Bayesian inference is applicable here, because we are talking about the subjective probability - ie, confidence - that one single fact is true. There is no way to reduce a single "event" (that there is Higgs particle or there isn't) to a frequentist, or "objective", probability.
As you correctly say, the influence that the results we already got about the possibility that Higgs boson exists with a high mass have on the global possibility that there is a Higgs boson depend on the a-priori (to the current experiment) confidence that we give to the high mass/low mass hypotheses. So there is for sure not a 95% drop in confidence, but there is indeed a drop, unless you gave 0 confidence to the high-mass hypothesis before the experiment.
I'm not saying Bayesian inference isn't applicable, I'm just cautioning against an careless interpretation of its results. But if you insist on interpreting it in this way then yes, it means the probability of finding a Higgs is lower.
However, as I said above the term "95% confidence" is not related to this reasoning at all. Saying for example "the Higgs mass is not 140 GeV at 95% CL" means precisely: If the Higgs were at 140 GeV, it would have 5% probability of producing the results we measured experimentally. It does not mean "we are 95% sure the Higgs isn't at 140 GeV".
Of course not, but we should discount our belief that the Higgs has a mass at 140GeV by a factor roughly proportionate to the 95% confidence of the result. And I don't think anyone in this thread was actually claiming that we are 95% sure the Higgs is not at 140GeV, that's usually precisely the sort of mistake that relying on Bayesian methods helps you avoid.
"we should discount our belief that the Higgs has a mass at 140GeV by a factor roughly proportionate to the 95% confidence of the result"
I'm sorry but I don't understand what this means in practice. The first part is a Bayesian belief, while the 95% confidence result comes from frequentist analysis. I'm not sure how you can mix the two.
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 :)
As you correctly say, the influence that the results we already got about the possibility that Higgs boson exists with a high mass have on the global possibility that there is a Higgs boson depend on the a-priori (to the current experiment) confidence that we give to the high mass/low mass hypotheses. So there is for sure not a 95% drop in confidence, but there is indeed a drop, unless you gave 0 confidence to the high-mass hypothesis before the experiment.