Related papers: An Alternate Method for Minimizing $\chi^2$
I present a previously unpublished method for modeling multiple lens microlensing events that is based on the image centered ray shooting approach of Bennett and Rhie. It has been used to model all a wide variety of binary and triple lens…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
I describe a new, open-source astronomical image-fitting program called Imfit, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an…
It is shown that whenever the multiplicative normalization of a fitting function is not known, least square fitting by $\chi^2$ minimization can be performed with one parameter less than usual by converting the normalization parameter into…
Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main…
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a…
Gravitational microlensing events with high peak magnifications provide a much enhanced sensitivity to the detection of planets around the lens star. However, estimates of peak magnification during the early stages of an event by means of…
Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…
The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function $f$ observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
We describe an active-set method for the minimization of an objective function $\phi$ that is the sum of a smooth convex function and an $\ell_1$-regularization term. A distinctive feature of the method is the way in which active-set…
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We…
In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the…
The problem of fitting an event distribution when the total expected number of events is not fixed, keeps appearing in experimental studies. In a chi-square fit, if overall normalization is one of the parameters parameters to be fit, the…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
This paper presents a statistical method to subtract background in maximum likelihood fit, without relying on any separate sideband or simulation for background modeling. The method, called sFit, is an extension to the sPlot technique…
Event reconstruction is a central step in many particle physics experiments, turning detector observables into parameter estimates; for example estimating the energy of an interaction given the sensor readout of a detector. A corresponding…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
We investigate quasi-Newton methods for minimizing a strictly convex quadratic function which is subject to errors in the evaluation of the gradients. The methods all give identical behavior in exact arithmetic, generating minimizers of…