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Despite their popularity, conventional propensity score estimators (PSEs) do not take into account uncertainties in propensity scores. This paper develops Bayesian propensity score estimators (BPSEs) to model the joint likelihood of both propensity score and outcome in one step, which naturally incorporates such uncertainties into causal inference. Simulations show that PSEs using estimated propensity scores tend to overestimate variations in the estimates of treatment effects-that is, too often they provide larger than necessary standard errors and lead to overly conservative inference-whereas BPSEs provide correct standard errors for the estimates of treatment effects and valid inference. Compared I am grateful for the comments and suggestions received from Nicholas 151 152 AN with other variance adjustment methods, BPSEs are guaranteed to provide positive standard errors, more reliable in small samples, can be readily employed to draw inference on individual treatment effects, etc. To illustrate the proposed methods, BPSEs are applied to evaluating a job training program. Accompanying software is available on the author's website.

Interest in social network analysis has exploded in the past few years, partly thanks to the advancements in statistical methods and computing for network analysis. A wide range of the methods for network analysis is already covered by existent R packages. However, no comprehensive packages are available to calculate group centrality scores and to identify key players (i.e., those players who constitute the most central group) in a network. These functionalities are important because, for example, many social and health interventions rely on key players to facilitate the intervention. Identifying key players is challenging because players who are individually the most central are not necessarily the most central as a group due to redundancy in their connections. In this paper we develop methods and tools for computing group centrality scores and for identifying key players in social networks. We illustrate the methods using both simulated and empirical examples. The package keyplayer providing the presented methods is available from Comprehensive R Archive Network (CRAN).

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