Monograph records
https://feeds.library.caltech.edu/people/McKeown-R-D/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:57:03 +0000Statistical Evaluation of Experimental Determinations of Neutrino Mass Hierarchy
https://resolver.caltech.edu/CaltechAUTHORS:20121029-073821935
Authors: {'items': [{'id': 'Qian-X', 'name': {'family': 'Qian', 'given': 'X.'}}, {'id': 'Tan-A', 'name': {'family': 'Tan', 'given': 'A.'}}, {'id': 'Wang-W', 'name': {'family': 'Wang', 'given': 'W.'}}, {'id': 'Ling-J-J', 'name': {'family': 'Ling', 'given': 'J. J.'}}, {'id': 'McKeown-R-D', 'name': {'family': 'McKeown', 'given': 'R. D.'}}, {'id': 'Zhang-C', 'name': {'family': 'Zhang', 'given': 'C.'}, 'orcid': '0000-0001-8288-5823'}]}
Year: 2012
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)|.https://authors.library.caltech.edu/records/knp2r-aek24