Estimation of the passage time distribution on a graph via the EM algorithm

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

EM algorithm

maximum likelihood

first-passage percolation

phase-type dsitribution

Mathematical statistics

Matematisk statistik

Mathematical Statistics

matematisk statistik

Publication and Content Type

pop (subject category)

rap (subject category)