In this paper, we present several general policies for deciding when to share probabilistic beliefs between agents for distributed monitoring. In order to evaluate these policies, we have formulated an application in network intrusion detection as a multi-agent monitoring problem. We have evaluated our policies based on packet trace data from a real network. Based on this evaluation, we have demonstrated that our policies can reduce both the delay and communication overhead required to detect network intrusions. Although we have focused on network intrusion detection as an application, we contend that our policies can generally be applied to domains that use a probabilistic model for evaluating hypotheses, and have a method for combining beliefs from multiple agents.