I have a Bayesian model involving three parameters $\theta\_1$,$\theta\_2$ and $\theta\_3$. Experts think that $\theta\_1 > \theta\_2 > \theta\_3$. So I would like to test the submodel $M\_0$ corresonding to $\theta\_1 > \theta\_2 > \theta\_3$ versus $ M\_1:\{(\theta\_1,\theta\_2,\theta\_3) \not\in M\_0 \}$ regarding to the observations. I see two main options: 

1) run the full model and check the percentage of samples for which $\theta\_1 > \theta\_2 > \theta\_3$. Conclude to significance if its greater than $95\%$.

2) compute the bayes factor for the two models.

Are these two methods valid to you ? Are they equivalent in a certain sense ? One of my point is that it seems to me that there is no standard method to compute Bayes factor from MCMC sample without much trouble and point 1) looks as a good opportunity to me. Nevertheless any hints for bayes factor from MCMC samples (I used R and jags) are welcomed.