Interpretation of the shape of the likelihood function around its minimum

Abstract

It often happens that the solution of a minimum problem is itself straightforward, but the calculation or interpretation of the resulting parameter uncertainties, as determined by the shape of the function at the minimum, is considerably more complicated. The purpose of this note is to clarify the most commonly encountered difficulties in parameter error determination. These difficulties may arise in connection with any fitting program, but will be discussed here with the terminology of the program MINUIT for the convenience of MINUIT users. The most common causes of misinterpretation may be grouped into three categories: 1. 1. Proper normalization of the user-supplied chi-square or likelihood function, and appropriate ERROR DEF. 2. 2. Non-linearities in the problem formulation, leading to different errors being calculated by different techniques, such as 3. MIGRAD, HESSE and MINOS. 4. 3. Multiparameter error definition and interpretation. All these topic are discussed in some detail by Eadie et al., which may be consulted for further details.