Kundu and Gupta proposed to use the importance sampling
method to compute the Bayesian estimation of the unknown parameters of the Marshall-Olkin
bivariate Weibull distribution. However, we find that the performance of the importance
sampling method becomes worse as the sample size gets larger. In this paper, we introduce
latent variables to simplify the likelihood function, and use MCMC algorithm to estimate
the unknown parameters. Numerical simulations are carried out to assess the performance
of the proposed method by comparing with the maximum likelihood estimation, and we find
that the Bayesian estimates perform better even for the case of small sample size. A real
data is also analyzed for illustrative purpose.