Design and Analysis of Experiments in Networks: Reducing Bias from Interference

Estimating the effects of interventions in networks is complicated due to interference, such that the outcomes for one experimental unit may depend on the treatment assignments of other units. Familiar statistical formalism, experimental designs, and analysis methods assume the absence of this interference, and result in biased estimates of causal effects when it exists. While some assumptions can lead to unbiased estimates, these assumptions are generally unrealistic in the context of a network and often amount to assuming away the interference. In this work, we evaluate methods for designing and analyzing randomized experiments under minimal, realistic assumptions compatible with broad interference, where the aim is to reduce bias and possibly overall error in estimates of average effects of a global treatment. In design, we consider the ability to perform random assignment to treatments that is correlated in the network, such as through graph cluster randomization. In analysis, we consider incorporating information about the treatment assignment of network neighbors. We prove sufficient conditions for bias reduction through both design and analysis in the presence of potentially global interference; these conditions also give lower bounds on treatment effects. Through simulations of the entire process of experimentation in networks, we measure the performance of these methods under varied network structure and varied social behaviors, finding substantial bias reductions and, despite a bias–variance tradeoff, error reductions. These improvements are largest for networks with more clustering and data generating processes with both stronger direct effects of the treatment and stronger interactions between units.

Topological and pointwise upper Kuratowski limits of a sequence of lower quasi-continuous multifunctions

In this paper we deal with a connection between the upper Kuratowski limit of a sequence of graphs of multifunctions and the upper Kuratowski limit of a sequence of their values. Namely, we will study under which conditions for a graph cluster point (x,y) ? X x Y of a sequence {GrFn:n ? ?} of graphs of lower quasi-continuous multifunctions, y is a vertical cluster point of the sequence {Fn(x): n ? ?} of values of given multifunctions. The existence of a selection being quasi-continuous on a dense open set (a dense G?-set) for the topological (pointwise) upper Kuratowski limit is established.