Bayesian Statistics for Binomial Distributed Data

We now show how to use the Bayesian approach when the data comes from a population with a binomial distribution. In particular, we demonstrate different approaches to estimating the posterior distribution based on three techniques for representing the prior distribution.

We tend to use coin-tossing examples but keep in mind the same approaches can be used to address a great variety of practical problems.

Topics

• Grid Approximation
  • Creating a Grid
  • Creating a Grid using Real Statistics
  • Credible intervals and creating an HDI using Real Statistics
• Analytic Approach
  • Beta Conjugate Prior
  • High-density Interval (HDI)
• Markov-Chain Monte Carlo
  • Random Walk Metropolis Algorithm
  • Effective Sample Size
• Two-Sample Case
  • Analytic Approach
  • Grid Approximation
  • Metropolis Algorithm
  • Gibbs Sampler

References

Lee, P. M. (2012) Bayesian statistics an introduction. 4^th Ed. Wiley
https://www.wiley.com/en-us/Bayesian+Statistics%3A+An+Introduction%2C+4th+Edition-p-9781118332573

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B. (2014) Bayesian data analysis, 3^rd Ed. CRC Press
https://statisticalsupportandresearch.files.wordpress.com/2017/11/bayesian_data_analysis.pdf