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Bayesian Statistics and the Markov Chain Monte Carlo Technique for Neutrino Oscillation Analyses

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Predicting the T2K Neutrino Flux and Measuring Oscillation Parameters

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

The oscillation results presented in this thesis are to be interpreted in the Bayesian framework. This chapter starts with a brief discussion on Bayesian inference and Monte Carlo methods for sampling from multivariate posterior probability distributions. The probability distribution for oscillation parameters to take on certain values, given the collected T2K neutrino and anti-neutrino data, is also discussed. Finally, a summary of flux, cross section and detector inputs for the oscillation analysis has been presented.

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Notes

  1. 1.

    Strictly speaking, the probability for data is unity, since it has already happened.

  2. 2.

    Processes where the charge of the pion changes through scattering.

References

  1. Duffy, K (2016) Measurement of the neutrino oscillation parameters \(\sin ^{2}\theta _{23}, \Delta m^2_{32}, \sin ^{2}\theta _{13}\), and \(\delta _{\rm CP}\) in neutrino and antineutrino oscillation at T2K. Ph.D. thesis, University of Oxford. https://ora.ox.ac.uk/objects/uuid:4485185d-3f72-49d0-866c-af2bab55d916

  2. Beringer J et al. (Particle Data Group) (2012) Review of Particle Physics. Phys Rev D 86:010001. https://link.aps.org/doi/10.1103/PhysRevD.86.010001

  3. Metropolis N et al. (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092. https://doi.org/10.1063/1.1699114

  4. Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109. http://oup.prod.sis.lan/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf. https://doi.org/10.1093/biomet/57.1.97

  5. Tanabashi M et al (Particle Data Group) (2018) Review of particle physics. Phys Rev D 98:030001. https://link.aps.org/doi/10.1103/PhysRevD.98.030001

  6. Hayato O (2009) A neutrino interaction simulation program library NEUT. Acta Phys Pol B 40:2477–2489

    Google Scholar 

  7. Aguilar-Arevalo AA et al (2009) The MiniBooNE detector. In: Nuclear instruments and methods in physics research section a: accelerators, spectrometers, detectors and associated equipment, vol 599.1, pp 28–46. http://www.sciencedirect.com/science/article/pii/S0168900208015404

  8. Aliaga L et al (2014) Design, calibration, and performance of the MINERvA detector. In: Nuclear instruments and methods in physics research section a: accele rators, spectrometers, detectors and associated equipment, vol 743, pp 130–159. http://www.sciencedirect.com/science/article/pii/S0168900214000035

  9. The Neutrino Interaction Working Group (2017) NIWG model and uncertainties for 2017 oscillation analysis. www.t2k.org/docs/technotes/315

  10. Bernard V, Elouadrhiri L, Meißner U-G (2001) Axial structure of the nucleon. In: J Phys G: Nucl Part Phys 28(1):R1–R35. https://doi.org/10.1088/0954-3899/28/1/201

  11. Moniz EJ et al (1971) Nuclear Fermi momenta from quasielastic electron scattering. Phys Rev Lett 26:445–448

    Article  ADS  Google Scholar 

  12. Nieves J, Ruiz Simo I, Vicente Vacas MJ (2011) Inclusive charged-current neutrino-nucleus reactions. Phys Rev C 83:045501. https://link.aps.org/doi/10.1103/PhysRevC.83.045501

  13. Rein D, Sehgal LM (1981) Neutrino-excitation of baryon resonances and single pion production. Ann Phys 133(1):79–153. http://www.sciencedirect.com/science/article/pii/0003491681902426

  14. Adamson P et al (MINOS Collaboration) (2010) Neutrino and antineutrino inclusive charged-current cross section measurements with the MINOS near detector. Phys Rev D 81:072002. https://link.aps.org/doi/10.1103/PhysRevD.81.072002

  15. Higuera A et al (MINERvA Collaboration) (2014) Measurement of coherent production of \(\pi ^{\pm }\) in neutrino and antineutrino beams on carbon from \(E_{\nu }\) of 1.5 to 20 GeV. Phys Rev Lett 113:261802. https://link.aps.org/doi/10.1103/PhysRevLett.113.261802

  16. Wang E et al (2015) Photon emission in neutral current interactions at the T2K experiment. Phys Rev D 92:053005. https://link.aps.org/doi/10.1103/PhysRevD.92.053005

  17. Wang E et al (2014) Photon emission in neutral-current interactions at intermediate energies. Phys Rev C 89:015503. https://link.aps.org/doi/10.1103/PhysRevC.89.015503

  18. de Perio P (2014) NEUT pion final state interactions. arXiv:1405.3973

  19. Abe K et al (T2K Collaboration) (2017) Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of \({\nu }_e\) interactions at the far detector. Phys Rev D 96:092006. https://link.aps.org/doi/10.1103/PhysRevD.96.092006

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Correspondence to Tomislav Vladisavljevic .

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Vladisavljevic, T. (2020). Bayesian Statistics and the Markov Chain Monte Carlo Technique for Neutrino Oscillation Analyses. In: Predicting the T2K Neutrino Flux and Measuring Oscillation Parameters. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-51174-6_7

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