“Generic and consistent confidence and credible regions”

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Christian Bartels sends along this paper, which begins:

A generic, consistent, efficient and exact method is proposed for set selection. The method is generic in that its definition and implementation uses only the likelihood function. The method is consistent in that the same criterion is used to select confidence and credible sets making the two kinds of sets consistent even though the two sets may differ since they answer different questions. The method is exact in that no approximations are used except numerical integration which can be made as exact as needed by investing computational resources. The method is efficient to the point that it makes possible confidence set determinations by numerical integration which are otherwise impractical. The method requires computational resources comparable to what is needed for a Bayesian analysis and may be more efficient than bootstrap of maximum likelihood estimates as it avoids repeated minimizations of randomly perturbed data.

It’s not quite what I do, but I think it might interest some of you who are interested in numerical integration and the foundations of statistics. Enjoy, and feel free to give your comments below!

2 thoughts on ““Generic and consistent confidence and credible regions”

  1. Maybe I’m dumb but when I read it through I saw a series of statements that you can do this and then a single example “assumed to come from a negative binomial distribution”, and a few pictures but I’m not going to parse every sentence to try to figure out why this might work when the author should say that for me. In other words, I have 2 issues without thinking about this deeper and they’re versions of this blog’s basic topics: a sample size of 1 and the lack of explanation why this process generates this result. In other words, not generalized except as a description of this process yields these results given this input.

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