Confidence intervals with a priori parameter bounds
- PDF / 591,384 Bytes
- 19 Pages / 612 x 792 pts (letter) Page_size
- 103 Downloads / 218 Views
nfidence Intervals with a priori Parameter Bounds1 A. V. Lokhov* and F. V. Tkachov Institute for Nuclear Research RAS, Moscow, 117312 Russia *email: [email protected] Abstract—We review the methods of constructing confidence intervals that account for a priori information about onesided constraints on the parameter being estimated. We show that the socalled method of sensi tivity limit yields a correct solution of the problem. Derived are the solutions for the cases of a continuous distribution with nonnegative estimated parameter and a discrete distribution, specifically a Poisson process with background. For both cases, the best upper limit is constructed that accounts for the a priori information. A table is provided with the confidence intervals for the parameter of Poisson distribution that correctly accounts for the information on the known value of the background along with the software for calculating the confidence intervals for any confidence levels and magnitudes of the background (the software is freely available for download via Internet). DOI: 10.1134/S1063779615030089 1
1. INTRODUCTION
The Neyman construction [1] of confidence inter vals for estimated parameters is a basic element of experimental data processing. Often one also pos sesses a priori information about the estimated param eters, and it is important to include that information into the confidence intervals in a consistent way. A limited domain of the parameters is an example of such a priori information. The problem with the conventional confidence intervals is seen if the exper imental estimate of the parameter falls out of the domain. For instance, in the Troitsknumass experi ment on the direct measurement of the mass of neu 2 trino in tritium betadecay [2] the parameter m ν is nonnegative while the formal fit yields a negative 2 value of m ν . The construction of confidence intervals for Pois son distribution with Poissondistributed background is another situation where one should take into account the a priori information about the back ground. The situation is usual for studying rare events (in experiments on neutrinoless double betadecay [3], and neutrino oscillations, for instance T2K, MINOS [4], etc.). Several candidate solutions were proposed. These can be divided into two groups according to how the freedom inherent in the Neyman construction of con fidence intervals is used. The first group of candidate solutions incorporates the a priori information at the stage of constructing the acceptance regions. This group includes the Feldman Cousins construction [6] and the power constrained 1 The article was translated by the authors.
limits advocated by Cowan et al. (the CCGV method [7]). However, the intervals constructed e.g. via the FeldmanCousins recipe do not allow one to mean ingfully compare the results of different experiments (because an experiment with worse sensitivity could yield a smaller interval), thus failing to achieve the very goal of data processing: to produce numbers that directly expr
Data Loading...
