Multiple‐systems estimation is a key approach for quantifying hidden populations such as the number of victims of modern slavery. The UK Government published an estimate of 10000–13000 victims, constructed by the present author, as part of the strategy leading to the Modern Slavery Act 2015. This estimate was obtained by a stepwise multiple‐systems method based on six lists. Further investigation shows that a small proportion of the possible models give rather different answers, and that other model fitting approaches may choose one of these. Three data sets collected in the field of modern slavery, together with a data set about the death toll in the Kosovo conflict, are used to investigate the stability and robustness of various multiple‐systems‐estimate methods. The crucial aspect is the way that interactions between lists are modelled, because these can substantially affect the results. Model selection and Bayesian approaches are considered in detail, in particular to assess their stability and robustness when applied to real modern slavery data. A new Markov chain Monte Carlo Bayesian approach is developed; overall, this gives robust and stable results at least for the examples considered. The software and data sets are freely and publicly available to facilitate wider implementation and further research.

中文翻译：

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量化现代奴隶制的多系统分析：古典和贝叶斯方法

多系统估计是量化隐性人口（例如现代奴隶制受害者人数）的关键方法。英国政府发布了由本报告构成的10000-13000名受害者的估计数，作为导致实施《 2015年现代奴役法案》的战略的一部分。该估计数是基于六个清单的逐步多系统方法得出的。进一步的研究表明，一小部分可能的模型给出了完全不同的答案，其他模型拟合方法可能会选择其中一种。在现代奴隶制领域收集的三个数据集，以及与科索沃冲突中的死亡人数有关的数据集，用于研究各种多系统估计方法的稳定性和鲁棒性。至关重要的方面是对列表之间的交互进行建模的方式，因为这些会严重影响结果。详细考虑了模型选择和贝叶斯方法，尤其是在将其应用于真实的现代奴隶制数据时评估其稳定性和鲁棒性。提出了一种新的马尔可夫链蒙特卡洛贝叶斯方法。总的来说，这至少在所考虑的示例中给出了可靠且稳定的结果。该软件和数据集可免费和公开获得，以促进更广泛的实施和进一步的研究。