An Alternate Method for Minimizing $\chi^2$

TL;DR

This paper introduces sfit_minimize, an algorithm that efficiently minimizes $$ to fit models, providing reliable parameter uncertainties, and demonstrates its superior performance over standard methods in microlensing light curve analysis.

Contribution

The paper presents a novel algorithm for $$ minimization that estimates second derivatives from first derivatives, improving speed and reliability in astrophysical data fitting.

Findings

sfit_minimize outperforms Nelder-Mead in speed.

sfit_minimize is more reliable than BFGS.

Newton-CG is ineffective for microlensing fits.

Abstract

In this paper, we describe an algorithm and associated software package (sfit_minimize) for maximizing the likelihood function of a set of parameters by minimizing $\chi^2$. The key element of this method is that the algorithm estimates the second derivative of the $\chi^2$ function using first derivatives of the function to be fitted. These same derivatives can also be used to calculate the uncertainties in each parameter. We test this algorithm against several standard minimization algorithms in SciPy.optimize.minimize() by fitting point lens models to light curves from the 2018 Korea Microlensing Telescope Network event database. We show that for fitting microlensing events, SFit works faster than the Nelder-Mead simplex method and is more reliable than the BFGS gradient method; we also find that the Newton-CG method is not effective for fitting microlensing events.