Abstract
It is argued that the high degree of trust in the Higgs particle before its discovery raises the question of a Bayesian perspective on data analysis in high energy physics in an interesting way that differs from other suggestions regarding the deployment of Bayesian strategies in the field.
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This denotes the idea that some kind of Higgs-like particle existed. Whether the Higgs sector was standard-model-like, supersymmetric, composite or else remained an open question.
To be sure, the Higgs particle is not the first example of a prediction in HEP that was strongly believed before empirical confirmation. Still, it offers a particularly nice example for discussing the probabilistic status of a hypothesis prior to empirical testing.
We will come back to p values in Sect. 3.
Another excellent recent example is the case of a hypothesis that was considered most likely false despite seemingly significant empirical data in its support. When the OPERA experiment seemed to measure superluminal neutrinos in 2011, the very low prior probability of the hypothesis that neutrinos could be faster than light (due to very strong, data-based and conceptual trust in the viability of the theory of special relativity) led to a situation where conventional frequentist methods of data assessments were disregarded by most physicists in their assessment of the OPERA data and an implicitly Bayesian assessment of the situation took over. While the prior probability of a mistake in the OPERA experiment was arguably fairly low, it was still considered much higher than the prior probability of neutrinos moving faster than light. In effect, Bayesian updating thus led most physicists to infer from the data an experimental mistake rather than the truth of the hypothesis.
Howson points out that Mayo’s strategy achieves decoupling from the theory’s truth probability only at the price of becoming insensitive to the threat of the so-called base-rate fallacy. Therefore, Howson argues, Mayo’s reasoning cannot justify trust in a theory that has been “severely tested” in Mayo’s sense.
It will be important for the analysis of later sections that this requirement can’t be upheld for the interpretation of the published data.
It would mean going too far to assert that probabilities zero or ”zero for all practical purposes” must not occur in Bayesian analysis. If a hypothesis H is directly inconsistent with a certain empirical outcome E, Bayesian updating under data E sends the posterior probability P(H|E) to zero. We may call that ”zero for all practical purposes” because of the Duhem-Quine thesis, which rejects the idea of an inconsistency between data and an individual hypothesis. One may always save the hypothesis by rejecting other, albeit well entrenched, hypotheses. But one may in certain cases deem that possibility negligable for all practical purposes. The step of setting to zero negative mass square values is of a more problematic kind, however, since it sets to zero the probability of an experimental outcome, namely of certain electron emission rates.
Note that this form of Bayesian analysis would indeed correspond to actual reasoning if measured ”negative mass square” values became overly significant. In that case, physicists would start wondering whether something is wrong with Formula (2) or the basic physical laws that forbid negative mass squares.
This knowledge, as of December 2011, was partly based on calculations which showed that a Higgs with a higher mass would have had an observable effect already in earlier experiments based on virtual Higgs effects, even though no real Higgs particles would have been generated there.
At 5 \(\sigma \), the p value is about 6 times the probability density. Accordingly, \(P(N|E_+)\) would underestimate the probability of the null hypothesis by a factor 6.
In Dawid et al. (2015), the set of assumption is a little more extensive since our assessment of the scientists’ capacity of developing new theories is included in the analysis. For our present purposes, however, it is sufficient to state the following reduced set of assumptions.
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Acknowledgments
I am grateful to three undisclosed referees for very helpful comments. This work was funded in part by the FWF grant P19450-N16 and the DFG grant DA 1633 2-1.
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Dawid, R. Bayesian perspectives on the discovery of the Higgs particle. Synthese 194, 377–394 (2017). https://doi.org/10.1007/s11229-015-0943-6
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DOI: https://doi.org/10.1007/s11229-015-0943-6