"A method is presented for unravelling the demographic equation for structured populations. A solution to the McKendrick-von Foerster equation is constructed using spline functions and this is fitted to stage-structured population data in such a way that the solution is smooth, positive, and does not imply negative death rates. The smoothness of the surface, and hence the complexity of the population model, is determined in a statistically optimum manner using cross validation. Time- and age-dependent death rates can be obtained as well as time-dependent birth rates. Confidence intervals are obtained for population size and death rates that give a 95% probability that the true population dynamics are within the intervals. Practical application of the method is demonstrated, and comparison made with three alternative methods."

中文翻译：

---

从结构化人口轨迹获得出生和死亡模式。

“提供了一种方法，用于解开结构化人口的人口统计学方程。使用样条函数构造McKendrick-von Foerster方程的解决方案，并将其拟合到阶段结构化的人口数据，以使解决方案平滑，积极，并且不表示负死亡率。表面的光滑度以及总体模型的复杂性通过使用交叉验证以统计学上最佳的方式确定，可以得到与时间和年龄有关的死亡率以及与时间有关的死亡率。得出人口数量和死亡率的置信区间，使真实人口动态在区间内的可能性为95％。该方法的实际应用得到了证明，并与三种替代方法进行了比较。”