Why scoring functions cannot assess tail properties

Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of distribution tails be elicitable, i.e. be the unique minimizer of an expected score? We demonstrate that expected scores are not suitable to distinguish genuine tail properties in a very strong sense. Specifically, we introduce the class of max-functionals, which contains key characteristics from extreme value theory, for instance the extreme value index. We show that its members fail to be elicitable and that their elicitation complexity is in fact infinite under mild regularity assumptions. Further we prove that, even if the information of a max-functional is reported via the entire distribution function, a proper scoring rule cannot separate max-functional values. These findings highlight the caution needed in forecast evaluation and statistical inference if relevant information is encoded by such functionals.Comment: 18 page

Pushing Higgs Effective Theory over the Edge

Based on a vector triplet model we study a possible failure of dimension-6 operators in describing LHC Higgs kinematics. First, we illustrate that including dimension-6 contributions squared can significantly improve the agreement between the full model and the dimension-6 approximation, both in associated Higgs production and in weak-boson-fusion Higgs production. Second, we test how a simplified model with an additional heavy scalar could improve the agreement in critical LHC observables. In weak boson fusion we find an improvement for virtuality-related observables at large energies, but at the cost of sizeable deviations in interference patterns and angular correlations.Comment: 19 pages. v2: references added. v3: minor corrections, more references added, matches published versio

Mining gold from implicit models to improve likelihood-free inference

Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based inference techniques that go beyond the traditional Approximate Bayesian Computation approach, which struggles in a high-dimensional setting, and extend methods that use surrogate models based on neural networks. We show that additional information, such as the joint likelihood ratio and the joint score, can often be extracted from simulators and used to augment the training data for these surrogate models. Finally, we demonstrate that these new techniques are more sample efficient and provide higher-fidelity inference than traditional methods.Comment: Code available at https://github.com/johannbrehmer/simulator-mining-example . v2: Fixed typos. v3: Expanded discussion, added Lotka-Volterra example. v4: Improved clarit

Symmetry Restored in Dibosons at the LHC?

A number of LHC resonance search channels display an excess in the invariant mass region of 1.8 - 2.0 TeV. Among them is a $3.4\,\sigma$ excess in the fully hadronic decay of a pair of Standard Model electroweak gauge bosons, in addition to potential signals in the $HW$ and dijet final states. We perform a model-independent cross-section fit to the results of all ATLAS and CMS searches sensitive to these final states. We then interpret these results in the context of the Left-Right Symmetric Model, based on the extended gauge group $SU(2)_L\times SU(2)_R\times U(1)'$, and show that a heavy right-handed gauge boson $W_R$ can naturally explain the current measurements with just a single coupling $g_R \sim 0.4$. In addition, we discuss a possible connection to dark matter.Comment: 25 pages, 12 figures, V2: references added, extended discussion of Minimal Left-Right Dark Matter, small correction to decay width - conclusions unchanged, V3: expanded discussion of input parameters and statistical procedure, V4: matches published versio

An Exactly Solvable Model of Generalized Spin Ladder

A detailed study of an $S={1\over2}$ spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R-matrix and L-operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation