학술논문
The Profiled Feldman-Cousins technique for confidence interval construction in the presence of nuisance parameters
Document Type
Working Paper
Author
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.; Tonguino, D. Dueñas; 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.; Plata, M. Manrique; 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.; Falero, S. Sánchez; 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.; Oregui, B. Tapia; 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.; Dombara, A. Yallappa; Yankelevich, A.; Yonehara, K.; Yu, S.; Yu, Y.; Zadorozhnyy, S.; Zalesak, J.; Zhang, Y.; Zwaska, R.
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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. Here, we present the method used in the NOvA experiment, which we call `Profiled Feldman--Cousins.' We show that it achieves more accurate frequentist coverage in toy experiments approximating a neutrino oscillation measurement than other methods commonly in use. Finally, we describe an implementation of this method in the context of the NOvA experiment.
Comment: 28 pages, 14 figures
Comment: 28 pages, 14 figures