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

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2021
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Peden, William
De Pretis, Francesco
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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.

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100 Philosophie
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Bayesianism, Decision theory, Formal epistemology, Frequentism, Philosophy of statistics, Probability
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ISO 690RADZVILAS, Mantas, William PEDEN, Francesco DE PRETIS, 2021. A Battle in the Statistics Wars : a simulation-based comparison of Bayesian, Frequentist and Williamsonian methodologies. In: Synthese. Springer. 2021, 199(5-6), pp. 13689-13748. ISSN 0039-7857. eISSN 1573-0964. Available under: doi: 10.1007/s11229-021-03395-y
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@article{Radzvilas2021-12Battl-57877,
  year={2021},
  doi={10.1007/s11229-021-03395-y},
  title={A Battle in the Statistics Wars : a simulation-based comparison of Bayesian, Frequentist and Williamsonian methodologies},
  number={5-6},
  volume={199},
  issn={0039-7857},
  journal={Synthese},
  pages={13689--13748},
  author={Radzvilas, Mantas and Peden, William and De Pretis, Francesco}
}
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