differences in posterior probabilities between two states that are in transition (Metropolis et al., 1953). This algorithm ensures that states with high probability form the majority of the Markov chain and is mathematically represented as: 

$$(14)$$

If ) ( | ) ( | P Mn+1 D > P Mn D **then accept** Mn+1
 , (14) 

else accept if $P(M_{n+1}\mid D)$$P(M_{n}\mid D)$$\geq\xi$ where $\xi\in$ [0,I] (15)
else reject and randomly generate another model Mn+1
. 

## Experimental Investigation: Modelling Of Hiv

The proposed method is applied to create a model that uses demographic characteristics to estimate the risk of HIV. In the last 20 years, over 60 million people have been infected with HIV (Human immunodeficiency virus), and of those cases, 95% are in developing countries (Lasry et al, 2007). HIV has been identified as the cause of AIDS. 

Early studies on HIV/AIDS focused on the individual characteristics and behaviors in determining HIV risk and Fee and Krieger (1993) refer to this as biomedical individualism. But it has been determined that the study of the distribution of health outcomes and their social determinants is of more importance and this is referred to as social epidemiology (Poundstone et. al., 2004). This study uses individual characteristics as well as social and demographic factors in determining the risk of HIV using rough set models formulated using Bayesian approach and trained using Monte Carlo method. Previously, computational intelligence techniques have been used extensively to analyze HIV and Leke et al (2006, 2006, 2007) used autoencoder network classifiers, inverse neural networks, as well as conventional feed-forward neural networks to estimate HIV 
risk from demographic factors. Although good accuracy was achieved when using the 