Huh.

This is an interesting post but the author’s usage of Lindley’s paradox seems to be unrelated to the Lindley’s paradox I’m familiar with:

> If we raise the power even further, we get to “Lindley’s paradox”, the fact that p-values in this bin can be less likely then they are under the null.

Lindley’s paradox as I know it (and as described by Wikipedia [1]) is about the potential for arbitrarily large disagreements between frequentist and Bayesian analyses of the same data. In particular, you can have an arbitrarily small p-value (p < epsilon) from the frequentist analysis while at the same time having arbitrarily large posterior probabilities for the null hypothesis model (P(M_0|X) > 1-epsilon) from the Bayesian analysis of the same data, without any particularly funky priors or anything like that.

I don’t see any relationship to the phenomenon given the name of Lindley’s paradox in the blog post.

[1] https://en.wikipedia.org/wiki/Lindley%27s_paradox