Log Gaussian Cox Process Background Modeling in High Energy Physics

TL;DR

This work introduces Log Gaussian Cox Processes (LGCP) as a flexible, non-parametric method for modeling smooth backgrounds in bump-hunt analyses at the LHC. By treating event counts as a non-homogeneous Poisson process with intensity lambda(x) = N_E * exp(Z(x)) where Z is a Gaussian process, LGCP provides posterior uncertainties and unbinned fitting, addressing limitations of analytic functions and Gaussian-process regression. The authors develop a two-stage MCMC inference scheme to optimize kernel hyperparameters and sample the latent log-intensity, and extend LGCP to joint background+signal fits with a Gaussian signal shape. Through toy studies and spurious-signal tests, LGCP is shown to perform well for background-only modeling and can recover injected signals up to ~5% of the total yield, offering a practical, uncertainty-quantified alternative for LHC analyses with sidebands. Overall, LGCP complements existing approaches by enabling flexible background modeling without strong shape assumptions while providing interpretable uncertainties for inference in high energy physics.

Abstract

Background modeling is one of the most critical components in high energy physics data analyses, and for smooth backgrounds it is often performed by fitting using an analytic functional form. In this paper a novel method based on Log Gaussian Cox Processes (LGCP) is introduced to model smooth backgrounds while making minimal assumptions on the underlying shape. In LGCP, samples are assumed to be drawn from a non-homogeneous Poisson process, with an intensity function drawn from a Gaussian process. Markov Chain Monte Carlo is used for optimizing the hyper parameters and drawing the final fit for the background estimate from the posterior. Synthetic experiments comparing background modeling from functional forms and the LGCP are used to compare the different methods.

Figures (19)

• Figure 1: Example of a complex background model taken from the very low mass analysis diphoton
• Figure 2: Examples of the MCMC values (left) and profiles (right) for the $\ell$ (blue) and $\sigma^2$ (red) hyper-parameters. The means of the histograms on the right are the optimized hyper-parameters.
• Figure 3: Progression of the posterior MCMC. Each curve represents $Z_i(x)$ for iteration $i$ in the MCMC, defining the posterior distribution $p(Z(x)|X,\ell_o,\sigma^2_o)$
• Figure 4: Examples of toy datasets generated from $F_1$ and $F_2$ with different statistics ($100$, $1000$, and $10,000$ events). The toy datasets are normalized for shape comparison. The dashed line shows the true value of the analytic function (left: $F_1$, right: $F_2$) used to generate the toy datasets.
• Figure 5: Fits (LGCP in blue, GP in green, estimated MLE in orange, and optimal MLE in pink) to an example toy dataset (shown by the black points) with: (left) 100 events, (middle) 1000 events, and (right) 10,000 events. The shaded band denotes the fit uncertainty from each method. The dashed black line denotes the true shape of the function $F_1$ used to generate the toy dataset.