Inference in a Partially Observed Percolation Process

Abstract: In this licentiate thesis, inference in a partially oberved percolation process living on a graph, is considered. Each edge of the graph is declared open with probability $ heta$ and closed with probability $1- heta$ independently of the states of all other edges. The inference problem is to draw inference about $ heta$ based on the information on whether or not particular pairs of vertices are connected by open paths. Consistency results under certain conditions on the graph are given for both a Bayesian and a frequentist approach to the inference problem. Moreover, a simulation study is presented which in addition to illustrating the consistency results, also indicates that the consistency results might hold for percolation processes on more general graphs.