Simple and statistically sound recommendations for analysing physical theories

Shehu S. Abdussalam, Fruzsina J. Agocs, Benjamin C. Allanach, Peter Athron, Csaba Balázs, Emanuele Bagnaschi, Philip Bechtle, Oliver Buchmueller, Ankit Beniwal, Jihyun Bhom, Sanjay Bloor, Torsten Bringmann, Andy Buckley, Anja Butter, José Eliel Camargo-Molina, Marcin Chrzaszcz, Jan Conrad, Jonathan M. Cornell, Matthias Danninger, Jorge De BlasAlbert De Roeck, Klaus Desch, Matthew Dolan, Herbert Dreiner, Otto Eberhardt, John Ellis, Ben Farmer, Marco Fedele, Henning Flächer, Andrew Fowlie, Tomás E. Gonzalo, Philip Grace, Matthias Hamer, Will Handley, Julia Harz, Sven Heinemeyer, Sebastian Hoof, Selim Hotinli, Paul Jackson, Felix Kahlhoefer, Kamila Kowalska, Michael Krämer, Anders Kvellestad, Miriam Lucio Martinez, Farvah Mahmoudi, Diego Martinez Santos, Gregory D. Martinez, Satoshi Mishima, Keith Olive, Ayan Paul, Markus Tobias Prim, Werner Porod, Are Raklev, Janina J. Renk, Christopher Rogan, Leszek Roszkowski, Roberto Ruiz De Austri, Kazuki Sakurai, Andre Scaffidi, Pat Scott, Enrico Maria Sessolo, Tim Stefaniak, Patrick Stöcker, Wei Su, Sebastian Trojanowski, Roberto Trotta, Yue Lin Sming Tsai, Jeriek Van Den Abeele, Mauro Valli, Aaron C. Vincent, Georg Weiglein, Martin White, Peter Wienemann, Lei Wu, Yang Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.

Original languageEnglish (US)
Article number052201
JournalReports on Progress in Physics
Issue number5
StatePublished - May 2022

Bibliographical note

Funding Information:
BCA has been partially supported by the UK Science and Technology Facilities Council (STFC) Consolidated HEP theory Grants ST/P000681/1 and ST/T000694/1. PA is supported by Australian Research Council (ARC) Future Fellowship FT160100274, and PS by FT190100814. PA, CB, TEG and MW are supported by ARC Discovery Project DP180102209. CB and YZ are supported by ARC Centre of Excellence CE110001104 (Particle Physics at the Tera-scale) and WS and MW by CE200100008 (Dark Matter Particle Physics). ABe is supported by F.N.R.S. through the F.6001.19 convention. ABuc is supported by the Royal Society Grant UF160548. JECM is supported by the Carl Trygger Foundation Grant No. CTS 17:139. JdB acknowledges support by STFC under Grant ST/P001246/1. JE was supported in part by the STFC (UK) and by the Estonian Research Council. BF was supported by EU MSCA-IF project 752162—DarkGAMBIT. MF and FK are supported by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center TRR 257 ‘Particle Physics Phenomenology after the Higgs Discovery’ under Grant 396021762—TRR 257 and FK also under the Emmy Noether Grant No. KA 4662/1-1. AF is supported by an NSFC Research Fund for International Young Scientists Grant 11950410509. SHe was supported in part by the MEINCOP (Spain) under contract PID2019-110058GB-C21 and in part by the Spanish Agencia Estatal de Investigación (AEI) through the Grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597. SHoof is supported by the Alexander von Humboldt Foundation. SHoof and MTP are supported by the Federal Ministry of Education and Research of Germany (BMBF). KK is supported in part by the National Science Centre (Poland) under research Grant No. 2017/26/E/ST2/00470, LR under No. 2015/18/A/ST2/00748, and EMS under No. 2017/26/D/ST2/00490. LR and ST are supported by Grant AstroCeNT: Particle Astrophysics Science and Technology Centre, carried out within the International Research Agendas programme of the Foundation for Polish Science financed by the European Union under the European Regional Development Fund. MLM acknowledges support from NWO (Netherlands). SM is supported by JSPS KAKENHI Grant No. 17K05429. The work of KAO was supported in part by DOE Grant DE-SC0011842 at the University of Minnesota. JJR is supported by the Swedish Research Council, contract 638-2013-8993. KS was partially supported by the National Science Centre, Poland, under research Grants 2017/26/E/ST2/00135 and the Beethoven Grants DEC-2016/23/G/ST2/04301. AS is supported by MIUR research Grant No. 2017X7X85K and INFN. ST is partially supported by the Polish Ministry of Science and Higher Education through its scholarship for young and outstanding scientists (decision No. 1190/E-78/STYP/14/2019). RT was partially supported by STFC under Grant No. ST/T000791/1. The work of MV is supported by the NSF Grant No. PHY-1915005. ACV is supported by the Arthur B McDonald Canadian Astroparticle Physics Research Institute. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development, and by the Province of Ontario through MEDJCT. LW is supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 117050934, by Jiangsu Specially Appointed Professor Program. WS is supported by KIAS Individual Grant (PG084201) at Korea Institute for Advanced Study.

Publisher Copyright:
© 2022 IOP Publishing Ltd.


  • methodology
  • particle physics
  • statistics


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