Extending the Fully Bayesian Unfolding with Regularization Using a Combined Sampling Method

• Main Authors: Petr Baroň, Jiří Kvita
• Format: Article
• Language: English
• Published: MDPI AG 2020-12-01
• Series: Symmetry
• Subjects: unfolding; Bayes theorem; regularization; MCMC
• Online Access: https://www.mdpi.com/2073-8994/12/12/2100

Regularization extensions to the Fully Bayesian Unfolding are implemented and studied with an algorithm of combined sampling to find, in a reasonable computational time, an optimal value of the regularization strength parameter in order to obtain an unfolded result of a desired property, like smoothness. Three regularization conditions using the curvature, entropy and derivatives are applied, as a model example, to several simulated spectra of top-pair quark pairs that are produced in high energy <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula> collisions. The existence of a minimum of a <inline-formula><math display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> between the unfolded and particle-level spectra is discussed, with recommendations on the checks and validity of the usage of the regularization feature in Fully Bayesian Unfolding (FBU).