The difference is that frequentist practice would be to stop at the 95% confidence interval and leave it there, whereas a Bayesian would use that observation to update their probability estimate of the theory being true.
"If the Higgs were at 140 GeV, it would have 5% probability of producing the results we measured experimentally" is the same as
P(Observation | Higgs at 140Gev) = .05
So given that getting your new belief about the probability of a Higgs Boson at some energy is going to be updated based on your observation, you can see that it ends up being scaled by that exact confidence result. That's sort of an oversimplification, since really you end up calculating the P(O) scaling factor based on P(O|H) among other things, but I hope you can see how they're closely related in practice.
Thank you, now I understand what you meant. I concede (again) that using Bayesian analysis the new results do lower the probability that the Higgs exists. Personally I don't subscribe to this point of view since, if the Higgs exists and has a low mass, the most likely chain of events is: Bayesian probability for Higgs existence starts at some subjective value, goes down (with a subjective slope that depends on your priors), then goes up and reaches 1. Not only is it subjective, this just doesn't feel to me like it is describing anything "real"; it seems like we're just playing with numbers. But I guess this is already way off topic for this discussion.
For me the important point to communicate was that the article is, let's say, mostly nonsense. Just consider the title:
> A Higgs Setback: Did Stephen Hawking Just Win the Most Outrageous Bet in Physics History?
Never mind the superlatives. There was no "Higgs setback", and the answer to the question is "No". The article does not leave out the correct details, but I'm quite certain it leaves the layman with the feeling that the Higgs search is all but doomed.
I agree with you about the article being just sensationalistic non-journalism.
About not using a Bayesian approach, though, I don't understand how could you infer the existence or not of the Higgs without it, considering that we can only measure something that is probabilistically correlated to what we want to find.
In other words, what should happen for you to say that we have verified that there is a Higgs boson? I'm pretty confident that it would be some application of Bayes theorem :)
"If the Higgs were at 140 GeV, it would have 5% probability of producing the results we measured experimentally" is the same as P(Observation | Higgs at 140Gev) = .05
So we can say that
So given that getting your new belief about the probability of a Higgs Boson at some energy is going to be updated based on your observation, you can see that it ends up being scaled by that exact confidence result. That's sort of an oversimplification, since really you end up calculating the P(O) scaling factor based on P(O|H) among other things, but I hope you can see how they're closely related in practice.