If we assume a beta prior, which includes a non-informational prior that follows a uniform distribution, then for binomially distributed data, the posterior distribution is also a beta distribution. This enables us to easily determine the high-density interval.
Topics
- Conjugate Prior
- High-density Interval
- Hypothesis Testing
- Hypothesis Testing Tools
- Bayesian Characterization of a Beta Distribution
- Bayesian Beta Test Sample and Effect Sizes
Link
↑ Bayesian statistics for binomial distributions
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B. (2014) Bayesian data analysis, 3rd Ed. CRC Press
https://statisticalsupportandresearch.files.wordpress.com/2017/11/bayesian_data_analysis.pdf
Marin, J-M and Robert, C. R. (2014) Bayesian essentials with R. 2nd Ed. Springer
https://www.springer.com/gp/book/9781461486862
Jordan, M. (2010) Bayesian modeling and inference. Course notes
https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/lectures/index.html
Lee, P. M. (2012) Bayesian statistics an introduction. 4th Ed. Wiley
https://www.wiley.com/en-us/Bayesian+Statistics%3A+An+Introduction%2C+4th+Edition-p-9781118332573
Reich, B. J., Ghosh, S. K. (2019) Bayesian statistics methods. CRC Press