# Inference in a Partially Observed Percolation Process Licentiatavhandling, 2010

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

Bayesian inference

Percolation

frequentistic inference

Monte Carlo Expectation Maximization

consistency

Pascal
Opponent: Eric Järpe

## Författare

#### Oscar Hammar

Chalmers, Matematiska vetenskaper

Göteborgs universitet

#### Ämneskategorier

Sannolikhetsteori och statistik

Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University: 2010:44

Pascal

Opponent: Eric Järpe