I'm training a Hidden Markov Model using EM, and want to get some estimation of how "certain" I can be about the learned parameters (i.e- the estimated transition, emission, and prior probabilities). In general, different initial conditions result in different parameters, but in many of the cases the different parameters have similar likelihood.
I'm looking for some way to probe the likelihood terrain to get an estimate of the number of local maximas, in-order to get a better idea about the different results I might get. (Running the algorithm takes quite a long time so I can't run it enough times to do a "naive" sensitivity analysis) Any standard methods to do so?