When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods—or developing methods related to matching—do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

Instrumental variable (IV) methods are becoming increasingly popular as they seem to offer the only viable way to overcome the problem of unobserved confounding in observational studies. However, some attention has to be paid to the details, as not all such methods target the same causal parameters and some rely on more restrictive parametric assumptions than others. We therefore discuss and contrast the most common IV approaches with relevance to typical applications in observational epidemiology. Further, we illustrate and compare the asymptotic bias of these IV estimators when underlying assumptions are violated in a numerical study. One of our conclusions is that all IV methods encounter problems in the presence of effect modification by unobserved confounders. Since this can never be ruled out for sure, we recommend that practical applications of IV estimators be accompanied routinely by a sensitivity analysis.

Putting data into the public domain is not the same thing as making those data accessible for intelligent analysis. A distinguished group of editors and experts who were already engaged in one way or another with the issues inherent in making research data public came together with statisticians to initiate a dialogue about policies and practicalities of requiring published research to be accompanied by publication of the research data. This dialogue carried beyond the broad issues of the advisability, the intellectual integrity, the scientific exigencies to the relevance of these issues to statistics as a discipline and the relevance of statistics, from inference to modeling to data exploration, to science and social science policies on these issues.

Causal mediation analysis is routinely conducted by applied researchers in a variety of disciplines. The goal of such an analysis is to investigate alternative causal mechanisms by examining the roles of intermediate variables that lie in the causal paths between the treatment and outcome variables. In this paper we first prove that under a particular version of sequential ignorability assumption, the average causal mediation effect (ACME) is nonparametrically identified. We compare our identification assumption with those proposed in the literature. Some practical implications of our identification result are also discussed. In particular, the popular estimator based on the linear structural equation model (LSEM) can be interpreted as an ACME estimator once additional parametric assumptions are made. We show that these assumptions can easily be relaxed within and outside of the LSEM framework and propose simple nonparametric estimation strategies. Second, and perhaps most importantly, we propose a new sensitivity analysis that can be easily implemented by applied researchers within the LSEM framework. Like the existing identifying assumptions, the proposed sequential ignorability assumption may be too strong in many applied settings. Thus, sensitivity analysis is essential in order to examine the robustness of empirical findings to the possible existence of an unmeasured confounder. Finally, we apply the proposed methods to a randomized experiment from political psychology. We also make easy-to-use software available to implement the proposed methods.

The Dempster–Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer science and engineering applications, but has yet to reach the statistical mainstream, perhaps because the DS belief functions do not satisfy long-run frequency properties. Recently, two of the authors proposed an extension of DS, called the weak belief (WB) approach, that can incorporate desirable frequency properties into the DS framework by systematically enlarging the focal elements. The present paper reviews and extends this WB approach. We present a general description of WB in the context of inferential models, its interplay with the DS calculus, and the maximal belief solution. New applications of the WB method in two high-dimensional hypothesis testing problems are given. Simulations show that the WB procedures, suitably calibrated, perform well compared to popular classical methods. Most importantly, the WB approach combines the probabilistic reasoning of DS with the desirable frequency properties of classical statistics.

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional sufficient statistics for parameters and/or states as particles. State smoothing in the presence of parameter uncertainty is also solved as a by-product of PL. In a number of examples, we show that PL outperforms existing particle filtering alternatives and proves to be a competitor to MCMC.

Residuals in regression models are often spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When unmeasured confounding introduces spatial structure into the residuals, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual: one can reduce bias by fitting a spatial model only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals are independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeated games was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II, Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play that apply to selecting the best forecaster.

James Hannan was born in Holyoke, Massachusetts on September 14, 1922. He attended St. Jerome’s High School and in January 1943 received the Ph.B. from St. Michael’s College in Colchester, Vermont. Jim enlisted in the US Army Air Force to train and serve as a meteorologist. This took him to army airbases in China by the close of the war. Following discharge from the army, Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To prepare for doctoral work in statistics at the University of North Carolina that fall, Jim went to the University of Michigan in the summer of 1947. The routine admissions’ physical revealed a spot on the lung and the possibility of tuberculosis. This caused Jim to stay at Ann Arbor through the fall of 1947 and then at a Veterans Administration Hospital in Framingham, Massachusetts to have his condition followed more closely. He was discharged from the hospital in the spring and started his study at Chapel Hill in the fall of 1948. There he began research in compound decision theory under Herbert Robbins. Feeling the need for teaching experience, Jim left Chapel Hill after two years and short of thesis to take a three year appointment as an instructor at Catholic University in Washington, DC. When told that renewal was not coming, Jim felt pressure to finish his degree. His 1953 UNC thesis contains results in compound decision theory, a density central limit theorem for the generalized binomial and exact and asymptotic distributions associated with a Kolmogorov statistic. He was encouraged to apply to the Department of Mathematics at Michigan State University and came as assistant professor in the fall of 1953. In the next few years, he accomplished his work on repeated games. The significance of the work was rediscovered by the on-line learning communities in computer science in the 1990s and the term Hannan consistency was coined. His retirement came in 2002 after a long career that included major contributions to compound and empirical Bayes decision theory and other areas. He and his colleague Václav Fabian co-authored Introduction to Probability and Mathematical Statistics (Wiley 1985).

A Hannan strategy is a strategy for the repeated play of a game that at each stage i plays a smoothed version of a component Bayes rule versus the empirical distribution Gi-1 of opponent’s past plays. [Play against the unsmoothed version is often called (one-sided) fictitious play.] As in compound decision theory, performance is measured in terms of modified regret, that is, excess of average risk across stages i=1, …, n over the component game Bayes envelope R evaluated at Gn. Hannan, James F., Approximation to Bayes Risk in Repeated Play, Contributions to the Theory of Games 3 97–139, Princeton University Press, is a paper rich with bounds on modified regrets. A Hannan consistent strategy is one where limsup (modified regret) is not greater than zero. In the 1990s, greater recognition of Hannan’s work began to emerge; the term Hannan consistency may have first appeared in Hart and Mas-Colell [J. Econom. Theory 98 (2001) 26–54].

Early on, only his students and a few others were aware of the specifics of his findings. The failure of others to recognize the specific results in the 1957 paper may be due to the cryptic writing style and notation of the author. The strategy for selecting forecasters in Foster and Vohra [8] [Operations Research 41 (1993) 704–709] is an unrecognized Hannan-strategy as is the strategy in Feder et al. [7] [IEEE Trans. Inform. Theory 38 (1992) 1258–1270]. Gina Kolata’s New York Times article, “Pity the Scientist who Discovers the Discovered” (February 5, 2006) uses the original Hannan discoveries as an example, although referring to him as a “statistician named James Hanna.”

In May 1998, the Department of Statistics and Probability hosted a Research Meeting in Mathematical Statistics in Honor of Professor James Hannan. Many came to honor Jim; the speakers included Václav Fabian, Stephen Vardeman, Suman Majumdar, Richard Dudley, Yoav Freund, Dean Foster, Rafail Khasminskii, Herman Chernoff, Michael Woodroofe, Somnath Datta, Anton Schick and Valentin Petrov.

Jim was ever generous in giving help to students. He enjoyed improving results and was very reluctant to submit research results until much effort was made to improve them. Jim directed or co-directed the doctoral research of twenty students: William Harkness (1958), Shashikala Sukatme (1960), John Van Ryzin (1964), Dennis Gilliland (1966), David Macky (1966), Richard Fox (1968), Allen Oaten (1969), Jin Huang (1970), Vyagherswarudu Susarla (1970), Benito Yu (1971), Radhey Singh (1974), Yoshiko Nogami (1975), Stephen Vardeman (1975), Somnath Datta (1988), Jagadish Gogate (1989), Chitra Gunawardena (1989), Mostafa Mashayekhi (1990), Suman Majumdar (1992), Jin Zhu (1992) and Zhihui Liu (1997). Most pursued academic careers and some ended up at research universities including Pennsylvania State, Columbia, Michigan State, UC-Santa Barbara, Guelph, SUNY-Binghamton, Iowa State, Louisville, Nebraska-Lincoln and Connecticut-Stamford.

It was in the Army in 1944 that Jim read his first statistics book. It was War Department Education Manual EM 327, An Introduction to Statistical Analysis, by C. H. Richardson, Professor of Mathematics, Bucknell University, published by United States Armed Forces Institute, Madison, Wisconsin (CQ).