%0 Generic %1 bonamente2023systematic %A Bonamente, M. %D 2023 %K counts statistics %T Systematic errors in the maximum likelihood regression of Poisson count data: introducing the overdispersed chi-square distribution %U http://arxiv.org/abs/2302.04011 %X 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.

@misc{bonamente2023systematic, abstract = {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.}, added-at = {2023-02-09T09:03:52.000+0100}, author = {Bonamente, M.}, biburl = {https://www.bibsonomy.org/bibtex/28c8d419e38cf12a54fe2eb88c06a0316/quark75}, description = {Systematic errors in the maximum likelihood regression of Poisson count data: introducing the overdispersed chi-square distribution}, interhash = {5381b2d1e4cbcf570c67a99dcc402802}, intrahash = {8c8d419e38cf12a54fe2eb88c06a0316}, keywords = {counts statistics}, note = {cite arxiv:2302.04011Comment: MNRAS accepted, MN-22-4879-MJ.R2}, timestamp = {2023-02-09T09:03:52.000+0100}, title = {Systematic errors in the maximum likelihood regression of Poisson count data: introducing the overdispersed chi-square distribution}, url = {http://arxiv.org/abs/2302.04011}, year = 2023 }