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The sex ratio at birth (SRB) is defined as the ratio of male to female live births. The SRB imbalance in parts of the world over the past several decades is a direct consequence of sex-selective abortion, driven by the co-existence of son preference, readily available technology of prenatal sex determination, and fertility decline. Estimation and projection of the degree of SRB imbalance is complicated because of variability in SRB reference levels and because of the uncertainty associated with SRB observations. We develop Bayesian hierarchical time series mixture models for SRB estimation and scenario-based projections for all countries from 1950 to 2100. We model the SRB regional and national reference levels, and the fluctuation around national reference levels. We identify countries at risk of SRB imbalances and model both (i) the absence or presence of sex ratio transitions in such countries and, if present, (ii) the transition process. The transition model of SRB imbalance captures three stages (increase, stagnation and convergence back to SRB baselines). The model identifies countries with statistical evidence of SRB inflation in a fully Bayesian approach. The scenario-based SRB projections are based on the sex ratio transition model with varying assumptions regarding the occurrence of a sex ratio transition in at-risk countries. Projections are used to quantify the future burden of missing female births due to sex-selective abortions under different scenarios.

We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions. We seek a method that is consistent with the UN's recently adopted Bayesian method for probabilistic TFR projections for all countries, and works well for all countries. We assess various possible methods using subnational TFR data for 47 countries. We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales the national trajectory by a region-specific scale factor that is allowed to vary slowly over time. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world.

The United Nations released official probabilistic population projections (PPP) for all countries for the first time in July 2014. These were obtained by projecting the period total fertility rate (TFR) and life expectancy at birth ($e_0$) using Bayesian hierarchical models, yielding a large set of future trajectories of TFR and $e_0$ for all countries and future time periods to 2100, sampled from their joint predictive distribution. Each trajectory was then converted to age-specific mortality and fertility rates, and population was projected using the cohort-component method. This yielded a large set of trajectories of future age- and sex-specific population counts and vital rates for all countries. In this paper we describe the methodology used for deriving the age-specific mortality and fertility rates in the 2014 PPP, we identify limitations of these methods, and we propose several methodological improvements to overcome them. The methods presented in this paper are implemented in the publicly available bayesPop R package.

The United Nations regularly publishes projections of the populations of all the world's countries broken down by age and sex. These projections are the de facto standard and are widely used by international organizations, governments and researchers. Like almost all other population projections, they are produced using the standard deterministic cohort-component projection method and do not yield statements of uncertainty. We describe a Bayesian method for producing probabilistic population projections for most countries which are projections that the United Nations could use. It has at its core Bayesian hierarchical models for the total fertility rate and life expectancy at birth. We illustrate the method and show how it can be extended to address concerns about the UN's current assumptions about the long-term distribution of fertility. The method is implemented in the R packages bayesTFR, bayesLife, bayesPop and bayesDem., Comment: Published in at http://dx.doi.org/10.1214/13-STS419 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The original version of Bayesian reconstruction, a method for estimating age-specific fertility, mortality, migration and population counts of the recent past with uncertainty, produced estimates for female-only populations. Here we show how two-sex populations can be similarly reconstructed and probabilistic estimates of various sex ratio quantities obtained. We demonstrate the method by reconstructing the populations of India from 1971 to 2001, Thailand from 1960 to 2000, and Laos from 1985 to 2005. We found evidence that in India, sex ratio at birth exceeded its conventional upper limit of 1.06, and, further, increased over the period of study, with posterior probability above 0.9. In addition, almost uniquely, we found evidence that life expectancy at birth was lower for females than for males in India (posterior probability for 1971--1976 0.79), although there was strong evidence for a narrowing of the gap through to 2001. In both Thailand and Laos, we found strong evidence for the more usual result that life expectancy at birth was greater for females and, in Thailand, that the difference increased over the period of study., Comment: 43 pages, 12 tables, 15 figures. Since last version: Text of main article unchanged: - Added citation to auxiliary source files. - Added institution report number