相关论文: Chi-square and Poissonian Data: Biases Even in the…

The C statistics, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. One of the challenges of the C statistic is that its probability distribution, under the null hypothesis that the…

Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…

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…

It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…

This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…

I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…

[ABRIDGED] The Cash statistic, also known as the C stat, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially…

The C statistic is a widely used likelihood-ratio statistic for model fitting and goodness-of-fit assessments with Poisson data in high-energy physics and astrophysics. Although it enjoys convenient asymptotic properties, the statistic is…

The paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the…

We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…

Reduced chi-squared is a very popular method for model assessment, model comparison, convergence diagnostic, and error estimation in astronomy. In this manuscript, we discuss the pitfalls involved in using reduced chi-squared. There are two…

We propose a new statistic that has been designed to be used in situations where the intrinsic dispersion of a data set is not well known: The Crossing Statistic. This statistic is in general less sensitive than `chi^2' to the intrinsic…

Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…

The problem of error analysis is addressed in stages beginning with the case of uncorrelated parameters and proceeding to the Bayesian problem that takes into account all possible correlations when a great deal of prior information about…

Traditional binned statistics such as $\chi^2$ suffer from information loss and arbitrariness of the binning procedure. We point out that the underlying statistical quantity (the log likelihood $L$) does not require any binning beyond the…

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…

The method of obtaining confidence intervals on a subset of the total number of parameters (p) of a model used for fitting X-ray spectra is to perturb the best-fitting model until, for each parameter, a range is found for which the change…

Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…

As it is well known, the standard deviation of a weighted average depends only on the individual standard deviations, but not on the dispersion of the values around the mean. This property leads sometimes to the embarrassing situation in…

For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…