No abstract

What does statistics have to offer science and society, in this age of massive data, machine learning algorithms, and multiple online sources of tools for data analysis? I recall a few situations where statistics made a real difference and reinforced the impact of our discipline on society. Sometimes the difference lay in the insightful analysis and inference enabled by groundbreaking methods in our field like hypothesis testing, likelihood ratios, Bayesian models, jackknife, and bootstrap. But perhaps more often, the impacts came from thoughtful analyses before data were collected, and the questions that arose after the statistical analysis. The impact of understanding the problem, designing the experiment and data collections, conducting the pilot surveys, and raising important questions, is substantial. Through sensible explorations following formal statistical procedures, statisticians have made contributions in many domains. In this presentation, I recall some examples which made a long-lasting impact. Some of them, like randomization in clinical trials, known and familiar to all, are so ingrained in our practice that the role of statistics has been forgotten. Others may be less familiar but nonetheless benefited greatly from the critical input of statisticians. All remind us that our field remains today not only relevant but critical to science and society.

Between 1960 and 2000, fertility fell sharply in Brazil, but this transition was unevenly distributed in space and time. Using Bayesian spatial statistical methods and microdata from five censuses, we develop and apply a procedure for fitting logistic curves to the fertility transitions in more than 500 small regions of Brazil over this 40-year period. Doing so enables us to map the main features of the Brazilian fertility transition in considerable detail. We detect early declines in some regions of the country and document large differences between early and late transitions in regard to both the initial level of fertility and the speed of the transition. We also use our results to test hypotheses regarding changes in the level of development at the onset of the fertility transition and identify a temporary stall in the Brazilian transition that occurred in the late 1990s. A web site with project details is at http://schmert.net/BayesLogistic . Copyright (c) 2010 The Population Council, Inc..

High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with probabilistic prior information on death registration coverage derived from demographic estimation techniques, such as Death Distribution Methods, and from field audits by public health experts. We test the model on small-area data from Brazil. Incorporating external estimates of vital registration coverage though priors improves small-area mortality estimates by accounting for underregistration and automatically producing measures of uncertainty. Bayesian estimates show that when mortality levels in small areas are compared, noise often dominates signal. Differences in local point estimates of life expectancy are often small relative to uncertainty, even for relatively large areas in a populous country like Brazil.

High variability in recorded vital events creates serious problems for small-area mortality estimation by age and sex. Many existing approaches to fitting local mortality schedules, including those most often used in Brazil, estimate rates by making rigid mathematical assumptions about local age patterns. Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality schedules by age. We propose a more flexible statistical estimation method that combines Poisson regression with the TOPALS relational model (DE BEER, 2012). We use the new method to estimate age-specific mortality rates in Brazilian small areas (states, mesoregions, microregions, and municipalities) in 2010. Results for Minas Gerais show notable differences in the age patterns of mortality between adjacent small areas, demonstrating the advantages of using a flexible functional form in regression models.