They were indeed in the spam list, sorry about this!

]]>Thanks! I do not know why the earlier comments did not make it! I will check in the spam list…

]]>I think that the fact that there are two alternatives (theta_0) in Theorem 2 may be a good thing, as many practitioners seem to use confidence intervals for directional conclusions anyway. (“The interval only contains positive values of theta, so we conclude that theta is non-zero and positive.”) It is therefore very much in line with what people tend to do in practice.

While Theorems 3 and 4 deal with composite hypotheses with positive prior probabilities (I realize know that this could be made clearer in the paper), Theorem 2 is concerned with point-null hypotheses, and allows for testing without a prior mass on the null… as long as the statistician is willing to accept that the decision to reject the null hypothesis always comes with additional information about in which direction it is rejected. The benefits of avoiding a prior mass on the null hypothesis include that you can use noninformative priors and avoid Lindley’s paradox.

Stack Exchange was a great resource for finding relevant papers when I started this research (although I didn’t realize at the time that it would turn into a research problem – I expected there to be a well-known solution!). It is certainly something that I can recommend to other researchers to try.

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