Propose example notebook on Bayesian Power Analysis

Notebook proposal

Title: Bayesian Power Analysis

Why should this notebook be added to pymc-examples?

As pointed out in #349, we don't have anything currently on hypothesis testing, and nothing (nearly nothing?) on decision making. Filling this gap in the topic coverage would be good.

The notebook could go into a new category of "Hypothesis Testing" or the existing "How to" category.

PS This issue was inspired by the proposal by @cetagostini to bring Bayesian Power Analysis to CasusalPy

Suggested categories:

• Level: Beginner or intermediate

Related notebooks

I don't believe there would be any overlap or redundancy caused by adding this. However the proposed notebook might be grouped in with one on hypothesis testing (see #349) and with currently WIP PR #477 on decision utility functions.

References

Indicative references:

• https://stats.stackexchange.com/questions/65754/is-power-analysis-necessary-in-bayesian-statistics
• https://www.rdatagen.net/post/2021-06-01-bayesian-power-analysis/
• Kruschke, J.K., Liddell, T.M. The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychon Bull Rev 25, 178–206 (2018). https://doi.org/10.3758/s13423-016-1221-4
• Peter Rosenfeld, J., Olson, J.M. Bayesian Data Analysis: A Fresh Approach to Power Issues and Null Hypothesis Interpretation. Appl Psychophysiol Biofeedback 46, 135–140 (2021). https://doi.org/10.1007/s10484-020-09502-y
• Baker, R., & Hirudayaraj, M. (2019). Power Analysis, p Values, and Bayesian Techniques: How Bayesian Techniques Can Be Used in HRD Literature. Advances in Developing Human Resources, 21(4), 438-465. https://doi.org/10.1177/1523422319870565

Start by reading related issue #349 and WIP PR #477, then review the existing notebook categories and related examples in pymc-examples. Clarify the Bayesian power analysis scope, intended audience, and category before implementation. Done means an agreed, non-redundant example notebook is added with the relevant references.