Numerical Computation of p-values with myFitter

Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are, however, many realistic situations where Wilks' theorem does not apply. In particular, no simple formula exists for the comparison of models that are not nested, in the sense that one model can be obtained from the other by fixing some of its parameters. In this paper I present methods for efficient numerical computations of p-values, which work for both nested and non-nested models and do not rely on additional approximations. These methods have been implemented in a publicly available C++ framework for maximum likelihood fits called myFitter and have recently been applied in a global analysis of the Standard Model with a fourth generation of fermions

A note on ‘good starting values’ in numerical optimisation

Many optimisation problems in finance and economics have multiple local optima or discontinuities in their objective functions. In such cases it is stressed that ‘good starting points are important’. We look into a particular example: calibrating a yield curve model. We find that while ‘good starting values’ suggested in the literature produce parameters that are indeed ‘good’, a simple best-of-n–restarts strategy with random starting points gives results that are never worse, but better in many cases.

A robust inverse approach for estimating the magnetic material properties of an electromagnetic device with minimum influence of the uncertainty in the geometrical parameters

The magnetic properties of the magnetic circuit of an electromagnetic device (EMD) can be identified by solving an inverse problem, where sets of measurements are properly interpreted using a forward numerical model of the device. However, the uncertainties of the geometrical parameter values in the forward model result in recovery errors in the reconstructed material parameter values. This paper proposes a novel inverse approach technique, in which the propagations of the uncertainties in the model are limited. The proposed methodology adapts the cost function that needs to be minimized with respect to the uncertain geometrical model parameters. We applied the methodology onto the identification of the magnetizing B-H curve of a switched reluctance motor (SRM) core material. The numerical results show a significant reduction of the recovery errors in the identified magnetic material parameter values