Epistemic probability and naturalness in global fits of supersymmetric models
thesisposted on 01.03.2017, 03:56 by Farmer, Benjamin
With increasingly large amounts of computational resources becoming cheaply available, Bayesian statistical methods are growing in popularity in many fields of science. In theoretical high energy physics they have found applications in “global fits” (that is, parameter extraction and model comparison) of new physics models, particularly supersymmetric models. Unfortunately, in the most interesting cases, prior probabilities can play a very strong role. In such cases an analyst has two general options available: either attempt to isolate the analysis from the impacts of prior considerations as far as possible, or embark on a very careful prior elucidation process. The first path leads back to orthodox ‘frequentist’ analyses if followed to conclusion, though one can remove some of the impact of prior choice without completely abandoning the Bayesian framework and the advantages it offers. The second path requires careful consideration of the theoretical motivation behind the models under consideration. In this thesis I will explore both options. To begin, I review the theoretical foundations of supersymmetry, before discussing the deep connections that exist between the naturalness principle and epistemic (Bayesian) probability, particularly in the form of ‘naturalness priors’. These naturalness priors and related fine-tuning measures are derived for the MSSM and the NMSSM. Following this a large numerical study of the CMSSM is performed, with a focus on the use of partial Bayes factors to partially isolate the impact of searches at the Large Hadron Collider from prior considerations. Next I include the results of a study of naturalness priors in the constrained NMSSM. I conclude with a discussion on the future prospects for employing subjectivist techniques in phenomenological studies. Accompanying the thesis are several large appendices. These provide background material regarding the philosophy of probability, particularly subjectivist/epistemic probability, along with reviews of the frequentist and Bayesian statistical techniques used in the thesis body. Along with these reviews, I explore the implications of taking seriously an ‘operational’ subjectivist position when performing Bayesian calculations.