I would like to know how many degrees of freedom are in this model, and whether it the following makes sense. I have a set of parameters ($\theta_i$) that I constrain to have a mean of one ($\bar\theta_i = 1$ & $\theta_i > 0$). I impose this constraint by estimating a set of separate parameters $x_i$ with ($x_i > 0$) where
$$\theta_i = \frac{x_i}{\bar x}$$
The issue I have run into using this method is I am doing a Bayesian analysis and my a priori belief is on $\theta_i$ but I am estimating $x_i$.
I would like to know what degrees of freedom are in this model, and if someone has a better way of dealing with the constraints assumed with this model?