  This paper proposes an approach to training rough set models using Bayesian
framework trained using Markov Chain Monte Carlo (MCMC) method. The prior
probabilities are constructed from the prior knowledge that good rough set
models have fewer rules. Markov Chain Monte Carlo sampling is conducted through
sampling in the rough set granule space and Metropolis algorithm is used as an
acceptance criteria. The proposed method is tested to estimate the risk of HIV
given demographic data. The results obtained shows that the proposed approach
is able to achieve an average accuracy of 58% with the accuracy varying up to
66%. In addition the Bayesian rough set give the probabilities of the estimated
HIV status as well as the linguistic rules describing how the demographic
parameters drive the risk of HIV.
