Abstract
We perform a Bayesian analysis of current neutrino oscillation data. When estimating the oscillation parameters we find that the results generally agree with those of the $\chi^2$ method, with some differences involving $s_{23}^2$ and CP-violating effects. We discuss the additional subtleties caused by the circular nature of the CP-violating phase, and how it is possible to obtain correlation coefficients with $s_{23}^2$. When performing model comparison, we find that there is no significant evidence for any mass ordering, any octant of $s_{23}^2$ or a deviation from maximal mixing, nor the presence of CP-violation.
Highlights
Several global analyses exist in the literature [7,8,9], which, by fitting the results from the bulk of oscillation experiments, obtain best estimates and allowed ranges for these six oscillation parameters
One may question to what degree the current determination of the oscillation parameters is dependent on the assumed statistical approach, and whether Bayesian statistics can shed some light on the presently open issues related to the mass ordering, the octant of θ23, and the presence of CP-violation
We have presented the results of a Bayesian global analysis of solar, atmospheric, reactor and accelerator neutrino data in the framework of three-neutrino oscillations and compared them with those from the standard χ2 analysis in NuFIT-2.0 [10]
Summary
We will be using Bayesian probability theory, where each proposition is associated with a probability or plausibility, defined to lie between 0 and 1. There are some so-called information criteria which have been used to compare different models (see, e.g., [13, 14]) These do not explicitly depend on any prior, but typically are derived using quite restrictive assumptions. Under the assumption that a model M is true, complete inference of its parameters is given by the posterior distribution, Pr(D|Θ, M ) Pr(Θ|M ) L(Θ)π(Θ) In this case, the evidence is only a normalization factor, since it is independent of the values of the parameters Θ and it is often disregarded in parameter estimation. In this work we use MultiNest [16,17,18], a Bayesian inference tool which, given the prior and the likelihood, calculates the evidence with an uncertainty estimate, and generates posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
