A frequent challenge when using graphical models in applications is that the sample size is limited relative to the number of parameters to be learned. Our motivation stems from applications where one has external data, in the form of networks between variables, that provides valuable...

This paper surveys some of the recent literature on inference in partially identified models. After reviewing some basic concepts, including the definition of a partially identified model and the identified set, we turn our attention to the construction of confidence regions in partially...

This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so...