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Estimates of future migration patterns are a crucial input to world population projections. Forced migration, including refugee and asylum seekers, plays an important role in overall migration patterns, but is notoriously difficult to forecast. We propose a modeling pipeline based on Bayesian hierarchical time-series modeling for projecting combined refugee and asylum seeker populations by country of origin using data from the United Nations High Commissioner for Human Rights (UNHCR). Our approach is based on a conceptual model of refugee crises 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 with ongoing refugee crises., Comment: 31 pages, 3 tables, 6 figures

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., Comment: 29 pages, 8 figures, 3 tables

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 are have a nonlinear relationship. Performance of standard multiple imputation methods can also suffer if the substantive analysis model of interest is uncongenial to the imputation model, which can be a common occurrence for social science data if the imputation phase is conducted independently of the analysis phase. 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., Comment: 36 pages, 5 figures

Professor Adrian E. Raftery is the Boeing International Professor of Statistics and Sociology, and an adjunct professor of Atmospheric Sciences, at the University of Washington in Seattle. He was born in Dublin, Ireland, and obtained a B.A. in Mathematics and an M.Sc. in Statistics and Operations Research at Trinity College Dublin. He obtained a doctorate in mathematical statistics from the Universit\'e Pierre et Marie Curie under the supervision of Paul Deheuvels. He was a lecturer in statistics at Trinity College Dublin, and then an associate and full professor of statistics and sociology at the University of Washington. He was the founding Director of the Center for Statistics and Social Sciences. Professor Raftery has published over 200 articles in peer-reviewed statistical, sociological and other journals. His research focuses on Bayesian model selection and Bayesian model averaging, model-based clustering, inference for deterministic models, and the development of new statistical methods for demography, sociology, and the environmental and health sciences. He is a member of the United States National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, an Honorary Member of the Royal Irish Academy, a member of the Washington State Academy of Sciences, a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an elected Member of the Sociological Research Association. He has won multiple awards for his research. He was Coordinating and Applications Editor of the Journal of the American Statistical Association and Editor of Sociological Methodology. He was identified as the world's most cited researcher in mathematics for the period 1995-2005. Thirty-three students have obtained Ph.D.'s working under Raftery's supervision, of whom 21 hold or have held tenure-track university faculty positions., Comment: 17 pages, 8 figures

We propose an easily computed estimator of marginal likelihoods 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. 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.

In this chapter, we present a review of latent position models for networks. We review the recent literature in this area and illustrate the basic aspects and properties of this modeling framework. Through several illustrative examples we highlight how the latent position model is able to capture important features of observed networks. We emphasize how the canonical design of this model has made it popular thanks to its ability to provide interpretable visualizations of complex network interactions. We outline the main extensions that have been introduced to this model, illustrating its flexibility and applicability., Comment: 26 pages, 4 figures

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold representing similarity. We propose a Bayesian approach to multidimensional scaling when the low-dimensional manifold is hyperbolic. Using hyperbolic space facilitates representing tree-like structures common in many settings (e.g. text or genetic data with hierarchical structure). A Bayesian approach provides regularization that minimizes the impact of measurement error in the observed data and assesses uncertainty. We also propose a case-control likelihood approximation that allows for efficient sampling from the posterior distribution in larger data settings, reducing computational complexity from approximately $O(n^2)$ to $O(n)$. We evaluate the proposed method against state-of-the-art alternatives using simulations, canonical reference datasets, Indian village network data, and human gene expression data.

The bayesTFR package for R provides a set of functions to produce probabilistic projections of the total fertility rates (TFR) for all countries, and is widely used, including as part of the basis for the UN's official population projections for all countries. Liu and Raftery (2020) extended the theoretical model by adding a layer that accounts for the past TFR estimation uncertainty. A major update of bayesTFR implements the new extension. Moreover, a new feature of producing annual TFR estimation and projections extends the existing functionality of estimating and projecting for five-year time periods. An additional autoregressive component has been developed in order to account for the larger autocorrelation in the annual version of the model. This article summarizes the updated model, describes the basic steps to generate probabilistic estimation and projections under different settings, compares performance, and provides instructions on how to summarize, visualize and diagnose the model results.

There are many sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results come with a big delay. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effects of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining the main available data sources. It is based on a discrete-time SIR model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data of deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the USA. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress towards herd immunity.

We describe the vote package in R, which implements the plurality (or first-past-the-post), two-round runoff, score, approval and single transferable vote (STV) electoral systems, as well as methods for selecting the Condorcet winner and loser. We emphasize the STV system, which we have found to work well in practice for multi-winner elections with small electorates, such as committee and council elections, and the selection of multiple job candidates. For single-winner elections, the STV is also called instant runoff voting (IRV), ranked choice voting (RCV), or the alternative vote (AV) system. The package also implements the STV system with equal preferences, for the first time in a software package, to our knowledge. It also implements a new variant of STV, in which a minimum number of candidates from a specified group are required to be elected. We illustrate the package with several real examples.

Boundaries on spatial fields divide regions with particular features from surrounding background areas. These boundaries are often described with contour lines. To measure and record these boundaries, contours are often represented as ordered sequences of spatial points that connect to form a line. Methods to identify boundary lines from interpolated spatial fields are well-established. Less attention has been paid to how to model sequences of connected spatial points. For data of the latter form, we introduce the Gaussian Star-shaped Contour Model (GSCM). GSMCs generate sequences of spatial points via generating sets of distances in various directions from a fixed starting point. The GSCM is designed for modeling contours that enclose regions that are star-shaped polygons or approximately star-shaped polygons. Metrics are introduced to assess the extent to which a polygon deviates from star-shaped. Simulation studies illustrate the performance of the GSCM in various scenarios and an analysis of Arctic sea ice edge contour data highlights how GSCMs can be applied to observational data.

Smoking is one of the main risk factors that has affected human mortality and life expectancy over the past century. Smoking accounts for a large part of the nonlinearities in the growth of life expectancy and of the geographic and sex differences in mortality. As Bongaarts (2006) and Janssen (2018) suggested, accounting for smoking could improve the quality of mortality forecasts due to the predictable nature of the smoking epidemic. We propose a new Bayesian hierarchical model to forecast life expectancy at birth for both sexes and for 69 countries with good data on smoking-related mortality. The main idea is to convert the forecast of the non-smoking life expectancy at birth (i.e., life expectancy at birth removing the smoking effect) into life expectancy forecast through the use of the age-specific smoking attributable fraction (ASSAF). We introduce a new age-cohort model for the ASSAF and a Bayesian hierarchical model for non-smoking life expectancy at birth. The forecast performance of the proposed method is evaluated by out-of-sample validation compared with four other commonly used methods for life expectancy forecasting. Improvements in forecast accuracy and model calibration based on the new method are observed.

Sea ice, or frozen ocean water, freezes and melts every year in the Arctic. Forecasts of where sea ice will be located weeks to months in advance have become more important as the amount of sea ice declines due to climate change, for maritime planning and other uses. Typical sea ice forecasts are made with ensemble models, physics-based models of sea ice and the surrounding ocean and atmosphere. This paper introduces Mixture Contour Forecasting, a method to forecast sea ice probabilistically using a mixture of two distributions, one based on post-processed output from ensembles and the other on observed sea ice patterns in recent years. At short lead times, these forecasts are better calibrated than unadjusted dynamic ensemble forecasts and other statistical reference forecasts. To produce these forecasts, a statistical technique is introduced that directly models the sea ice edge contour, the boundary around the region that is ice-covered. Mixture Contour Forecasting and reference methods are evaluated for monthly sea ice forecasts for 2008-2016 at lead times ranging from 0.5-6.5 months using one of the European Centre for Medium-Range Weather Forecasts ensembles.

Smoking is one of the preventable threats to human health and is a major risk factor for lung cancer, upper aero-digestive cancer, and chronic obstructive pulmonary disease. Estimating and forecasting the smoking attributable fraction (SAF) of mortality can yield insights into smoking epidemics and also provide a basis for more accurate mortality and life expectancy projection. Peto et al. (1992) proposed a method to estimate the SAF using the lung cancer mortality rate as an indicator of exposure to smoking in the population of interest. Here we use the same method to estimate the all-age SAF (ASAF) for both genders for over 60 countries. We document a strong and cross-nationally consistent pattern of the evolution of the SAF over time. We use this as the basis for a new Bayesian hierarchical model to project future male and female ASAF from over 60 countries simultaneously. This gives forecasts as well as predictive distributions that can be used to find uncertainty intervals for any quantities of interest. We assess the model using out-of-sample predictive validation, and find that it provides good forecasts and well calibrated forecast intervals.

Since the 1940s, population projections have in most cases been produced using the deterministic cohort component method. However, in 2015, for the first time, 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 UN'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 is a first attempt to remedy this for total fertility rates, by extending the UN model for the future 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 current method have somewhat less than nominal coverage, we find that our proposed method achieves close 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.

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of interest. This paper explores two extensions of the BIC for evaluating order constrained models, one where a truncated unit information prior is used under the order-constrained model, and the other where a truncated local unit information prior is used. The first prior is centered around the maximum likelihood estimate and the latter prior is centered around a null value. Several analyses show that the order-constrained BIC based on the local unit information prior works better as an Occam's razor for evaluating order-constrained models and results in lower error probabilities. The methodology based on the local unit information prior is implemented in the R package `BICpack' which allows researchers to easily apply the method for order-constrained model selection. The usefulness of the methodology is illustrated using data from the European Values Study., Comment: 25 pages, 4, figures, 2 tables

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 (UN) issued official probabilistic population projections for all countries to 2100 in July 2015. This was done by simulating future levels of total fertility and life expectancy from Bayesian hierarchical models, and combining the results using a standard cohort-component projection method. The 40 countries with generalized HIV/AIDS epidemics were treated differently from others, in that the projections used the highly multistate Spectrum/EPP model, a complex 15-compartment model that was designed for short-term projections of quantities relevant to policy for the epidemic. Here we propose a simpler approach that is more compatible with the existing UN probabilistic projection methodology for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression model on current life expectancy, HIV prevalence and ART coverage. These are then converted to age- and sex-specific mortality rates using a new family of model life tables designed for countries with HIV/AIDS epidemics that reproduces the characteristic hump in middle adult mortality. These are then input to the standard cohort-component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar population projections to Spectrum/EPP in the short run, while being simpler and avoiding multistate modeling.

While probabilistic projection methods for projecting life expectancy exist, few account for covariates related to life expectancy. Generalized HIV/AIDS epidemics have a large, immediate negative impact on the life expectancy in a country, but this impact can be mitigated by widespread use of antiretroviral therapy (ART). Thus projection methods for countries with generalized HIV/AIDS epidemics could be improved by accounting for HIV prevalence, the future course of the epidemic and coverage of ART. We propose a method for making probabilistic projections of life expectancy to 2100 for all countries in the world accounting for HIV prevalence, the future course of the epidemic and its uncertainty, and adult ART coverage. We extend the current Bayesian probabilistic life expectancy projection methods of Raftery et al. (2013) to account for HIV prevalence and adult ART coverage. We evaluate our method using out-of-sample validation. We find that the proposed method performs better than the method that does not account for HIV prevalence or ART coverage for projections of life expectancy in countries with a generalized epidemic, while projections for countries without an epidemic remain essentially unchanged.

The United Nations is the major organization producing and regularly updating probabilistic population projections for all countries. International migration is a critical component of such projections, and between-country correlations are important for forecasts of regional aggregates. However, there are 200 countries and only 12 data points, each one corresponding to a five-year time period. Thus a $200 \times 200$ correlation matrix must be estimated on the basis of 12 data points. Using Pearson correlations produces many spurious correlations. We propose a maximum a posteriori estimator for the correlation matrix with an interpretable informative prior distribution. The prior serves to regularize the correlation matrix, shrinking a priori untrustworthy elements towards zero. Our estimated correlation structure improves projections of net migration for regional aggregates, producing narrower projections of migration for Africa as a whole and wider projections for Europe. A simulation study confirms that our estimator outperforms both the Pearson correlation matrix and a simple shrinkage estimator when estimating a sparse correlation matrix.

Inferring gene regulatory networks is an important problem in systems biology. However, these networks can be hard to infer from experimental data because of the inherent variability in biological data as well as the large number of genes involved. We propose a fast, simple method for inferring regulatory relationships between genes from knockdown experiments in the NIH LINCS dataset by calculating posterior probabilities, incorporating prior information. We show that the method is able to find previously identified edges from TRANSFAC and JASPAR and discuss the merits and limitations of this approach.

The NIH Library of Integrated Network-based Cellular Signatures (LINCS) contains gene expression data from over a million experiments, using Luminex Bead technology. Only 500 colors are used to measure the expression levels of the 1,000 landmark genes measured, and the data for the resulting pairs of genes are deconvolved. The raw data are sometimes inadequate for reliable deconvolution leading to artifacts in the final processed data. These include the expression levels of paired genes being flipped or given the same value, and clusters of values that are not at the true expression level. We propose a new method called model-based clustering with data correction (MCDC) that is able to identify and correct these three kinds of artifacts simultaneously. We show that MCDC improves the resulting gene expression data in terms of agreement with external baselines, as well as improving results from subsequent analysis., Comment: 28 pages

Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among the several approaches available in the literature, model-based agglomerative hierarchical clustering is used to provide initial partitions in the popular MCLUST R package. This choice is computationally convenient and often yields good clustering partitions. However, in certain circumstances, poor initial partitions may cause the EM algorithm to converge to a local maximum of the likelihood function. We propose several simple and fast refinements based on data transformations and illustrate them through data examples.

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However for data sets where the number of variables $p$ is large (e.g. $p>5,000$) the algorithm can become prohibitively expensive, computationally. Another method which is popular for high dimensional data is random forests, a machine learning algorithm which grows trees using a greedy search for the best split points. However, as it is not a statistical model, it cannot produce probabilistic estimates or predictions. We propose an alternative algorithm for BART called BART-BMA, which uses Bayesian Model Averaging and a greedy search algorithm to produce a model which is much more efficient than BART for datasets with large $p$. BART-BMA incorporates elements of both BART and random forests to offer a model-based algorithm which can deal with high-dimensional data. We have found that BART-BMA can be run in a reasonable time on a standard laptop for the "small $n$ large $p$" scenario which is common in many areas of bioinformatics. We showcase this method using simulated data and data from two real proteomic experiments; one to distinguish between patients with cardiovascular disease and controls and another to classify agressive from non-agressive prostate cancer. We compare our results to their main competitors. Open source code written in R and Rcpp to run BART-BMA can be found at: https://github.com/BelindaHernandez/BART-BMA.git

We propose Bayesian model averaging (BMA) as a method for postprocessing the results of model-based clustering. Given a number of competing models, appropriate model summaries are averaged, using the posterior model probabilities, instead of being taken from a single "best" model. We demonstrate the use of BMA in model-based clustering for a number of datasets. We show that BMA provides a useful summary of the clustering of observations while taking model uncertainty into account. Further, we show that BMA in conjunction with model-based clustering gives a competitive method for density estimation in a multivariate setting. Applying BMA in the model-based context is fast and can give enhanced modeling performance.

We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree correlations. We introduce the Gaussian Latent Position Model, and derive analytic expressions and asymptotic approximations for its network properties. We pay particular attention to one special case, the Gaussian Latent Position Models with Random Effects, and show that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients and small-world behaviours that are often observed in social networks. Several real and simulated examples illustrate the ability of the models to capture important features of observed networks.

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.

Finite mixture modelling provides a framework for cluster analysis based on parsimonious Gaussian mixture models. Variable or feature selection is of particular importance in situations where only a subset of the available variables provide clustering information. This enables the selection of a more parsimonious model, yielding more efficient estimates, a clearer interpretation and, often, improved clustering partitions. This paper describes the R package clustvarsel which performs subset selection for model-based clustering. An improved version of the methodology of Raftery and Dean (2006) is implemented in the new version 2 of the package to find the (locally) optimal subset of variables with group/cluster information in a dataset. Search over the solution space is performed using either a stepwise greedy search or a headlong algorithm. Adjustments for speeding up these algorithms are discussed, as well as a parallel implementation of the stepwise search. Usage of the package is presented through the discussion of several data examples.