Conjugate priors for generalized MaxEnt families

Bayes theorem can be seen as the result of an optimization problem. By slightly altering this optimization problem many generalized Bayes rules can be constructed. In this work we show that a notion of a conjugate prior for non exponential family distributions can be recovered if one uses one of these generalized rules. We prove some theorems concerning this new updating rule before giving a simple example of such a generalized conjugate prior.