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A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic:

Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian Intervals,' in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, W. L. Harper and C. A. Hooker (eds.), D. Reidel, Dordrecht, p. 175; (pdf)

In the abstract, Jaynes writes:

...we exhibit the Bayesian and orthodox solutions to six common statistical problems involving confidence intervals (including significance tests based on the same reasoning). In every case, we find the situation is exactly the opposite, i.e. the Bayesian method is easier to apply and yields the same or better results. Indeed, the orthodox results are satisfactory only when they agree closely (or exactly) with the Bayesian results. NO CONTRARY EXAMPLE HAS YET BEEN PRODUCED

(the SHOUTING being mine not Jaynes')

The paper was published in 1976, so perhaps things have moved on, so my question is, are there examples where the frequentist confidence interval is clearly superior to the Bayesian credible interval (as per the challenge implicitly made by Jaynes).

Examples based on incorrect prior assumptions are not acceptable as they say nothing about the internal consistency of the different approaches.

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic:

Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian Intervals,' in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, W. L. Harper and C. A. Hooker (eds.), D. Reidel, Dordrecht, p. 175; (pdf)

In the abstract, Jaynes writes:

...we exhibit the Bayesian and orthodox solutions to six common statistical problems involving confidence intervals (including significance tests based on the same reasoning). In every case, we find the situation is exactly the opposite, i.e. the Bayesian method is easier to apply and yields the same or better results. Indeed, the orthodox results are satisfactory only when they agree closely (or exactly) with the Bayesian results. No contrary example has yet been produced.

(emphasis mine)

The paper was published in 1976, so perhaps things have moved on. My question is, are there examples where the frequentist confidence interval is clearly superior to the Bayesian credible interval (as per the challenge implicitly made by Jaynes)?

Examples based on incorrect prior assumptions are not acceptable as they say nothing about the internal consistency of the different approaches.

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic:

Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian Intervals,' in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, W. L. Harper and C. A. Hooker (eds.), D. Reidel, Dordrecht, p. 175; (pdf)

In the abstract, Jaynes writes:

"...we exhibit the Bayesian and orthodox solutions to six common statistical problems involving confidence intervals (including significance tests based on the same reasoning). In every case, we find the situation is exactly the opposite, i.e. the Bayesian method is easier to apply and yields the same or better results. Indeed, the orthodox results are satisfactory only when they agree closely (or exactly) with the Bayesian results. NO CONTRARY EXAMPLE HAS YET BEEN PRODUCED". (the SHOUTING being mine not Jaynes')

The paper was published in 1976, so perhaps things have moved on, so my question is, are there examples where the frequentist confidence interval is clearly superior to the Bayesian credible interval (as per the challenge implicitly made by Jaynes).

Examples based on incorrect prior assumptions are not acceptable as they say nothing about the internal consistency of the different approaches.

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic:

Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian Intervals,' in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, W. L. Harper and C. A. Hooker (eds.), D. Reidel, Dordrecht, p. 175; (pdf)

In the abstract, Jaynes writes:

...we exhibit the Bayesian and orthodox solutions to six common statistical problems involving confidence intervals (including significance tests based on the same reasoning). In every case, we find the situation is exactly the opposite, i.e. the Bayesian method is easier to apply and yields the same or better results. Indeed, the orthodox results are satisfactory only when they agree closely (or exactly) with the Bayesian results. NO CONTRARY EXAMPLE HAS YET BEEN PRODUCED

(the SHOUTING being mine not Jaynes')

The paper was published in 1976, so perhaps things have moved on, so my question is, are there examples where the frequentist confidence interval is clearly superior to the Bayesian credible interval (as per the challenge implicitly made by Jaynes).

Examples based on incorrect prior assumptions are not acceptable as they say nothing about the internal consistency of the different approaches.