Signature Verification Using Bayesian Model and MCMC Method

Bayesian model and Markov chain Monte Carlo method were used to verify a sample of signature in Iran. In the Bayesian model, parameters were considered as quantities whose variations can be described by the prior distributions. A sample is taken from a population indexed by the parameters and prior distributions were updated and then posterior distribution was calculated. Markov chain Monte Carlo method used to generate samples from the posterior distribution. The goals were (a) to define parameters of Bayesian model, obtain log-likelihood and propose the prior distribution and the posterior distribution (b) to introduce appropriate Markov chain Monte Carlo to explore the posterior (c) to propose a forgery index to determine correctness of this signature. In this method, off-line signature was representing via its curvature, and smoothness of the signature curve seems to be a necessity. In order to explore the variation in the signature samples, we used time warping functions as a random effect in the model. The performance of the proposed model was presented through a simulation example of an Iranian signature. For this signature sample, required times for preprocessing stages and signature verification stage were about 15 and 2 minutes and Type I and Type II error rate were 0.06 and 0.16 respectively. So this method seems to be appropriate to verify Iranian signatures.