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.
Cite
@article{arxiv.2207.14353,
title = {Monte Carlo method for constructing confidence intervals with unconstrained and constrained nuisance parameters in the NOvA experiment},
author = {M. A. Acero and B. Acharya and P. Adamson and L. Aliaga and N. Anfimov and A. Antoshkin and E. Arrieta-Diaz and L. Asquith and A. Aurisano and A. Back and C. Backhouse and M. Baird and N. Balashov and P. Baldi and B. A. Bambah and S. Bashar and A. Bat and K. Bays and R. Bernstein and V. Bhatnagar and D. Bhattarai and B. Bhuyan and J. Bian and A. C. Booth and R. Bowles and B. Brahma and C. Bromberg and N. Buchanan and A. Butkevich and S. Calvez and T. J. Carroll and E. Catano-Mur and A. Chatla and R. Chirco and B. C. Choudhary and S. Choudhary and A. Christensen and T. E. Coan and M. Colo and L. Cremonesi and G. S. Davies and P. F. Derwent and P. Ding and Z. Djurcic and M. Dolce and D. Doyle and D. Dueñas Tonguino and E. C. Dukes and A. Dye and R. Ehrlich and M. Elkins and E. Ewart and G. J. Feldman and P. Filip and J. Franc and M. J. Frank and H. R. Gallagher and R. Gandrajula and F. Gao and A. Giri and R. A. Gomes and M. C. Goodman and V. Grichine and M. Groh and R. Group and B. Guo and A. Habig and F. Hakl and A. Hall and J. Hartnell and R. Hatcher and H. Hausner and M. He and K. Heller and V Hewes and A. Himmel and B. Jargowsky and J. Jarosz and F. Jediny and C. Johnson and M. Judah and I. Kakorin and D. M. Kaplan and A. Kalitkina and J. Kleykamp and O. Klimov and L. W. Koerner and L. Kolupaeva and S. Kotelnikov and R. Kralik and Ch. Kullenberg and M. Kubu and A. Kumar and C. D. Kuruppu and V. Kus and T. Lackey and K. Lang and P. Lasorak and J. Lesmeister and S. Lin and A. Lister and J. Liu and M. Lokajicek and J. M. C. Lopez and R. Mahji and S. Magill and M. Manrique Plata and W. A. Mann and M. T. Manoharan and M. L. Marshak and M. Martinez-Casales and V. Matveev and B. Mayes and B. Mehta and M. D. Messier and H. Meyer and T. Miao and V. Mikola and W. H. Miller and S. Mishra and S. R. Mishra and A. Mislivec and R. Mohanta and A. Moren and A. Morozova and W. Mu and L. Mualem and M. Muether and K. Mulder and D. Naples and A. Nath and N. Nayak and S. Nelleri and J. K. Nelson and R. Nichol and E. Niner and A. Norman and A. Norrick and T. Nosek and H. Oh and A. Olshevskiy and T. Olson and J. Ott and A. Pal and J. Paley and L. Panda and R. B. Patterson and G. Pawloski and D. Pershey and O. Petrova and R. Petti and D. D. Phan and R. K. Plunkett and A. Pobedimov and J. C. C. Porter and A. Rafique and L. R. Prais and V. Raj and M. Rajaoalisoa and B. Ramson and B. Rebel and P. Rojas and P. Roy and V. Ryabov and O. Samoylov and M. C. Sanchez and S. Sánchez Falero and P. Shanahan and P. Sharma and S. Shukla and A. Sheshukov and I. Singh and P. Singh and V. Singh and E. Smith and J. Smolik and P. Snopok and N. Solomey and A. Sousa and K. Soustruznik and M. Strait and L. Suter and A. Sutton and S. Swain and C. Sweeney and A. Sztuc and B. Tapia Oregui and P. Tas and B. N. Temizel and T. Thakore and R. B. Thayyullathil and J. Thomas and E. Tiras and J. Tripathi and J. Trokan-Tenorio and Y. Torun and J. Urheim and P. Vahle and Z. Vallari and J. Vasel and T. Vrba and M. Wallbank and T. K. Warburton and M. Wetstein and D. Whittington and D. A. Wickremasinghe and T. Wieber and J. Wolcott and M. Wrobel and W. Wu and Y. Xiao and B. Yaeggy and A. Yallappa Dombara and A. Yankelevich and K. Yonehara and S. Yu and Y. Yu and S. Zadorozhnyy and J. Zalesak and Y. Zhang and R. Zwaska},
journal= {arXiv preprint arXiv:2207.14353},
year = {2025}
}
Comments
28 pages, 14 figures