Illia Babounikau

Forecast quality should be assessed in the context of what is possible in theory and what is reasonable to expect in practice. Often, one can identify an approximate upper bound to a probabilistic forecast's sharpness, which sets a lower, not necessarily achievable, limit to error metrics. In retail forecasting, a simple, but often unconquerable sharpness limit is given by the Poisson distribution. When evaluating forecasts using traditional metrics such as Mean Absolute Error, it is hard to judge whether a certain achieved value reflects unavoidable Poisson noise or truly indicates an overdispersed prediction model. Moreover, every evaluation metric suffers from precision scaling: Perhaps surprisingly, the metric's value is mostly defined by the selling rate and by the resulting rate-dependent Poisson noise, and only secondarily by the forecast quality. For any metric, comparing two groups of forecasted products often yields "the slow movers are performing worse than the fast movers" or vice versa, the na\"ive scaling trap. To distill the intrinsic quality of a forecast, we stratify predictions into buckets of approximately equal predicted value and evaluate metrics separately per bucket. By comparing the achieved value per bucket to benchmarks, we obtain an intuitive visualization of forecast quality, which can be summarized into a single rating that makes forecast quality comparable among different products or even industries. The thereby developed scaling-aware forecast rating is applied to forecasting models used on the M5 competition dataset as well as to real-life forecasts provided by Blue Yonder's Demand Edge for Retail solution for grocery products in Sainsbury's supermarkets in the United Kingdom. The results permit a clear interpretation and high-level understanding of model quality by non-experts.

Searches for supersymmetry are presented that target direct and indirect stau pair production. The analyses exploit the final states with two taus of opposite charge and significant missing transverse momentum. The results are based on a data set of proton-proton collisions, recorded by the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 36 $fb^{−1}$ . Exclusion limits on parameters of simplified SUSY models are calculated. For direct $\tilde{τ}$ production we use three different $\tilde{τ}$ “chiral states”: a purely left-handed $\tilde{τ}$ , a purely right-handed $\tilde{τ}$ and maximal mixing between the right- and left-handed eigenstates. For indirect $\tilde{τ}$ production we consider simplified models of mass-degenerate chargino-neutralino and chargino pair production. Stau mass is an average value between the mass of the parent sparticles and LSP. For chargino pair production equal branching fractions are assumed for each of the two possible chargino decay chains and for chargino-neutralino production we set chargino mass to be equal to neutralino mass. Since the tau leptons can decay hadronically or leptonically, we target different decay channels in order to increase the number of signal events combining two analyses. The first analysis has both taus decay hadronically. The second has one tau decays to a lighter lepton and neutrinos, while the other one decays hadronically or first (second) tau decays to electron (muon) and neutrinos. No significant deviation from the SM in any signal region was observed. We exclude heavy neutralinos and charginos decaying through $\tilde{τ}$ up to 725 GeV for chargino-neutralino production and chargino decaying through $\tilde{τ}$ up to 650 GeV for chargino pair production. Direct $\tilde{τ}$ production is not yet excluded due to low cross section. For left-handed stau of around 90 (125) GeV and the massless LSP we exclude 1.26 (1.34) times the expected SUSY cross-section.