Correction to: A probabilistic projection of beneficiaries of long‑term care insurance in Germany by severity of disability

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Probabilistic Projection of Subnational Life Expectancy

Projecting mortality for subnational units, or regions, is of great interest to practicing demographers. We seek a probabilistic method for projecting subnational life expectancy that is based on the national Bayesian hierarchical model used by the United Nations, and at the same time is easy to use. We propose three methods of this kind. Two of them are variants of simple scaling methods. The third method models life expectancy for a region as equal to national life expectancy plus a region-specific stochastic process which is a heteroskedastic first-order autoregressive process (AR(1)), with a variance that declines to a constant as life expectancy increases. We apply our models to data from 29 countries. In an out-of-sample comparison, the proposed methods outperformed other comparative methods and were well calibrated for individual regions. The AR (1) method performed best in terms of crossover patterns between regions. Although the methods work well for individual regions, there are some limitations when evaluating within-country variation. We identified four countries for which the AR(1) method either underestimated or overestimated the predictive between-region within-country standard deviation. However, none of the competing methods work better in this regard than the AR(1) method. In addition to providing the full distribution of subnational life expectancy, the methods can be used to obtain probabilistic forecasts of age-specific mortality rates.

Introducing Quantile Mapping to a Regression Model Using a Multi-Model Ensemble to Improve Probabilistic Projections of Monthly Precipitation

A new method was proposed for the probabilistic projection of future climate that introduced quantile mapping to a regression method using a multi-model ensemble (QM_RMME). Results of this method were then compared with those of the traditional regression method (RMME). Six stations in Japan where 100 year observation records were available were used to evaluate the performance of the methods. An initial 50-year period (1901–1950) was used to develop the regression models and the final period (1951–2000) was used for evaluation. Results showed that the estimation errors at the 50th and 90th percentile were smaller for QM_RMME as compared to RMME at most sites. Conversely, when the model development and evaluation periods were limited to 20 years (1901–1920 and 1951–1970, respectively), the 90th percentile error was larger for QM_RMME. This was attributed to quantile mapping resulting in over-fitting of the data during the model development period. Furthermore, the QM_RMME error increased when the difference of observations between the model development and verification periods was large. Therefore, results indicated that the RMME method was more stable for relatively short data verification periods.

Simulation of Migration and Forecast of Population in the Baltic Countries by the Year 2096 / Имитационное моделирование миграций и прогноз численности населения в странах Балтии до 2096 года

The aim of the study is the forecast of the migration and population to 2096 in Baltic States (Estonia, Latvia and Lithuania). This article is prepared on the basis of several Bayesian probabilistic projection according to the Population Division of the Department of economic and social Affairs of the UN Secretariat. The main research method is a simulation of multifactor modeling. In general, migration in the Baltic States adversely affecting the projected population. However, the influence of net migration differs between the countries. It is necessary to take into account what according to the main provisions of UN and Eurostat net migration should be minimized until 2035. If the expected minimization of net migration will not happen, decrease in population of the Baltic States could be catastrophic.