Inference in a Partially Observed Percolation Process
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 $\theta$ and closed with probability $1-\theta$ independently of the states of all other edges.
The inference problem is to draw inference about $\theta$ 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.
Markov chain Monte Carlo
Monte Carlo Expectation Maximization