I understand that I'm asking a very pedantic question, but as far as I'm aware a confidence region is a multi-dimensional generalization of a confidence interval and therefore as a credible interval is not a confidence interval, it is not a confidence region, however despite this I'm seen many sources act as if this is not the case. One such example being Hoff's A First Course in Bayesian Statistical Methods, which spends its entire 'confidence regions' chapter talking about credible intervals. Have I missed something? Why are there sources that treat credible intervals as confidence regions despite them not being the same things?

  • $\begingroup$ I have voted to close as a duplicate. If you don't think the earlier question addresses your concerns, perhaps you could edit your question to be more specific? Incidentally, browsing previous threads tagged both "credible-interval" and "confidence-interval" yields some questions that may be helpful. $\endgroup$ – Stephan Kolassa Nov 3 '17 at 16:59
  • $\begingroup$ Not a duplicate, even if the question was entirely about the difference between confidence intervals and credible intervals, neither the linked question nor its answers make any mention of confidence regions. $\endgroup$ – J. Min Nov 3 '17 at 17:01
  • $\begingroup$ Confidence regions are simply the multidimensional analogue of confidence intervals. Or: confidence intervals are confidence regions of dimension 1. Just as you can talk of credible regions as the multidimensional analogue for credible intervals, and of course the linked question applies equally well to the difference between confidence regions and credible regions as to the difference between confidence and credible intervals. Maybe I am not understanding your question. If so, that would be another argument for clarifying what you are asking about. $\endgroup$ – Stephan Kolassa Nov 3 '17 at 17:30
  • $\begingroup$ Point taken. Will edit. $\endgroup$ – J. Min Nov 3 '17 at 17:33
  • $\begingroup$ I don't think we can speculate about "sources" in general. That leaves us searching for a question and since the focus of this text is comparing confidence intervals and credible intervals, the duplicate appears appropriate. $\endgroup$ – whuber Nov 3 '17 at 18:16