Frequentist–Bayesian Divide and Coherence of Hybrid Methods

Determine whether the divide between frequentist and Bayesian approaches in statistics is philosophically substantive; ascertain whether hybrid statistical methods that combine frequentist and Bayesian components (such as those initiated by Freedman 1963) constitute a coherent middle way or are an incoherent mixture of ideas.

Background

The paper highlights the historical and philosophical tension between frequentist and Bayesian paradigms in statistics, noting longstanding debates about their foundations and practice. It also points out the existence of hybrid approaches dating back to the 1960s that integrate elements of both traditions, raising the question of whether these hybrids provide a principled synthesis or merely an ad hoc combination.

Clarifying this issue would inform both epistemological analysis and methodological guidance in statistics, especially as the boundary between statistics and machine learning continues to blur.

References

Open Question I (from Statistics). The greatest divide in philosophy of statistics is between frequentist and Bayesian approaches (although the present paper has largely ignored the development of Bayesianism). However, hybrid methods have been developed since the 1960s (Freedman 1963). Is the divide real? Is the hybrid a coherent middle way, or just a mixed bag of incoherent ideas?

— A Plea for History and Philosophy of Statistics and Machine Learning (2506.22236 - Lin, 27 Jun 2025) in Section 9 (Closing): Open Question I (from Statistics)