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Bridges, M., Cranmer, K., Feroz, F., Hobson, M., Ruiz de Austri, R., & Trotta, R. (2011). A coverage study of the CMSSM based on ATLAS sensitivity using fast neural networks techniques. J. High Energy Phys., 03(3), 012–23pp.
Abstract: We assess the coverage properties of confidence and credible intervals on the CMSSM parameter space inferred from a Bayesian posterior and the profile likelihood based on an ATLAS sensitivity study. In order to make those calculations feasible, we introduce a new method based on neural networks to approximate the mapping between CMSSM parameters and weak-scale particle masses. Our method reduces the computational effort needed to sample the CMSSM parameter space by a factor of similar to 10(4) with respect to conventional techniques. We find that both the Bayesian posterior and the profile likelihood intervals can significantly over-cover and identify the origin of this effect to physical boundaries in the parameter space. Finally, we point out that the effects intrinsic to the statistical procedure are conflated with simplifications to the likelihood functions from the experiments themselves.
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Cranmer, K. et al, & Sanz, V. (2022). Publishing statistical models: Getting the most out of particle physics experiments. SciPost Phys., 12(1), 037–55pp.
Abstract: The statistical models used to derive the results of experimental analyses are of incredible scientific value and are essential information for analysis preservation and reuse. In this paper, we make the scientific case for systematically publishing the full statistical models and discuss the technical developments that make this practical. By means of a variety of physics cases – including parton distribution functions, Higgs boson measurements, effective field theory interpretations, direct searches for new physics, heavy flavor physics, direct dark matter detection, world averages, and beyond the Standard Model global fits – we illustrate how detailed information on the statistical modelling can enhance the short- and long-term impact of experimental results.
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Feroz, F., Cranmer, K., Hobson, M., Ruiz de Austri, R., & Trotta, R. (2011). Challenges of profile likelihood evaluation in multi-dimensional SUSY scans. J. High Energy Phys., 06(6), 042–23pp.
Abstract: Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MULTINEST, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration previously used in the literarture is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MULTINEST configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MULTINEST is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.
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