Monte Carlo method for constructing confidence intervals with unconstrained and constrained nuisance parameters in the NOvA experiment

Acero, M.A.; Acharya, B.; Adamson, P.; Aliaga, L.; Anfimov, N.; Antoshkin, A.; Arrieta-Diaz, E.; Asquith, L.; Aurisano, A.; Back, A.; Backhouse, C.; Baird, M.; Balashov, N.; Baldi, P.; Bambah, B.A.; Bashar, S.; Bat, A.; Bays, K.; Bernstein, R.; Bhatnagar, V.; Bhattarai, D.; Bhuyan, B.; Bian, J.; Booth, A.C.; Bowles, R.; Brahma, B.; Bromberg, C.; Buchanan, N.; Butkevich, A.; Calvez, S.; Carroll, T.J.; Catano-Mur, E.; Chatla, A.; Chirco, R.; Choudhary, B.C.; Choudhary, S.; Christensen, A.; Coan, T.E.; Colo, M.; Cremonesi, L.; Davies, G.S.; Derwent, P.F.; Ding, P.; Djurcic, Z.; Dolce, M.; Doyle, D.; Dueñas Tonguino, D.; Dukes, E.C.; Dye, A.; Ehrlich, R.; Elkins, M.; Ewart, E.; Feldman, G.J.; Filip, P.; Franc, J.; Frank, M.J.; Gallagher, H.R.; Gandrajula, R.; Gao, F.; Giri, A.; Gomes, R.A.; Goodman, M.C.; Grichine, V.; Groh, M.; Group, R.; Guo, B.; Habig, A.; Hakl, F.; Hall, A.; Hartnell, J.; Hatcher, R.; Hausner, H.; He, M.; Heller, K.; Hewes, V.; Himmel, A.; Jargowsky, B.; Jarosz, J.; Jediny, F.; Johnson, C.; Judah, M.; Kakorin, I.; Kaplan, D.M.; Kalitkina, A.; Kleykamp, J.; Klimov, O.; Koerner, L.W.; Kolupaeva, L.; Kotelnikov, S.; Kralik, R.; Kullenberg, Ch.; Kubu, M.; Kumar, A.; Kuruppu, C.D.; Kus, V.; Lackey, T.; Lang, K.; Lasorak, P.; Lesmeister, J.; Lin, S.; Lister, A.; Liu, J.; Lokajicek, M.; Lopez, J.M.C.; Mahji, R.; Magill, S.; Manrique Plata, M.; Mann, W.A.; Manoharan, M.T.; Marshak, M.L.; Martinez-Casales, M.; Matveev, V.; Mayes, B.; Mehta, B.; Messier, M.D.; Meyer, H.; Miao, T.; Mikola, V.; Miller, W.H.; Mishra, S.; Mishra, S.R.; Mislivec, A.; Mohanta, R.; Moren, A.; Morozova, A.; Mu, W.; Mualem, L.; Muether, M.; Mulder, K.; Naples, D.; Nath, A.; Nayak, N.; Nelleri, S.; Nelson, J.K.; Nichol, R.; Niner, E.; Norman, A.; Norrick, A.; Nosek, T.; Oh, H.; Olshevskiy, A.; Olson, T.; Ott, J.; Pal, A.; Paley, J.; Panda, L.; Patterson, R.B.; Pawloski, G.; Pershey, D.; Petrova, O.; Petti, R.; Phan, D.D.; Plunkett, R.K.; Pobedimov, A.; Porter, J.C.C.; Rafique, A.; Prais, L.R.; Raj, V.; Rajaoalisoa, M.; Ramson, B.; Rebel, B.; Rojas, P.; Roy, P.; Ryabov, V.; Samoylov, O.; Sanchez, M.C.; Sánchez Falero, S.; Shanahan, P.; Sharma, P.; Shukla, S.; Sheshukov, A.; Singh, I.; Singh, P.; Singh, V.; Smith, E.; Smolik, J.; Snopok, P.; Solomey, N.; Sousa, A.; Soustruznik, K.; Strait, M.; Suter, L.; Sutton, A.; Swain, S.; Sweeney, C.; Sztuc, A.; Tapia Oregui, B.; Tas, P.; Temizel, B.N.; Thakore, T.; Thayyullathil, R.B.; Thomas, J.; Tiras, E.; Tripathi, J.; Trokan-Tenorio, J.; Torun, Y.; Urheim, J.; Vahle, P.; Vallari, Z.; Vasel, J.; Vrba, T.; Wallbank, M.; Warburton, T.K.; Wetstein, M.; Whittington, D.; Wickremasinghe, D.A.; Wieber, T.; Wolcott, J.; Wrobel, M.; Wu, W.; Xiao, Y.; Yaeggy, B.; Yallappa Dombara, A.; Yankelevich, A.; Yonehara, K.; Yu, S.; Yu, Y.; Zadorozhnyy, S.; Zalesak, J.; Zhang, Y.; Zwaska, R.

doi:10.1088/1748-0221/20/02/t02001

Monte Carlo method for constructing confidence intervals with unconstrained and constrained nuisance parameters in the NOvA experiment

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Acero M., Acharya B., Adamson P., Aliaga L., Anfimov N., Antoshkin A., ...More

Journal of Instrumentation, vol.20, no.2, 2025 (SCI-Expanded)

Publication Type: Article / Article
Volume: 20 Issue: 2
Publication Date: 2025
Doi Number: 10.1088/1748-0221/20/02/t02001
Journal Name: Journal of Instrumentation
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, Index Islamicus, INSPEC
Keywords: Analysis and statistical methods, Computing (architecture, farms, GRID for recording, storage, archiving, and distribution of data)
Erciyes University Affiliated: Yes

Abstract

Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under certain conditions. These conditions, such as nested hypotheses and unbounded parameters, are often violated in neutrino oscillation measurements and other experimental scenarios. Monte Carlo methods can address these issues, albeit at increased computational cost. In the presence of nuisance parameters, however, the best way to implement a Monte Carlo method is ambiguous. This paper documents the method selected by the NOvA experiment, the profile construction. It presents the toy studies that informed the choice of method, details of its implementation, and tests performed to validate it. It also includes some practical considerations which may be of use to others choosing to use the profile construction.