A companion set of lecture slides is available at

This paper provides an overview of methods and systems developed for record linkage. Modern record linkage begins with the pioneering work of Newcombe and is especially based on the formal mathematical model of Fellegi and Sunter. In their seminal work, Fellegi and Sunter introduced many powerful ideas for estimating record linkage parameters and other ideas that still influence record linkage today. Record linkage research is characterized by its synergism of statistics, computer science, and operations research. Many difficult algorithms have been developed and put in software systems. Record linkage practice is still very limited. Some limits are due to existing software. Other limits are due to the difficulty in automatically estimating matching parameters and error rates, with current research highlighted by the work of Larsen and Rubin. Keywords: computer matching, modeling, iterative fitting, string comparison, optimization RsSUMs Cet article donne une vue d'ensemble sur les ...

We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naive-Bayes models having a hidden root node, we find that (1) the BIC/MDL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate. 1

INTRODUCTION Matching has a long history of uses in statistical surveys and administrative data development. A business register consisting of names, addresses, and other identifying information such as total financial receipts might be constructed from tax and employment data bases (see chapters by Colledge, Nijhowne, and Archer). A survey of retail establishments or agricultural establishments might combine results from an area frame and a list frame. To produce a combined estimator, units from the area frame would need to be identified in the list frame (see Vogel-Kott chapter). To estimate the size of a (sub)population via capture-recapture techniques, one needs to accurately determine units common to two or more independent listings (Sekar and Deming 1949; Scheuren 1983; Winkler 1989b). Samples must be drawn appropriately to estimate overlap (Deming and Gleser 1959). Rather than develop a special survey to collect data for policy decisions, it might be more appropriate t

We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraint-based approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that the constraint-based approach uses categorical information about conditional-independence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraint-based counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of finite size. Two, using the Bayesian approach, finer distinctions among model structures---both quantitative and qualitative---can be made. Three, information from several models can be combined to make better inferences and to better ...

Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the functions to integrate to one can be approximated by Monte Carlo, the only regularity conditions being a compactification of the parameter space such that the the evaluation maps ` 7! h ` (x) remain continuous. Then with probability one the Monte Carlo approximant to the log likelihood hypoconverges to the exact log likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile, and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painlev'e-Kuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...

Most problems in frequentist statistics involve optimization of a function such as a likelihood or a sum of squares. EM algorithms are among the most effective algorithms for maximum likelihood estimation because they consistently drive the likelihood uphill by maximizing a simple surrogate function for the loglikelihood. Iterative optimization of a surrogate function as exemplified by an EM algorithm does not necessarily require missing data. Indeed, every EM algorithm is a special case of the more general class of MM optimization algorithms, which typically exploit convexity rather than missing data in majorizing or minorizing an objective function. In our opinion, MM algorithms deserve to part of the standard toolkit of professional statisticians. The current article explains the principle behind MM algorithms, suggests some methods for constructing them, and discusses some of their attractive features. We include numerous examples throughout the article to illustrate the concepts described. In addition to surveying previous work on MM algorithms, this article introduces some new material on constrained optimization and standard error estimation. Key words and phrases: constrained optimization, EM algorithm, majorization, minorization, Newton-Raphson 1 1

Many applications of the Fellegi-Sunter model use simplifying assumptions and ad hoc modifications to improve matching efficacy. Because of model misspecification, distinctive approaches developed in one application typically cannot be used in other applications and do not always make use of advances in statistical and computational theory. An ExpectationMaximization (EMH) algorithm that constrains the estimates to a convex subregion of the parameter space is given. The EMH algorithm provides probability estimates that yield better decision rules than unconstrained estimates. The algorithm is related to results of Meng and Rubin (1993) on Multi-Cycle Expectation-Conditional Maximization algorithms and make use of results of Haberman (1977) that hold for large classes of loglinear models. Key Words: MCECM Algorithm, Latent Class, Computer Matching, Error Rate This paper provides a theory for obtaining constrained maximum likelihood estimates for latent-class, loglinear models on finite ...

The Bradley–Terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among the many studies of the model in the past 75 years, numerous authors have generalized it in several directions, sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations. Building on a theory of algorithms known by the initials MM, for minorization–maximization, this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the Bradley–Terry model. While algorithms for problems of this type have tended to be custom-built in the literature, the techniques in this paper enable their mass production. Simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator. Several of the algorithms and convergence results herein are new. 1. Introduction. In

Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternative approach is to approximate the intractable integrals using Monte Carlo averages. Several dierent algorithms based on this idea have been proposed. In this paper we discuss the relative merits of simulated maximum likelihood, Monte Carlo EM, Monte Carlo Newton-Raphson and stochastic approximation. Key words and phrases : Eciency, Monte Carlo EM, Monte Carlo Newton-Raphson, Rate of convergence, Simulated maximum likelihood, Stochastic approximation All three authors partially supported by NSF Grant DMS-00-72827. 1 1