3 ms·

I think we should be careful with Bayesian inference for the usual reason -- there is only one universe with one (or zero) Higgs particle. You can't really coll

I think we should be careful with Bayesian inference for the usual reason -- there is only one universe with one (or zero) Higgs particle. You can't really collect statistics over universes, so what is the meaning of probability in this case? More concretely, what prior probability would you assign to the distribution of the Higgs mass? This depends on your theory. For instance, supersymmetric theories tend to favor a lower Higgs mass, so if you are a proponent of such theories you wouldn't expect a heavy Higgs anyway. Note that physicists themselves do not phrase their results in these terms. The statement "Higgs excluded above 130 GeV at 95% confidence" does not mean there is 95% chance the Higgs isn't there. Rather, this statement has a precise meaning based on frequentist reasoning. But perhaps more importantly, the tone of the article is sensationalist and seems to imply that we are about to give up hope. This isn't true at all. I mean, look: "while CERN will continue it's search at least until the end of this year, if no positive results about the Higgs should come out, Stephen Hawking ... would be able to cash in on his wager."

deleted 15y ago
[deleted]
danmaz74 15y ago
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.
- guygurari 15y ago
  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".
  - Symmetry 15y ago
    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.
    - guygurari 15y ago
      "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.
      - Symmetry 15y ago
        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 we can say that P(Higgs|Observation) = P(Observation|Higgs) * P(Higgs) ------------------------------- P(Observation) 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.
        guygurari 15y ago
        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.
sskates 15y ago
I'm not saying there's a 95% chance the Higgs isn't there. I'm saying there was some non-zero probability that it was in the specified energy range before, and given these results the probability that it's now in that range is now 5% of the value it was before. Or more precisely, the probability that we're in the universe where the Higgs is in the specified energy range and it's detectable with this experiment just went down to 5% of it's original value. Even if we can't accurately identify what the value of the probability is, we can still say it went down to 5% of its original value on the basis of the evidence from this experiment. I would also argue that prior to this experiment the probability of the Higgs appearing in this energy range given our state of evidence of how the universe works was significant (more than 15% I'd say) otherwise we wouldn't have built the LHC. I understand you can't say this with a frequentist approach because we don't have a sample of universes to draw on to estimate priors. Finally we're not talking about the probability of some state of the universe in the absolute (as frequentists claim, we can't meaningfully talk about such things), we're talking about some state of the universe given the evidence we have.

deleted 15y ago

[deleted]

danmaz74 15y ago

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.

guygurari 15y ago
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".
- Symmetry 15y ago
  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.
  - guygurari 15y ago
    "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.
    - Symmetry 15y ago
      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 we can say that P(Higgs|Observation) = P(Observation|Higgs) * P(Higgs) ------------------------------- P(Observation) 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.
      - guygurari 15y ago
        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.

sskates 15y ago

I'm not saying there's a 95% chance the Higgs isn't there. I'm saying there was some non-zero probability that it was in the specified energy range before, and given these results the probability that it's now in that range is now 5% of the value it was before. Or more precisely, the probability that we're in the universe where the Higgs is in the specified energy range and it's detectable with this experiment just went down to 5% of it's original value. Even if we can't accurately identify what the value of the probability is, we can still say it went down to 5% of its original value on the basis of the evidence from this experiment. I would also argue that prior to this experiment the probability of the Higgs appearing in this energy range given our state of evidence of how the universe works was significant (more than 15% I'd say) otherwise we wouldn't have built the LHC. I understand you can't say this with a frequentist approach because we don't have a sample of universes to draw on to estimate priors. Finally we're not talking about the probability of some state of the universe in the absolute (as frequentists claim, we can't meaningfully talk about such things), we're talking about some state of the universe given the evidence we have.