Just following up on this! I was wondering if you had any chance to take a look at the data? I have used the artificial data with x_0 = F(x_1 - x_2 -dp) +C model, and the results are to some degree close to the underlying numbers of F, but overestimate dp and C (although the large posterior range includes the underlying distribution of dp and C). In addition, I still cannot make the argument which justifies calculating the probability of P(C,F, dp, x_0 | x_1, x_2) instead of P(C,F, dp | x_0, x_1, x_2) which has an actual physical meaning.