There have been significant developments in using extrapolative stochastic models for mortality forecasting (forward projection) in the literature. However, little attention has been devoted to mortality backcasting (backward projection). This article proposes a simple mortality backcasting framework that can be used in practice. Research and analysis of English demography in the 17th and 18th centuries have suffered from a lack of mortality data. We attempt to alleviate this problem by developing a technique that runs backward in time and produces estimates of mortality data before the time at which such data became available. After confirming the time reversibility of the mortality data, we compare the backcasting performance of some commonly used stochastic mortality models for the England and Wales data. The original Lee–Carter model is selected for backcasting purpose of this dataset. Finally, we examine the longevity of British artists between the 17th and the 20th centuries using the backcasted population mortality as benchmarks. The results show that artists living in Britain from 1600 to the mid 1800s had life expectancies similar to those of the general population, with a marked increase in longevity after the Industrial Revolution.

文献中在使用外推随机模型进行死亡率预测（前向预测）方面取得了重大进展。然而，很少有人关注死亡率回溯（反向预测）。本文提出了一个可以在实践中使用的简单死亡率回溯框架。对 17 世纪和 18 世纪英国人口统计的研究和分析一直缺乏死亡率数据。我们试图通过开发一种技术来缓解这个问题，该技术可以在时间上倒退，并在此类数据可用之前生成死亡率数据的估计值。在确认死亡率数据的时间可逆性后，我们比较了英格兰和威尔士数据的一些常用随机死亡率模型的回溯性能。选择原始 Lee-Carter 模型用于该数据集的回溯。最后，我们使用倒推的人口死亡率作为基准，研究了 17 世纪至 20 世纪英国艺术家的寿命。结果表明，从 1600 年到 1800 年代中期生活在英国的艺术家的预期寿命与普通人群相似，工业革命后的寿命显着增加。