Under the frequentist framework, one can use power analysis to determine sample size for a given effect size, significance level, and power. How are similar questions answered under Bayesian framework?

  • $\begingroup$ What fun. Well, let's begin with a comment power, which is defined as the probability that we do not make a Type II error, or that we do not reject the null hypothesis when the null is false. But Type I and Type II and hypothesis testing and reject and fail-to-reject and therefore power are all frequentist notions. So you've kind of stacked the deck here! No matter. Bayesian equivalents can be found for all. $\endgroup$ Jul 7, 2019 at 20:25
  • $\begingroup$ As I was preparing a long-ish answer, I noticed that this question has been asked and answered many times at Cross Validated. I'll survey the previous answers and will only comment if I can add something that the others cannot. $\endgroup$ Jul 8, 2019 at 21:44
  • $\begingroup$ I should also point out that the power calculation in the frequentist framework also requires a definition of the population standard deviation, without which standard errors cannot be calculated, so $\alpha$, $\beta$, $\sigma$, $\delta$ and $N$ are the five values, and any four need to be specified to uniquely define the fifth . . . in frequentist statistics. $\endgroup$ Jul 8, 2019 at 21:49