Hypothesis tests and model parameter estimation on data sets with missing correlation information

Abstract

Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was published without a covariance matrix, or because one tries to combine multiple results from separate publications. For simple hypothesis tests, it is possible to define robust test statistics that will behave conservatively in the presence on unknown correlations. For model parameter fits, one can inflate the variance by a factor to ensure that things remain conservative at least up to a chosen confidence level. This paper describes a class of robust test statistics for simple hypothesis tests, as well as an algorithm to determine the necessary inflation factor for model parameter fits and Goodness of Fit tests and composite hypothesis tests. It then presents some example applications of the methods to real neutrino interaction data and model comparisons.

18 pages, 10 figures; follow-up of arxiv.org:2102.06172; Fixed layout

References in corpus (8)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Characterisation of nuclear effects in muon-neutrino scattering on hydrocarbon with a measurement of final-state kinematics and correlations in charged-current pionless interactions at T2K
• Recent highlights from GENIE v3
• Measurement of final-state correlations in neutrino muon-proton mesonless production on hydrocarbon at $⟨E_{\nu }⟩=3$ GeV
• Nuclear binding energy and transverse momentum imbalance in neutrino-nucleus reactions
• Probing nuclear effects with neutrino-induced charged-current neutral pion production
• First T2K measurement of transverse kinematic imbalance in the muon-neutrino charged-current single-${\pi }^{+}$ production channel containing at least one proton
• Robust test statistics for data sets with missing correlation information

Cited by in corpus (1)

• Covering Unknown Correlations in Bayesian Priors by Inflating Uncertainties