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 goodness-of-fit statistic, indicate a poor fit that is attributable to overdispersion of the data. Overdispersion in Poisson data is treated as an intrinsic model variance that can be estimated from the best-fit model, using the maximum-likelihood Cmin statistic. The paper also studies the effects of such systematic errors on the Delta C likelihood-ratio statistic, which can be used to test for the presence of a nested model component in the regression of Poisson count data. The paper introduces an overdispersed chi-square distribution that results from the convolution of a chi-square distribution that models the usual Delta C statistic, and a zero-mean Gaussian that models the overdispersion in the data. This is proposed as the distribution of choice for the Delta C statistic in the presence of systematic errors. The methods presented in this paper are applied to XMM-Newton data of the quasar 1ES 1553+113 that were used to detect absorption lines from an intervening warm-hot intergalactic medium (WHIM). This case study illustrates how systematic errors can be estimated from the data, and their effect on the detection of a nested component, such as an absorption line, with the Delta C statistic.

翻译：本文提出了一种估计计数数据最大似然回归中系统误差的新方法。该方法特别适用于X射线光谱分析中，当泊松对数似然或Cash拟合优度统计量显示数据因过度离散导致拟合不良的情形。我们将泊松数据中的过度离散视为一种固有模型方差，可利用最佳拟合模型基于最大似然Cmin统计量进行估计。本文还研究了此类系统误差对Delta C似然比统计量的影响，该统计量可用于检验泊松计数数据回归中嵌套模型分量的存在性。通过卷积描述常规Delta C统计量的卡方分布与表征数据过度离散的零均值高斯分布，本文引入了一种过度离散卡方分布，并将其作为存在系统误差时Delta C统计量的优选分布。文中方法应用于类星体1ES 1553+113的XMM-Newton数据，该数据曾用于探测介入暖-热星际介质（WHIM）的吸收线。该案例研究阐明了如何从数据中估计系统误差，以及利用Delta C统计量检测吸收线等嵌套分量时系统误差的影响。