Estimation of the passage time distribution on a graph via the EM algorithm
2010 (English)Report (Other (popular science, discussion, etc.))
e propose EM algorithms to estimate the passage time distribution on a graph. Data is obtained by observing a flow only at the nodes -- what happens on the edges is unknown. Therefore the sample of passage times, i.e. the times it takes for the flow to stream between two neighbors, consists of right censored and uncensored observations where it sometimes is unknown which is which. For discrete passage time distributions, we show that the maximum likelihood (ML) estimate is strongly consistent under certain weak conditions. We also show that the EM algorithm converges to the ML estimate if the sample size is sufficiently large and the starting value is sufficiently close to the true parameter. In a special case we show that it always converges. In the continuous case, we propose an EM algorithm for fitting phase-type distributions to data.
Place, publisher, year, edition, pages
2010. , 61 p.
Research report in mathematical statistics, ISSN 1653-0829 ; 1
EM algorithm, maximum likelihood, first-passage percolation, phase-type dsitribution
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-33760OAI: oai:DiVA.org:umu-33760DiVA: diva2:317878