Submitted - 1210.3651v2.pdf

", "abstract": "Statistical methods of presenting experimental results in constraining the neutrino mass hierarchy\n(MH) are discussed. Two problems are considered and are related to each other: how to report the\nfindings for observed experimental data, and how to evaluate the ability of a future experiment to\ndetermine the neutrino mass hierarchy, namely, sensitivity of the experiment. For the first problem\nwhere experimental data have already been observed, the classical statistical analysis involves constructing confidence intervals for the parameter \u0394m^2_(32). These intervals are deduced from the parent\ndistribution of the estimation of \u0394m^2_(32)\nbased on experimental data. Due to existing experimental\nconstraints on |\u0394m^2_(32)|, the estimation of \u0394m^2_(32) is better approximated by a Bernoulli distribution\n(a Binomial distribution with 1 trial) rather than a Gaussian distribution. Therefore, the Feldman-\nCousins approach needs to be used instead of the Gaussian approximation in constructing confidence\nintervals. Furthermore, as a result of the definition of confidence intervals, even if it is correctly\nconstructed, its confidence level does not directly reflect how much one hypothesis of the MH is\nsupported by the data rather than the other hypothesis. We thus describe a Bayesian approach\nthat quantifies the evidence provided by the observed experimental data through the (posterior)\nprobability 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.\nIllustrations are made using a simple example with a confined parameter space, which approximates\nthe MH determination problem with experimental constraints on the |\u0394m^2_(32)|.", "date": "2012-11-01", "date_type": "published", "publisher": "Caltech Library", "id_number": "CaltechAUTHORS:20121029-073821935", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121029-073821935", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech" }, { "agency": "NSF" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC05-06OR23177" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC02-98CH10886" } ] }, "primary_object": { "basename": "1210.3651v2.pdf", "url": "https://authors.library.caltech.edu/records/knp2r-aek24/files/1210.3651v2.pdf" }, "resource_type": "monograph", "pub_year": "2012", "author_list": "Qian, X.; Tan, A.; et el." } ]