Robust Calibration of Non-Perturbative Models with History Matching

Abstract

We apply, for the first time, Bayes Linear Emulation and History Matching to the calibration of non-perturbative models in Monte Carlo event generators. In contrast to the usual approach of "Monte Carlo tuning", History Matching does not result in best-fit plus ellipsoidal parameter uncertainty estimates but instead identifies all parameter space regions that are consistent with data. This approach leads to a systematic and robust quantification of parametric uncertainties in the models, especially in those challenging cases where different, possibly disjoint, regions of parameter space deliver similar results, which are usually not properly treated with current methodology. We highlight the power of this method with the hadronisation models available through Sherpa: the built-in cluster fragmentation Ahadic and string fragmentation through an interface to Pythia.

Figures (15)

• Figure 1: The structure linking the real-world process $y$ to the observations $z$ and the simulator $f(x)$ via the observational error $e$ and the model discrepancy $\epsilon(x)$.
• Figure 2: Plots of the diagnostics performed on each emulator at each HM wave, for a late-wave PYTHIA output. From left to right, the diagnostics check predictive agreement between simulator ($x$-axis) and emulator ($y$-axis) output; implausibility classifications for simulator and emulator; and standardised prediction errors for the emulator. The top right quadrant of the central plot also indicates the proportion of space we expect this emulator to cut out, based on the proportion of validation points lying in this quadrant. Any diagnostic failures would be highlighted in red, rather than blue/black.
• Figure 3: The active variables, and strength of effect, for all observable outputs from an ALEPH measurement of the $C$-parameter event shape ALEPH:2003obs at the final HM wave. Any tile with a border indicates that the parameter is active for that output; the colour of the tile determines the strength of the linear effect with deeper blue (red) shades indicating a stronger positive (negative) output response to the parameter. The observed data is overlaid above as a histogram.
• Figure 4: The emulator predictions (left) and corresponding uncertainty (right) for an output from DELPHI DELPHI:1996sen at wave $1$, plotted with respect to two of the AHADIC parameters. All other parameters are held at their mid-range values.
• Figure 5: Selected two-dimensional projections of the non-implausible AHADIC parameter space for the final HM wave. The densities are estimated from $10^4$ sampled points and normalised such that each contour region represents an increment of $10\%$ probability. The full collection of two-dimensional projections can be found in Appendix \ref{['app:additional_figures']}.