record values. Communications in Statistics-Simulation and Computation 48 (2):350–71.
   Web of Science ®Google Scholar
• Lehmann, E. L, and G. Casella. 1998. Theory of point estimation. 2nd ed. NewYork: Springer-Verlag.
   Google Scholar
• Lindley, D. V, and A. F. M. Smith. 1972. Bayes estimates for the linear model. Journal of the Royal Statistical Society. Series B 34:1–41.
   Google Scholar
• Manandhar, B, and B. Nandram. 2021. Hierarchical Bayesian models for continuous and positively skewed data from small areas. Communications in Statistics-Theory and Methods 50 (4):944–62. doi: 10.1080/03610926.2019.1645853.
   Web of Science ®Google Scholar
• Mao, S. 1999. Bayes statistics. Beijing: China Statistics Press.
   Google Scholar
• Nassar, M., H. Okasha, and M. Albassam. 2021. E-Bayesian estimation and associated propoerties of simple step-stress model for exponential distribution based on type-II censoring. Quality and Reliability Engineering International 37 (3):997–1016. doi: 10.1002/qre.2778.
   Web of Science ®Google Scholar
• Okasha, H. M, and J. Wang. 2016. E-Bayesian estimation for the geometric model based on record statistics. Applied Mathematical Modelling 40 (1):658–70. doi: 10.1016/j.apm.2015.05.004.
   Web of Science ®Google Scholar
• Osei, F. B., A. A. Duker, and A. Stein. 2011. Hierarchical Bayesian modeling of the space-time diffusion patterns of cholera epidemic in Kumasi, Ghana. Statistica Neerlandica 65 (1):84–100. doi: 10.1111/j.1467-9574.2010.00475.x.
   Web of Science ®Google Scholar
• Parsian, A, and N. Nematollahi. 1996. Estimation of scale parameter under entropy loss function. Journal of Statistical Planning Inference 52 (1):77–91. doi: 10.1016/0378-3758(95)00026-7.
   Web of Science ®Google Scholar
• Piriaei, H., G. Yari, and R. Farnoosh. 2020. E-Bayesian estimations for the cumulative hazard rate and mean residual life based on exponential distribution and record data. Journal of Statistical Computation and Simulation 90 (2):271–90. doi: 10.1080/00949655.2019.1678623.
   Web of Science ®Google Scholar
• Rabie, A, and J. Li. 2020. E-Bayesian estimation for Burr-X distribution based on generalized type-I hybrid censoring scheme. American Journal of Mathematical and Management Sciences 39 (1):41–55. doi: 10.1080/01966324.2019.1579123.
   Google Scholar
• Varian, H. R. 1975. A Bayesian approach to real estate assessment. In Studies in Bayesian econometrics and statistics in honor of Leonard J Savage, ed. S. E. Feinberge and A. Zellner, 195–208. Amsterdam: North Holland Publishing Co.
   Google Scholar
• Yousefzadeh, F. 2017. E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function. Communications in Statistics-Theory and Methods 46 (1):1–8. doi: 10.1080/03610926.2014.968736.
   Web of Science ®Google Scholar
• Zellner, A. 1986. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association 81 (394):446–51. doi: 10.1080/01621459.1986.10478289.
   Web of Science ®Google Scholar
• Zhang, Y., M. Zhao, S. Zhang, J. Wang, and Y. Zhang. 2017. An integrated approach to estimate storage reliability with initial failures based on E-Bayesian estimates. Reliability Engineering & System Safety 159:24–36. doi: 10.1016/j.ress.2016.10.024.
   Web of Science ®Google Scholar