Qian, X. and Tan, A. and Wang, W. and Ling, J. J. and McKeown, R. D. and Zhang, C. (2012) Statistical Evaluation of Experimental Determinations of Neutrino Mass Hierarchy. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20121029073821935

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Abstract
Statistical methods of presenting experimental results in constraining the neutrino mass hierarchy (MH) are discussed. Two problems are considered and are related to each other: how to report the findings for observed experimental data, and how to evaluate the ability of a future experiment to determine the neutrino mass hierarchy, namely, sensitivity of the experiment. For the first problem where experimental data have already been observed, the classical statistical analysis involves constructing confidence intervals for the parameter Δm^2_(32). These intervals are deduced from the parent distribution of the estimation of Δm^2_(32) based on experimental data. Due to existing experimental constraints on Δm^2_(32), the estimation of Δm^2_(32) is better approximated by a Bernoulli distribution (a Binomial distribution with 1 trial) rather than a Gaussian distribution. Therefore, the Feldman Cousins approach needs to be used instead of the Gaussian approximation in constructing confidence intervals. Furthermore, as a result of the definition of confidence intervals, even if it is correctly constructed, its confidence level does not directly reflect how much one hypothesis of the MH is supported by the data rather than the other hypothesis. We thus describe a Bayesian approach that quantifies the evidence provided by the observed experimental data through the (posterior) probability that either one hypothesis of MH is true. This Bayesian presentation of observed experimental results is then used to develop several metrics to assess the sensitivity of future experiments. Illustrations are made using a simple example with a confined parameter space, which approximates the MH determination problem with experimental constraints on the Δm^2_(32).
Item Type:  Report or Paper (Discussion Paper)  

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Additional Information:  Submitted on 12 Oct 2012 (v1); last revised 21 Oct 2012 (this version, v2). We would like to thank Petr Vogel, Haiyan Gao, Jianguo Liu, Alan Gelfand, and Laurence Littenberg for fruitful discussions and careful reading. This work was supported in part by Caltech, the National Science Foundation, and the Department of Energy under contracts DEAC0506OR23177, under which Jefferson Science Associates, LLC, operates the Thomas Jefferson National Accelerator Facility, and DEAC0298CH10886.  
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Record Number:  CaltechAUTHORS:20121029073821935  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20121029073821935  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  35136  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  01 Nov 2012 19:49  
Last Modified:  27 Dec 2012 02:55 
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