Power analysis from Bayesian point of view [duplicate]

Question

I was reading an article on a power analysis and sample size calculations for a class of models that known as joint longitudinal-survival models. The paper derives a closed form formula for power and sample size calculation. This paper is a frequentist paper in a sense that it assumes parametric assumptions and based on those assumptions, it gets likelihood, score function, … and it eventually gets the formula.

I was wondering how power analysis and sample size calculations are done in Bayesian framework?

Probably my question is naive especially given that I'm not expert in power analysis, but I think no matter how we approach a problem, once we have a hypothesis, power analysis is essential. So, I wanted to ask:

1. Is power analysis also done in Bayesian framework?

2. Could someone kindly references some papers on power analysis from Bayesian perspective? Would be great if I can find a power analysis for problems tackled with Bayesian nonparameteric approaches.

Answer 1

1. Here is where the difference between the Bayesian and the Classical paradigm becomes more evident. A power analysis is not strictly necessary in a Bayesian context since the goal is to update your prior beliefs about the null hypothesis with the data. Moreover, there are other ingredients in a Bayesian hypothesis test that play an important role, such as the prior distribution and the type of decision criterion used as a test (e.g. Bayes factors). However, a power analysis is still useful in order to understand the influence of the data and the prior on the chosen criterion. For example, there are recent studies about priors that improve the "power" of the test induced by the use of Bayes factors:

• Johnson & Rossell, 2010, On the use of non-local prior densities in Bayesian hypothesis tests

2. Please, take a look at the paper mentioned above and the references therein.

If you want to use BNP, then you have another kind of difference since the dimensionality of the parameter space is infinite in this context, which has other philosophical implications. Then, you have to specify the sort of hypotheses of interest. The following paper provides an example of a basic BNP test:

• Holmes et al., 2012, Two-sample Bayesian nonparametric hypothesis testing

They conduct a "power" analysis in page 7.