: In this thesis, Markov chain Monte carlo (MCMC) for Bayesian inference for non – Gaussian Ornstein – Uhlenbeck (OU) stochastic volatility processes is developed. The aim of this thesis is to provide a general methodology for performing Bayesian inference for a wide hit finite rate and the corresponding jump size are generated from an exponential distribution. The resulting OU process has a gamma marginal distribution and is known as shot noise process. A latent structure model formulation based on marked point measure is proposed and suitable MCMC algorithms for Bayesian inference, using data augmentation is developed. Two different MCMC algorithm are constructed and by simulation study on S am share index data, it will be shown that the performance of the first, based on standard hierarchical parameterization for the model, is not robust. However, the second algorithm is considerably more robust and produces satisfactorily mixing chain