Adrian E. Raftery

Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this issue for logistic regression, but their relative performance under realistic conditions remains poorly understood. We therefore conducted a preregistered, simulation-based comparison of 28 established methods for variable selection and inference under model uncertainty, using 11 empirical datasets spanning a range of sample sizes and numbers of predictors, in cases both with and without separation. We found that Bayesian model averaging (BMA) methods based on g –priors, particularly g = max ( n , p 2 ) , show the strongest overall performance when separation is absent. When separation occurs, penalized likelihood approaches, especially the LASSO, provide the most stable results, while BMA with the local empirical Bayes (EB-local) prior is competitive in both situations. These findings offer practical guidance for applied researchers on how to effectively address model uncertainty in logistic regression in modern empirical and machine learning research.

Existing models of country-level net migration ignore the effect of population age distribution on past and projected migration rates. We propose a method to estimate and forecast international net migration rates for the 200 most populous countries, taking account of changes in population age structure. We use age-standardized estimates of country-level net migration rates and in-migration (i.e., immigration) rates over five-year periods from 1990 through 2020 to decompose past net migration rates into in-migration rates and out-migration (i.e., emigration) rates. We then recalculate historic migration rates on a scale that removes the influence of the population age distribution. This is done by scaling past and projected migration rates in terms of a reference population and period using a quantity we call the migration age structure index (MASI). We use a Bayesian hierarchical model to generate joint probabilistic forecasts of net migration rates over five-year periods for all countries through 2100. We find that accounting for population age structure in historic and forecast net migration rates leads to narrower prediction intervals by the end of the century for most countries. Furthermore, accounting for population age structure leads to less out-migration among countries with rapidly aging populations that are forecast to contract most rapidly by the end of the century. This approach leads to less drastic population declines than are forecast without accounting for population age structure.

In the fourth of an occasional series of explainers on the statistics and data underpinning our understanding of climate change, Adrian E. Raftery, Andrew Garrett and David B. Stephenson look at how global warming is felt very differently in different parts of the world

Estimates of future migration patterns are of broad interest in demography. Forced migration, including refugee and asylum seekers, plays an important role in overall migration patterns but is notoriously difficult to forecast. Focusing on refugees and asylum seekers, we propose a modeling pipeline based on Bayesian hierarchical time-series modeling for projecting refugee population official statistics by country of origin using data from the United Nations High Commissioner for Refugees. Our approach is based on a conceptual model of refugee and asylum seeker populations following growth and decline phases, separated by a peak. The growth and decline phases are modeled by logistic growth and decline through an interrupted logistic process model. We evaluate our method through a set of validation exercises that show it has good performance for forecasts at 1-, 5-, and 10-year horizons, and we present projections for 35 countries of origin of large refugee and asylum seeker populations.

Projecting future climate change is important for implementing the 2015 Paris Agreement, which aims to limit greenhouse gas emissions to a level that would keep the global average temperature increase to 2100 below 2 °C. The Intergovernmental Panel on Climate Change uses emissions scenarios for projecting climate change, but since 2017, an alternative fully statistical Bayesian probabilistic approach has been developed. Both approaches rely on an equation that expresses emissions as the product of population, Gross Domestic Product (GDP) per capita, and carbon intensity, namely carbon emissions per unit of GDP. Here, we use data on these quantities for 2015–2024 to probabilistically assess the changes in climate change prospects associated with post-Paris emissions. These show that carbon intensity declined (i.e., improved) substantially over that period, but that overall carbon emissions rose, due to the rapid rise in world GDP, which more than canceled out the progress made. We found that the projected temperature increase to 2100 declined only slightly, from 2.6° C to 2.4 °C. Meanwhile, the chance of staying below 2 °C remained low, at 17%. However, the chance of the most catastrophic climate change, above 3 °C, has gone down substantially, from 26% to 9%.

International comparisons of hierarchical time series data sets based on survey data, such as annual country-level estimates of school enrollment rates, can suffer from large amounts of missing data due to differing coverage of surveys across countries and across times. A popular approach to handling missing data in these settings is through multiple imputation, which can be especially effective when there is an auxiliary variable that is strongly predictive of and has a smaller amount of missing data than the variable of interest. However, standard methods for multiple imputation of hierarchical time series data can perform poorly when the auxiliary variable and the variable of interest have a nonlinear relationship. Performance can also suffer if the multiple imputations are used to estimate an analysis model that makes different assumptions about the data compared to the imputation model, leading to uncongeniality between analysis and imputation models. We propose a Bayesian method for multiple imputation of hierarchical nonlinear time series data that uses a sequential decomposition of the joint distribution and incorporates smoothing splines to account for nonlinear relationships between variables. We compare the proposed method with existing multiple imputation methods through a simulation study and an application to secondary school enrollment data. We find that the proposed method can lead to substantial performance increases for estimation of parameters in uncongenial analysis models and for prediction of individual missing values.

We propose an easily computed estimator of the marginal likelihood from posterior simulation output, via reciprocal importance sampling, combining earlier proposals of DiCiccio et al (1997) and Robert and Wraith (2009). This involves only the unnormalized posterior densities from the sampled parameter values, and does not involve additional simulations beyond the main posterior simulation, or additional complicated calculations, provided that the parameter space is unconstrained. Even if this is not the case, the estimator is easily adjusted by a simple Monte Carlo approximation. It is unbiased for the reciprocal of the marginal likelihood, consistent, has finite variance, and is asymptotically normal. It involves one user-specified control parameter, and we derive an optimal way of specifying this. We illustrate it with several numerical examples.

Volume 51 - Article 1 | Pages 1–16

Women’s educational attainment and contraceptive prevalence are two mechanisms identified as having an accelerating effect on fertility decline and that can be directly impacted by policy. Quantifying the potential accelerating effect of education and family planning policies on fertility decline in a probabilistic way is of interest to policymakers, particularly in high-fertility countries. We propose a conditional Bayesian hierarchical model for projecting fertility, given education and family planning policy interventions. To illustrate the effect policy changes could have on future fertility, we create probabilistic projections of fertility that condition on scenarios such as achieving the sustainable development goals (SDGs) for universal secondary education and universal access to family planning by 2030.

The link between age and migration propensity is long established, but existing models of country-level net migration ignore the effect of population age distribution on past and projected migration rates. We propose a method to estimate and forecast international net migration rates for the 200 most populous countries, taking account of changes in population age structure. We use age-standardized estimates of country-level net migration rates and in-migration rates over quinquennial periods from 1990 through 2020 to decompose past net migration rates into in-migration rates and out-migration rates. We then recalculate historic migration rates on a scale that removes the influence of the population age distribution. This is done by scaling past and projected migration rates in terms of a reference population and period. We show that this can be done very simply, using a quantity we call the migration age structure index (MASI). We use a Bayesian hierarchical model to generate joint probabilistic forecasts of total and age- and sex- specific net migration rates over five-year periods for all countries from 2020 through 2100. We find that accounting for population age structure in historic and forecast net migration rates leads to narrower prediction intervals by the end of the century for most countries. Also, applying a Rogers & Castro-like migration age schedule to migration outflows reduces uncertainty in population pyramid forecasts. Finally, accounting for population age structure leads to less out-migration among countries with rapidly aging populations that are forecast to contract most rapidly by the end of the century. This leads to less drastic population declines than are forecast without accounting for population age structure.