> I am interested in, for example, particle physics. There we need need simple ways to communicate point estimates and the associated uncertainties for various parameters of nature.
Okay, but what do you _do_ with a confidence interval once you have it? It's just an abstract object that can't be used to take your knowledge and make better predictions about the future. If I tell you "This new particle decays with a half life of 28 years with a 95% confidence interval of +/- 5 years", can you take that information and use it to estimate the age of an object that started with 236 particles and now has 182 particles?
> this is not a question about estimating an unknown parameter of a distribution, so it's not statistical in the sense Wasserman is talking about
And a frequentist confidence interval doesn't answer a question about how you should update your knowledge so you can make better predictions in the future, so it's not statistical in the sense bayesians talk about.
The blog post talks about inference, not prediction, so I find it odd you keep bringing up prediction tasks. There are interesting questions and differences here, but it is very much not the subject of the post.
A standard frequentist tool for making predictions is the prediction interval. This is the appropriate comparison point for Bayesian prediction methods, and exactly the same issues arise as in the comparison of confidence intervals to credible intervals (or posteriors). Namely, frequentist prediction intervals have guaranteed error control, while Bayesian predictions generally do not. So in certain cases you have to choose between being right most of time about your predictions, and being Bayesian.
Okay, but what do you _do_ with a confidence interval once you have it? It's just an abstract object that can't be used to take your knowledge and make better predictions about the future. If I tell you "This new particle decays with a half life of 28 years with a 95% confidence interval of +/- 5 years", can you take that information and use it to estimate the age of an object that started with 236 particles and now has 182 particles?
> this is not a question about estimating an unknown parameter of a distribution, so it's not statistical in the sense Wasserman is talking about
And a frequentist confidence interval doesn't answer a question about how you should update your knowledge so you can make better predictions in the future, so it's not statistical in the sense bayesians talk about.