Consider Alice and Bob. Alice is a mainstream statistician, aka a frequentist. Bob is a Bayesian.
We take our clinical trial results and give them to both Alice and Bob.
Alice says: the p-value for the drug effectiveness is X. This means that there is X% probability that the results we see arose entirely by chance while the drug has no effect at all.
Bob says: my posterior probability for drug being useless is Y. This means Bob believes that there is (1-Y)% probability that drug is effective and Y% probability that is has no effect.
Given that both are competent and Bob doesn't have strong priors X should be about the same as Y.
Do note that both Alice and Bob provided a probability as the outcome.
Now after that statistical analysis someone, let's call him Trent, needs to make a binary decision. Trent says "I have a threshold of certainty/confidence Z. If the probability of the drug working is greater than Z, I will make a positive decision. If it's lower, I will make a negative decision".
Alice comes forward and says: here is my probability of the drug working, it is (1-X).
Bob comes forward and says: here is my probability of the drug working, it is (1-Y).
So, you're saying that if Trent relies on Alice's number (which was produced in the frequentist way) he is in danger of committing a Type I error. But if Trent relies on Bob's number (which was produced in the Bayesian way) he cannot possibly commit a Type I error. Yes?
And then you start to fight the hypothetical and say that Trent really should not make a binary decision. He should just publish the probability and let everyone make their own decisions. Maybe -- that works in some cases and doesn't work in others. But Trent can publish Alice's number, and he can publish Bob's number -- they are pretty much the same and both can be adequate inputs into some utility function. So where exactly is the Bayesian advantage?
Given that both are competent and Bob doesn't have strong priors X should be about the same as Y.
Why? X is P(results >= what we saw | effect = 0), whereas Y is P(effect < costs | results = what we saw). I can see no obvious reason those would be similar, not even if we assume costs = 0; p(results = what we saw | effect = 0) = p(effect = 0 | results = what we saw) iff p_{prior}(result = what we saw) = p_{prior}(effect = 0) (where the small p's are probability densities, not probability masses), but that's another story.
For those who haven't heard, NIH and NSF are no longer processing grants, leading to many negative downstream effects.
I've been directing my attention elsewhere lately and don't have anything informative to say about this. However, my uninformed intuition is that people who care about effective altruism (research in general, infrastructure development, X-risk mitigation, life-extension...basically everything, actually) or have transhumanist leanings should be very concerned.
The consequences have already been pretty disastrous. To provide just one, immediate example, the article says that the Center for Disease Control and Prevention has shut down. I think that this is almost certain to directly cause a nontrivial number of deaths. Each additional day that this continues could have huge negative impact down the line, perhaps delaying some key future discoveries by years. This event *might* be a small window of opportunity to prevent a lot of harm very cheaply.
So the question is:
1) Can we do anything to remedy the situation?
2) If so, is it worth doing it? (Opportunity costs, etc)