Good evening,
I have a situation where \sum_{j=1}^N t_j = a. Here the t_j's are parameters of interest and a is also a parameter of interest. I have three questions:

Can I have the constraint \sum_{j=1}^N t_j = a even if the t_j's are parameters and a is a parameter? The prior for each t_j is Gamma(1,1) and a's prior is Gamma(1,2).

If the answer to (1) is true, then how exactly is this accomplished?

Assuming (1) and (2), is there a reference (i.e. journal article, book, etc.) that you can point me to? I searched for articles related to this topic and I found â€śSpherical Hamiltonian Monte Carlo for Constrained Target Distributionsâ€ť by Lan, Zhou, and Shahbaba (2014; Proceedings of Machine Learning Research). The No UTurn paper by Hoffman and Gelman mentions constraints briefly as does Bayesian Data Analysis by Gelman. My goal is to understand this aspect of HMC in detail.
Thank you for your time.