I am trying to find a reference and/or guidance for fitting a mixture model to a population of data within an MCMC framwork where the global mean is constrained to a particular value, in this case 1. That is, E(X) = 1 where f(X) = \sum \omega_i f_i(x| \theta_i) and the standard constraint \sum \omega_i = 1 where, ideally, f_i are log normal distributions.

Any help will be appreciated.