Whether the goal is to estimate the number of people that live in a congressional district, to estimate the number of individuals that have died in an armed conflict, or to disambiguate individual authors using bibliographic data, all these applications have a common theme—integrating information from multiple sources. Before such questions can be answered, databases must be cleaned and integrated in a systematic and accurate way, commonly known as structured entity resolution (record linkage or deduplication). Here, we review motivational applications and seminal papers that have led to the growth of this area. We review modern probabilistic and Bayesian methods in statistics, computer science, machine learning, database management, economics, political science, and other disciplines that are used throughout industry and academia in applications such as human rights, official statistics, medicine, and citation networks, among others. Last, we discuss current research topics of practical importance.

A simple method is shown to provide optimal variational bounds on f -divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.

Whether the goal is to estimate the number of people that live in a congressional district, to estimate the number of individuals that have died in an armed conflict, or to disambiguate individual authors using bibliographic data, all these applications have a common theme -integrating information from multiple sources. Before such questions can be answered, databases must be cleaned and integrated in a systematic and accurate way, commonly known as record linkage, de-duplication, or entity resolution. In this article, we review motivational applications and seminal papers that have led to the growth of this area. Specifically, we review the foundational work that began in the 1940's and 50's that have led to modern probabilistic record linkage. We review clustering approaches to entity resolution, semi-and fully supervised methods, and canonicalization, which are being used throughout industry and academia in applications such as human rights, official statistics, medicine, citation networks, among others. Finally, we discuss current research topics of practical importance.

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The quantification of modern slavery has received increased attention recently as organizations have come together to produce global estimates, where multiple systems estimation (MSE) is often used to this end. Echoing a long‐standing controversy, disagreements have re‐surfaced regarding the underlying MSE assumptions, the robustness of MSE methodology and the accuracy of MSE estimates in this application. Our goal was to help address and move past these controversies. To do so, we review MSE, its assumptions, and commonly used models for modern slavery applications. We introduce all of the publicly available modern slavery datasets in the literature, providing a reproducible analysis and highlighting current issues. Specifically, we utilize an internal consistency approach that constructs subsets of data for which ground truth is available, allowing us to evaluate the accuracy of MSE estimators. Next, we propose a characterization of the large sample bias of estimators as a function of misspecified assumptions. Then, we propose an alternative to traditional (e.g. bootstrap‐based) assessments of reliability, which allows us to visualize trajectories of MSE estimates to illustrate the robustness of estimates. Finally, our complementary analyses are used to provide guidance regarding the application and reliability of MSE methodology.