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Authentication of handwritten signatures is becoming increasingly important. With a rapid increase in the number of people who access Tablet PCs and PDAs, online signature verification is one of the most promising techniques for signature verification. This paper proposes a new algorithm that performs a Monte Carlo based Bayesian scheme for online signature verification. The new algorithm consists of a learning phase and a testing phase. In the learning phase, semi-parametric models are trained using the Markov Chain Monte Carlo (MCMC) technique to draw posterior samples of the parameters involved. In the testing phase, these samples are used to evaluate the probability that a signature is genuine. The proposed algorithm achieved an EER of 1.2% against the MCYT signature corpus where random forgeries are used for learning and skilled forgeries are used for evaluation. An experimental result is also reported with skilled forgery data for learning.