I have a very general question. As we all know, in Bayesian Inference, we introduce several hyper-parameters to define a prior PDF, together with the likelihood function, we can obtain a posterior PDF from which we can obtain a Maximum-A-posterior(MAP) solution. Once those hyper-parameters are determined, we can obtain the MAP solution.
And we can use Expectation Maximization (EM) to calculate those hyper-parameters. My question is what if some of the hyper-parameters have constraints?
To be more specific, we have $$N$$ hyper-parameters in total, where we denoted as $$\Phi\,=\,{\phi_1,\phi_2,...,\phi_N}$$, and we know the first $$K$$ parameters should be less than a pre-given value $$\theta$$,i.e., $$\phi_i<\theta, i=1,2,...K$$.
Any idea?