We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world from the present to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we did an out-of-sample cross-validation experiment, fitting the model to the data from 1950–1995, and using the estimated model to forecast for the subsequent ten years. The ten-year predictions had a mean absolute error of about 1 year, about 40% less than the current UN methodology. The probabilistic forecasts were calibrated, in the sense that (for example) the 80% prediction intervals contained the truth about 80% of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free publicly available R software packages called bayesLife and bayesDem are available to implement the method.
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机译：我们提出了一种贝叶斯分层模型，用于产生从现在到2100年世界所有国家的男性预期寿命预期出生概率预测。这种预测将成为当前所有国家概率人口预测的输入。正在联合国考虑之中。为了评估该方法，我们进行了样本外交叉验证实验，将该模型与1950-1995年的数据进行拟合，然后使用估计的模型进行后续十年的预测。十年的预测的平均绝对误差约为1年，比目前的联合国方法要低40％。在（例如）80％的预测间隔包含大约80％的时间真相的意义上，对概率预测进行了校准。我们以马达加斯加（一个典型的国家，其预期寿命正在稳步提高），拉脱维亚（一个存在死亡危机的国家）和日本（一个领先的国家）的研究结果来说明我们的方法。我们还显示了具有八个国家/地区的南亚的汇总结果。可以免费使用名为 bayesLife 和 bayesDem 的免费公开获得的 R 软件包来实现该方法。
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