Posts tagged ‘steepest descent’

On the unreliability of fitting

Despite some recent significant advances in Statistics and its applications to Astronomy (Cash 1976, Cash 1979, Gehrels 1984, Schmitt 1985, Isobe et al. 1986, van Dyk et al. 2001, Protassov et al. 2002, etc.), there still exist numerous problems and limitations in the standard statistical methodologies that are routinely applied to astrophysical data. For instance, the basic algorithms used in non-linear curve-fitting in spectra and images have remained unchanged since the 1960′s: the downhill simplex method of Nelder & Mead (1965) modified by Powell, and methods of steepest descent exemplified by Levenberg-Marquardt (Marquardt 1963). All non-linear curve-fitting programs currently in general use (Sherpa, XSPEC, MPFIT, PINTofALE, etc.) with the exception of Monte Carlo and MCMC methods are implementations based on these algorithms and thus share their limitations.
Continue reading ‘On the unreliability of fitting’ »