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"... We consider several statistical approaches to binary classification and multiple hypothesis testing problems. Situations in which a binary choice must be made are common in science. Usually, there is uncertainty involved in making the choice and a great number of statistical techniques have been put ..."

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We consider several statistical approaches to binary classification and multiple hypothesis testing problems. Situations in which a binary choice must be made are common in science. Usually, there is uncertainty involved in making the choice and a great number of statistical techniques have been put forth to help researchers deal with this uncertainty in separating signal from noise in reasonable ways. For example, in genetic studies, one may want to identify genes that affect a certain biological process from among a larger set of genes. In such examples, costs are attached to making incorrect choices and many choices must be made at the same time. Reasonable ways of modeling the cost structure and choosing the appropriate criteria for evaluating the performance of statistical techniques are needed. The following three chapters have proposals of some Bayesian methods for these issues. In the first chapter, we focus on an empirical Bayes approach to a popular binary classification problem formulation. In this framework, observations are treated as independent draws from a hierarchical model with a mixture prior distribution. The mixture prior combines prior distributions for the ``noise' ' and for the ``signal' ' observations. In the literature, parametric assumptions are usually made about the prior distribution from which the ``signal' ' observations come. We suggest a Bayes classification rule which minimizes the

### Under consideration for publication in Network Science 1 Mixed-Membership of Experts Stochastic

, 2015

"... Social network analysis is the study of how links between a set of actors are formed. Typically, it is believed that links are formed in a structured manner, which may be due to, for example, political or material incentives, and which often may not be directly observable. The stochastic blockmodel ..."

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Social network analysis is the study of how links between a set of actors are formed. Typically, it is believed that links are formed in a structured manner, which may be due to, for example, political or material incentives, and which often may not be directly observable. The stochastic blockmodel represents this structure using latent groups which exhibit different connective properties, so that con-ditional on the group membership of two actors, the probability of a link being formed between them is represented by a connectivity matrix. The mixed membership stochastic blockmodel (MMSBM) extends this model to allow actors membership to different groups, depending on the interaction in question, providing further flexibility. Attribute information can also play an important role in explaining network formation. Network models that do not explicitly incorporate covariate information require the analyst to compare fitted network models to additional attributes in a post-hoc manner. We introduce the mixed membership of experts stochastic blockmodel, an extension to the MMSBM that incorporates covariate actor information into the existing model. The method is illustrated with application to the Lazega Lawyers dataset. Model and variable selection methods are also discussed.