No, because the Bayesian conditioning ends up being used twice. If you and a friend do an experiment independently, and he gets 10 and you later get 12, you might justifiably think the answer is closer to 11.

But you shouldn’t publish that you got 11. Because then somebody else will see that the measurements were 10 and 11, and think the true answer is closer to 10.5...

The correct approach would be to say something like "Previous experiments reported X, we observed X + Y, therefore the real answer is probably around X + Y/10." But it's very important to state the observation of X + Y, not X + Y/10, otherwise you'll take much too long to update to the correct value!

No, it isn't.

The appropriate approach is to accept the evidence, and correct your priors based on it, even if it's not good enough to believe. It's not to fiddle with the evidence until it's something you believe is correct.

Of course, it's much easier said than done. I don't think any group of scientists is safe from repeating this.

I was kind of wondering about this after reading the passage.

On the one hand the traditional Bayesian response is something like "yes, we're making our prior assumptions explicit and then incorporating that into a formal inferential paradigm."

However, this prior is being used to bias the estimates, rather than to avoid the bias. That is, it would be akin to Dunnington taking the current estimates of e/m and using that to shape any new estimates from data. The argument is then that at least he was being explicit about his biases and how they are used to make an estimate.

This has always seemed backwards to me, though. It seems what is more defensible is to use a formal theory about how prior biases affect estimates, and then to leverage that theory to minimize biases. This is basically the idea of the reference prior, to estimate things such that any role of the prior is minimized in an information-theoretic sense. This seems more analogous to what Dunnington was doing.

I really wish reference priors were more widespread, although they can be computationally pretty hefty. It's one of my hopes that quantum computing might make these types of approaches more feasible in general.

Being a good Bayesian would entail taking the evidence as-is, only adjusting your estimate of the "true" value after the fact taking other measurements into account.