A Battle in the Statistics Wars: a simulation-based comparison of Bayesian, Frequentist and Williamsonian methodologies

Mantas RADZVILAS, William PEDEN*, Francesco DE PRETIS

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

4 Citations (Scopus)


The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We used Big Data methods to conduct a large number of simulations using a straightforward decision problem based around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player served a benchmark function: any worthwhile statistical methodology should at least match the performance of simplistic induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. The Williamsonian player was also able to perform well given a low confidence level. However, the frequentist and Williamsonian players performed poorly with high confidence levels, while the Bayesian was surprisingly harmed by biased priors. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics.

Original languageEnglish
Pages (from-to)13689-13748
Number of pages60
Issue number5-6
Publication statusPublished - Dec 2021
Externally publishedYes

Bibliographical note

We thank Daniele Tortoli (University of Modena and Reggio Emilia, Italy) for his very valuable support in accelerating computations in our research. We are grateful to two anonymous referees for their helpful comments. We also thank the Erasmus Institute for Philosophy and Economics for their advice on the development of this article. Likewise, we thank Durham University for providing open access for this article.


  • Bayesianism
  • Decision theory
  • Formal epistemology
  • Frequentism
  • Philosophy of statistics
  • Probability


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