Related papers: Fitting Correlated Data
We discuss fitting hadronic Green functions versus time $t$ to extract mass values in quenched lattice QCD. These data are themselves strongly correlated in $t$. With only a limited number of data samples, the method of minimising…
We report a possible solution to the trouble that the covariance fitting fails when the data is highly correlated and the covariance matrix has small eigenvalues. As an example, we choose the data analysis of highly correlated $B_K$ data on…
When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been…
Observables in particle physics and specifically in lattice QCD calculations are often extracted from fits. Standard $\chi^2$ tests require a reliable determination of the covariance matrix and its inverse from correlated and…
We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…
Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…
Regression with $\chi^2$ constructed from the covariance matrix should not be used for some combinations of covariance matrices and fitting functions. Using the technique for unsuitable combinations can amplify systematic errors. This…
Spatial data exhibits the property that nearby points are correlated. This also holds for learnt representations across layers, but not for commonly used weight initialization methods. Our theoretical analysis quantifies the learning…
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…
We address a frequently asked question on the covariance fitting of the highly correlated data such as our $B_K$ data based on the SU(2) staggered chiral perturbation theory. Basically, the essence of the problem is that we do not have an…
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there…
A common problem in analysis of experiments or in lattice QCD simulations is fitting a parameterized model to the average over a number of samples of correlated data values. If the number of samples is not infinite, estimates of the…
In optical and infrared long-baseline interferometry, data often display significant correlated errors because of uncertain multiplicative factors such as the instrumental transfer function or the pixel-to-visibility matrix. In the context…
When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
The effect of correlations between model parameters and nuisance parameters is discussed, in the context of fitting model parameters to data. Modifications to the usual $\chi^2$ method are required. Fake data studies, as used at present,…
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance…
A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…
Supporting sampling in the presence of joins is an important problem in data analysis, but is inherently challenging due to the need to avoid correlation between output tuples. Current solutions provide either correlated or non-correlated…
We discuss a goodness-of-fit method which tests the compatibility between statistically independent data sets. The method gives sensible results even in cases where the chi^2-minima of the individual data sets are very low or when several…