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This book addresses from a methodological perspective a research problem, how to forecast the international migration component in a way that could be then used for population forecasts using the probabilistic approach. All forecasts are made in the conditions of uncertainty, which is an immanent feature of every inference about the future, a key issue in forecasting becomes not to offer a point estimate of the future values of the variables under study, but rather to provide a reliable assessment of the related uncertainty span, ideally, in a coherent and quantifiable manner. It consists of three major parts: an overview of existing theories, methods and models used for forecasting migration flows, followed by a proposition of a forecasting framework based on the Bayesian approach in statistics, and then by a discussion of the predictions from the point of view of forecast users (decision-makers).

A Bayesian hierarchical model is proposed to forecast outcomes of binary referenda based on opinion poll data acquired over a period of time. It is demonstrated how the model provides a consistent probabilistic predictions of the final outcomes over the preceding months, effectively smoothing the volatility exhibited by individual polls. The method is illustrated using opinion poll data published before the Scottish independence referendum in 2014, in which Scotland voted to remain a part of the United Kingdom, and subsequently validate it on the data related to the 2016 referendum on the continuing membership of the United Kingdom in the European Union.

European Union (EU) enlargements in 2004 and 2007 were accompanied by increased migration from new-accession to established-member (EU-15) countries. The impacts of these flows depend, in part, on the amount of time that persons from the former countries live in the latter over the life course. In this paper, we develop period estimates of duration expectancy in EU-15 countries among persons from new-accession countries. Using a newly developed set of harmonised Bayesian estimates of migration flows each year from 2002 to 2008 from the Integrated Modelling of European Migration (IMEM) Project, we exploit period age patterns of country-to-country migration and mortality to summarize the average number of years that persons from new-accession countries could be expected to live in EU-15 countries over the life course. In general, the results show that the amount of time that persons from new-accession countries could be expected to live in the EU-15 nearly doubled after 2004.

AbstractFlows of international migration are needed in the Asia-Pacific region to understand the patterns and corresponding effects on demographic, social, and economic change across sending and receiving countries. A major challenge to this understanding is that nearly all of the countries in this region do not gather or produce statistics on flows of international migration. The only information that are widely available represent immigrant population stocks measured at specific points in time—but these represent poor proxies for annual movements. In this paper, we present a methodology for indirectly estimating annual flows of international migration amongst 53 populations in the Asia-Pacific region and four macro world regions from 2000 to 2019 using a generation–distribution framework. The estimates suggest that 27–31 million persons from the Asia-Pacific region have changed their countries of usual residence during each year in the study. Southern Asia is estimated to have had the largest inflows and outflows, whilst intra-regional migration and return migration were highest in Eastern, Southern, and South-Eastern Asia. India, China, and Indonesia were estimated to have had the largest emigration flows and net migration losses. As a first attempt to estimate international migration flows in the Asia-Pacific region, this paper provides a basis for understanding the dynamics and complexity of the large-scale migration occurring in the region.

Abstract
Probability sample (PS) surveys are considered the gold standard for population-based inference but face many challenges due to decreasing response rates, relatively small sample sizes, and increasing costs. In contrast, the use of nonprobability sample (NPS) surveys has increased significantly due to their convenience, large sample sizes, and relatively low costs, but they are susceptible to large selection biases and unknown selection mechanisms. Integrating both sample types in a way that exploits their strengths and overcomes their weaknesses is an ongoing area of methodological research. We build on previous work by proposing a method of supplementing PSs with NPSs to improve analytic inference for logistic regression coefficients and potentially reduce survey costs. Specifically, we use a Bayesian framework for inference. Inference relies on a probability survey with a small sample size, and through the prior structure we incorporate supplementary auxiliary information from a less-expensive (but potentially biased) NPS survey fielded in parallel. The performance of several strongly informative priors constructed from the NPS information is evaluated through a simulation study and real-data application. Overall, the proposed priors reduce the mean-squared error (MSE) of regression coefficients or, in the worst case, perform similarly to a weakly informative (baseline) prior that does not utilize any nonprobability information. Potential cost savings (of up to 68 percent) are evident compared to a probability-only sampling design with the same MSE for different informative priors under different sample sizes and cost scenarios. The algorithm, detailed results, and interactive cost analysis are provided through a Shiny web app as guidance for survey practitioners.

AbstractWe improve upon the modelling of India's pandemic vulnerability. Our model is multidisciplinary and recognises the nested levels of the epidemic. We create a model of the risk of severe COVID-19 and death, instead of a model of transmission. Our model allows for socio-demographic-group differentials in risk, obesity and underweight people, morbidity status and other conditioning regional and lifestyle factors. We build a hierarchical multilevel model of severe COVID-19 cases, using three different data sources: the National Family Health Survey for 2015/16, Census data for 2011 and data for COVID-19 deaths obtained cumulatively until June 2020. We provide results for 11 states of India, enabling best-yet targeting of policy actions. COVID-19 deaths in north and central India were higher in areas with older and overweight populations, and were more common among people with pre-existing health conditions, or who smoke, or who live in urban areas. Policy experts may both want to 'follow World Health Organisation advice' and yet also use disaggregated and spatially specific data to improve wellbeing outcomes during the pandemic. The future uses of our innovative data-combining model are numerous.

Abstract
Survey data collection costs have risen to a point where many survey researchers and polling companies are abandoning large, expensive probability-based samples in favor of less expensive nonprobability samples. The empirical literature suggests this strategy may be suboptimal for multiple reasons, among them that probability samples tend to outperform nonprobability samples on accuracy when assessed against population benchmarks. However, nonprobability samples are often preferred due to convenience and costs. Instead of forgoing probability sampling entirely, we propose a method of combining both probability and nonprobability samples in a way that exploits their strengths to overcome their weaknesses within a Bayesian inferential framework. By using simulated data, we evaluate supplementing inferences based on small probability samples with prior distributions derived from nonprobability data. We demonstrate that informative priors based on nonprobability data can lead to reductions in variances and mean squared errors for linear model coefficients. The method is also illustrated with actual probability and nonprobability survey data. A discussion of these findings, their implications for survey practice, and possible research extensions are provided in conclusion.

Age and sex patterns of migration are essential for understanding drivers of population change and heterogeneity of migrant groups. We develop a hierarchical Bayesian model to estimate such patterns for international migration in the European Union and European Free Trade Association from 2002 to 2008, which was a period of time when the number of members expanded from 19 to 31 countries. Our model corrects for the inadequacies and inconsistencies in the available data and estimates the missing patterns. The posterior distributions of the age and sex profiles are then combined with a matrix of origin-destination flows, resulting in a synthetic database with measures of uncertainty for migration flows and other model parameters.

Age and sex patterns of migration are essential for understanding drivers of population change and heterogeneity of migrant groups. We develop a hierarchical Bayesian model to estimate such patterns for international migration in the European Union and European Free Trade Association from 2002 to 2008, which was a period of time when the number of members expanded from 19 to 31 countries. Our model corrects for the inadequacies and inconsistencies in the available data and estimates the missing patterns. The posterior distributions of the age and sex profiles are then combined with a matrix of origin–destination flows, resulting in a synthetic database with measures of uncertainty for migration flows and other model parameters.

Although up-to-date information on the nature and extent of migration within the European Union (EU) is important for policymaking, timely and reliable statistics on the number of EU citizens residing in or moving across other member states are difficult to obtain. In this paper, we develop a statistical model that integrates data on EU migrant stocks using traditional sources such as census, population registers and Labour Force Survey, with novel data sources, primarily from the Facebook Advertising Platform. Findings suggest that combining different data sources provides near real-time estimates that can serve as early warnings about shifts in EU mobility patterns. Estimated migrant stocks match relatively well to the observed data, despite some overestimation of smaller migrant populations and underestimation for larger migrant populations in Germany and the United Kingdom. In addition, the model estimates missing stocks for migrant corridors and years where no data are available, offering timely now-casted estimates.

IntroductionLength of Stay (LoS) in Intensive Care Units (ICUs) is an important measure for planning beds capacity during the Covid-19 pandemic. However, as the pandemic progresses and we learn more about the disease, treatment and subsequent LoS in ICU may change.
ObjectivesTo investigate the LoS in ICUs in England associated with Covid-19, correcting for censoring, and to evaluate the effect of known predictors of Covid-19 outcomes on ICU LoS.
Data sourcesWe used retrospective data on Covid-19 patients, admitted to ICU between 6 March and 24 May, from the "Covid-19 Hospitalisation in England Surveillance System" (CHESS) database, collected daily from England's National Health Service, and collated by Public Health England.
MethodsWe used Accelerated Failure Time survival models with Weibull and log-normal distributional assumptions to investigate the effect of predictors, which are known to be associated with poor Covid-19 outcomes, on the LoS in ICU.
ResultsPatients admitted before 25 March had significantly longer LoS in ICU (mean = 18.4 days, median = 12), controlling for age, sex, whether the patient received Extracorporeal Membrane Oxygenation, and a co-morbid risk factors score, compared with the period after 7 April (mean = 15.4, median = 10). The periods of admission reflected the changes in the ICU admission policy in England. Patients aged 50-65 had the longest LoS, while higher co-morbid risk factors score led to shorter LoS. Sex and ethnicity were not associated with ICU LoS.
ConclusionsThe skew of the predicted LoS suggests that a mean LoS, as compared with median, might be better suited as a measure used to assess and plan ICU beds capacity. This is important for the ongoing second and any future waves of Covid-19 cases and potential pressure on the ICU resources. Also, changes in the ICU admission policy are likely to be confounded with improvements in clinical knowledge of Covid-19.