The relation between frequentist confidence intervals and Bayesian credible intervals

We investigate the relation between frequentist and Bayesian approaches. Namely, we find the “frequentist” Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial \lambda}dx}{f(x_{obs},\lambda)} (here f(x,\lambda) is the probability density) for which the results of frequentist and Bayes approaches to the determination of confidence intervals coincide. In many cases (but not always) the “frequentist” prior which reproduces frequentist results coincides with the Jeffreys prior.

💡 Research Summary

The paper addresses a long‑standing question in statistical inference: under what conditions do frequentist confidence intervals and Bayesian credible intervals coincide? The authors introduce a novel “frequentist Bayes prior” π_f(λ, x_obs) defined as

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