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Prediction algorithms, such as deep neural networks (DNNs), are used in many domain sciences to directly estimate internal parameters of interest in simulator-based models, especially in settings where the observations include images or complex high-dimensional data. In parallel, modern neural density estimators, such as normalizing flows, are becoming increasingly popular for uncertainty quantification, especially when both parameters and observations are high-dimensional. However, parameter inference is an inverse problem and not a prediction task; thus, an open challenge is to construct conditionally valid and precise confidence regions, with a guaranteed probability of covering the true parameters of the data-generating process, no matter what the (unknown) parameter values are, and without relying on large-sample theory. Many simulator-based inference (SBI) methods are indeed known to produce biased or overly con- fident parameter regions, yielding misleading uncertainty estimates. This paper presents WALDO, a novel method to construct confidence regions with finite-sample conditional validity by leveraging prediction algorithms or posterior estimators that are currently widely adopted in SBI. WALDO reframes the well-known Wald test statistic, and uses a computationally efficient regression-based machinery for classical Neyman inversion of hypothesis tests. We apply our method to a recent high-energy physics problem, where prediction with DNNs has previously led to estimates with prediction bias. We also illustrate how our approach can correct overly confident posterior regions computed with normalizing flows. 

A description is presented of the algorithms used to reconstruct energy deposited in the CMS hadron calorimeter during Run 2 (2015–2018) of the LHC. During Run 2, the characteristic bunch-crossing spacing for proton-proton collisions was 25 ns, which resulted in overlapping signals from adjacent crossings. The energy corresponding to a particular bunch crossing of interest is estimated using the known pulse shapes of energy depositions in the calorimeter, which are measured as functions of both energy and time. A variety of algorithms were developed to mitigate the effects of adjacent bunch crossings on local energy reconstruction in the hadron calorimeter in Run 2, and their performance is compared.

 

A search for decays to invisible particles of Higgs bosons produced in association with a top-antitop quark pair or a vector boson, which both decay to a fully hadronic final state, has been performed using proton-proton collision data collected at$${\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}}$$$\sqrt{s}=13\text{Te}\text{V}$by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$. The 95% confidence level upper limit set on the branching fraction of the 125$$\,\text {Ge}\hspace{-.08em}\text {V}$$$\text{Ge}\text{V}$Higgs boson to invisible particles,$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$, is 0.54 (0.39 expected), assuming standard model production cross sections. The results of this analysis are combined with previous$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$searches carried out at$${\sqrt{s}=7}$$$\sqrt{s}=7$, 8, and 13$$\,\text {Te}\hspace{-.08em}\text {V}$$$\text{Te}\text{V}$in complementary production modes. The combined upper limit at 95% confidence level on$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$is 0.15 (0.08 expected).