CPL - Chalmers Publication Library

# Inference in a Partially Observed Percolation Process

Oscar Hammar (Institutionen för matematiska vetenskaper)
Göteborg : University of Gothenburg, 2010. - 61 s.
[Licentiatavhandling]

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.

Nyckelord: Percolation, Bayesian inference, frequentistic inference, consistency, Markov chain Monte Carlo, Monte Carlo Expectation Maximization

CPL Pubid: 137154

# Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

# Examination

Datum: 2010-11-02
Tid: 10:15
Lokal: Pascal
Opponent: Eric Järpe