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Network tomography, inferring internal network behavior based on the "external" end-to-end network measurements, is of particular interest when the network itself can not cooperate in characterizing its own behavior. In particular, it is impractical to directly measure packet losses or delays at every router. On the other hand, measuring end-to-end (from sources to receivers) losses is relatively easy. In this paper, the problems of characterizing links behavior in a network is formulated as Bayesian inference problems and develop several Markov chain Monte Carlo (MCMC) algorithms to solve them. The proposed link loss algorithms are then applied to data generated by the network simulator (NS2) software, and obtain good agreements between the theoretical results and the actual measurements.