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:本文介绍了一种新方法,用以估计计算数据最大似值回归回归中系统性错误的系统错误。 这种方法特别适用于X射线光谱, 因为Poisson log-slilish 或 Cash- good of-fit 统计显示, 显示数据过于分散导致差错。 Poisson 数据的过度分散被视为一种内在模型差异, 可以用最合适的模型来估计, 使用最大似性Cmin 统计。 本文还研究了这种系统错误对Delta C 概率拉比统计的影响, 该统计可用于测试Poisson 计数数据回归中嵌套模型组件的存在。 本文介绍了一种因数据过度分散的奇差分布, 其结果是数据过于分散。 Poisson 数据的过度分散被视为一种内在模型, 以最合适的模型模型为模型, 并用最接近的C- smollish- bestal 统计方法, 用于XMMIS 和 AS 15- AS AS 中度测算数据, 用于 XMM- 15- hyal AS 中测算。