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**Accounting for uncertainty about past values in probabilistic projections of the total fertility rate for most countries.**
*(English)*
Zbl 1446.62280

Summary: Since the 1940s, population projections have in most cases been produced using the deterministic cohort component method. However, in 2015, for the first time and in a major advance, the United Nations issued official probabilistic population projections for all countries based on Bayesian hierarchical models for total fertility and life expectancy. The estimates of these models and the resulting projections are conditional on the U.N.’s official estimates of past values. However, these past values are themselves uncertain, particularly for the majority of the world’s countries that do not have longstanding high-quality vital registration systems, when they rely on surveys and censuses with their own biases and measurement errors. This paper extends the U.N. model for projecting future total fertility rates to take account of uncertainty about past values. This is done by adding an additional level to the hierarchical model to represent the multiple data sources, in each case estimating their bias and measurement error variance. We assess the method by out-of-sample predictive validation. While the prediction intervals produced by the extant method (which does not account for this source of uncertainty) have somewhat less than nominal coverage, we find that our proposed method achieves closer to nominal coverage. The prediction intervals become wider for countries for which the estimates of past total fertility rates rely heavily on surveys rather than on vital registration data, especially in high fertility countries.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62N05 | Reliability and life testing |

62J15 | Paired and multiple comparisons; multiple testing |

### Keywords:

Bayesian hierarchical model; Markov chain Monte Carlo; measurement error; population projection; total fertility rate; vital registration
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\textit{P. Liu} and \textit{A. E. Raftery}, Ann. Appl. Stat. 14, No. 2, 685--705 (2020; Zbl 1446.62280)

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