I came across the concept of closed-form analytical solution while learning MCMC and got a bit confused. At this point, my understanding is that the problem does not have closed-form solution if it can not be expressed by explict mathmatical formula with specific parameters found through certain optimization of loss function.

If my understanding is correct, I guess methods like EM and sampling method (MCMC) are without closed-form analytical solution.

Please correct me if I am wrong.