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A method for estimating time delays between signals that are irregularly sampled is presented. The approach is based on postulating a latent variable model encoding the assumption of slow variability of the underlying source signal. The posterior distribution of the delay is obtained partly by exact marginalisation computable by a specific type of Kalman filter and partly by Markov chain Monte Carlo. Experiments with artificial data show the effectiveness of the proposed approach while results with real-world gravitational lens data provide the main motivation for this work.