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Supplemental Information

The proof of Beta conjugate to Bernoulli/Binomial distribution

DOI: 10.7287/peerj.preprints.27170v1/supp-1

The diagram of enumerating all possible 2x2 tables and exact probability calculation

DOI: 10.7287/peerj.preprints.27170v1/supp-2

Additional Information

Competing Interests

The authors declare that they have no competing interests.

Author Contributions

Juan Wang performed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the paper, approved the final draft.

Ryo Yamada conceived and designed the experiments, contributed reagents/materials/analysis tools, authored or reviewed drafts of the paper, approved the final draft.

Data Deposition

The following information was supplied regarding data availability:

The exact probability calculation and the Monte Carlo simulation were performed with our R code, which is available at GitHub:


This work was supported by the Core Research for Evolutionary Science and Technology (no.15656320) ( and Kiban-C (no. 14469361) ( The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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