It’s also not absolutely necessary to use Bayesian reasoning to come up with a concrete final answer, but still allow for scientific style “we have a significan

It’s also not absolutely necessary to use Bayesian reasoning to come up with a concrete final answer, but still allow for scientific style “we have a significant discovery, but it may not change our view from the status quo just yet” types of publications—significant changes in probability which nevertheless do not make unlikely things likely or vice versa. So there is a very convenient way to view Bayes’ theorem by looking at odds ratios, Pr(A)/Pr(A'), where A' is the complement of A (the event which obtains precisely when A does not), which are equivalent to probabilities but span the range from 0-∞ rather than the range 0-1: Pr(A | E) Pr(A E) Pr(E|A) Pr(A) ------------ = ---------- = ---------- x -------- Pr(A' | E) Pr(A' E) Pr(E|A') Pr(A') In other words the odds after obtaining some evidence E are a multiplicative factor times the prior odds. Taking the logarithm, one essentially can measure the impact of any new evidence in decibels as a linear result; the core of Bayes’ theorem can be stated as saying that evidence is measured in decibels. For example in the breast cancer example in the original article, you have a +13 dB evidence—Pr(E|A)/Pr(E|A') = 20—but the prior log-odds are given as -20dB and thus the shocking conclusion is that after the evidence your log-odds are still negative, -7dB, and you likely do not have cancer. For a life-or-death situation, resolving the relative nature of evidence to a specific probability is clearly essential. But in terms of p-values, if you have an experiment which gives +20dB evidence to something, I would say that this should still be meaningfully publishable as a relative increment even if it hits something whose prior is -30dB and therefore it still is only a ~1/10 chance that the thing is actually true. Like, I think that the key is having a vocabulary for relative results versus absolute results and I think that the Bayesian language can be used to take one step towards that, but perhaps it would be nice if we could have a standardized way in our language to indicate that numbers are relative rather than absolute, the way that we do habitually with decibels and pressures and such all the time...