Bayesian Inference and the Markov Chain Monte Carlo Method
Chapter
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Abstract
The analysis presented in this thesis is a Bayesian oscillation analysis, which uses a Markov Chain Monte Carlo fitting technique. This is quite unusual in the field of neutrino physics: traditionally, frequentist fitting methods and interpretations have been more widely used. For this reason, this chapter describes the Markov Chain Monte Carlo method, as well as the Bayesian approach to parameter estimation and interpretation of results.
References
- 1.W.R. Gilks, S. Richardson, D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman & Hall/CRC Interdisciplinary Statistics, Chapman and Hall/CRC, 1995)Google Scholar
- 2.R.G. Calland, A 3 flavour joint near and far detector neutrino oscillation analysis at T2K, Ph.D. thesis, University of Liverpool (2014), http://www.t2k.org/docs/thesis/059
- 3.S. Oser, Physics 509C—theory of measurement, slides from lecture series at University of British Columbia, http://www.phas.ubc.ca/oser/p509/
- 4.C.P. Robert, The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, 2nd edn. (Springer, 2007)Google Scholar
- 5.S. Brooks, A. Gelman, G. Jones, X.-L. Meng (eds.), Handbook of Markov Chain Monte Carlo, 1 edn. (Chapman & Hall/CRC Handbooks of Modern Statistical Methods, Chapman and Hall/CRC, 2011). doi: 10.1201/b10905
- 6.N. Metropolis et al., Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953). doi: 10.1063/1.1699114 ADSCrossRefGoogle Scholar
- 7.W.K. Hastings, Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1), 97–109 (1970). doi: 10.1093/biomet/57.1.97 MathSciNetCrossRefMATHGoogle Scholar
- 8.J. Dunkley et al., Fast and reliable markov chain monte carlo technique for cosmological parameter estimation. Month. Not. R. Astron. Soc. 356(3), 925–936 (2005). doi: 10.1111/j.1365-2966.2004.08464.x ADSCrossRefGoogle Scholar
- 9.F. James, MINUIT function minimization and error analysis—reference manual, version 94.1, CERN program library long Writeup D506, https://root.cern.ch/sites/d35c7d8c.web.cern.ch/files/minuit.pdf
- 10.Peter Mills, Efficient statistical classification of satellite measurements. Int. J. Remote Sens. 32(21), 6109–6132 (2011). doi: 10.1080/01431161.2010.507795 ADSCrossRefGoogle Scholar
- 11.K.A. Olive et al. (Particle Data Group), Review of particle physics, Chin. Phys. C 38, 090001 (2014). (and 2015 update). doi: 10.1088/1674-1137/38/9/090001
- 12.H. Jeffreys, The Theory of Probability (OUP Oxford, 1998)Google Scholar
- 13.A. Gelman, X.L. Meng, H. Stern, Posterior predictive assessment of model fitness via realized discrepancies. Stat. Sin. 6, 733–759 (1996), http://www3.stat.sinica.edu.tw/statistica/j6n4/j6n41/j6n41.htm
- 14.M. Hartz et al., Constraining the flux and cross section models with data from the ND280 detector for the 2014/15 oscillation analysis, Technical Report 220, T2K (2015), http://www.t2k.org/docs/technotes/220
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