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

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.

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Publication Details

Journal
Journal of Instrumentation
Published
2025-02-01
DOI
https://doi.org/10.1088/1748-0221/20/02/t02001
Citations
8
Primary Topic
Neutrino Physics Research
Type
article
Field-Weighted Citation Impact
14.96

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article

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

S. Nelleri, Alec Habig, B. Jargowsky, V. Kus et al.
8 citations
Journal of Instrumentation
Neutrino Physics Research
14.96
article

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

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

Abstract

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.

Journal of InstrumentationVol. 20(02)
University of Delhi (IN), P.N. Lebedev Physical Institute of the Russian Academy of Sciences (RU), Tufts University (US), California Institute of Technology (US), Argonne National Laboratory (US), University of Minnesota (US), Fermi National Accelerator Laboratory (US), Indian Institute of Technology Guwahati (IN), University of Wisconsin–Madison (US), Harvard University (US), University of South Carolina (US), University of Sussex (GB), William & Mary (US), National Institute of Science Education and Research (IN), Queen Mary University of London (GB), University of Pittsburgh (US), Iowa State University (US), Southern Methodist University (US), Illinois Institute of Technology (US), Czech Academy of Sciences (CZ), University of California, Irvine (US), Cochin University of Science and Technology (IN), Charles University (CZ), University of Magdalena (CO), University of Atlántico (CO), University of Minnesota System (US), Harvard University Press (US), Joint Institute for Nuclear Research (RU), University of Mississippi (US), University of Hyderabad (IN), Wichita State University (US), Czech Academy of Sciences, Institute of Sociology (CZ), Twin Cities Orthopedics (US), Institute for Nuclear Research (RU), University of Minnesota, Duluth (US), Indiana University Bloomington (US), FZU ‒ Institute of Physics of the Academy of Sciences of the Czech Republic (CZ), Czech Academy of Sciences, Institute of Computer Science (CZ), University of Houston (US), Czech Technical University in Prague (CZ), University College London (GB), Panjab University (IN), University of Virginia (US), University of Cincinnati (US), Indian Institute of Technology Hyderabad (IN), Universidade Federal de Goiás (BR), Syracuse University (US), University of South Alabama (US), The University of Texas at Austin (US), Michigan State University (US), Erciyes University (TR), Banaras Hindu University (IN), Colorado State University (US)
Science and Technology Facilities Council
Openalex Percentile: Top 1%
Neutrino Physics Research
14.96
DOIOpen Access PDFOpenAlex
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