by Susana » Tue Apr 24, 2012 7:09 pm
Thanks bkjecn for your reply!
My problem is that I'm trying to compute the "highest" mode (the global maximum). For that purpose, I repeatedly apply an optimizer to the likelihood function with initial conditions found by sampling 50-100 times from a uniform distribution (overdispersed with respect to the prior). I obtain the mode for each parameter and the corresponding value for the posterior density evaluated at the mode. Then, ideally I would compare the posterior densities and choose the mode corresponding to the highest one.
However, here is where my problem arises; I was expecting to obtain the same value for the posterior density when evaluating it at each of the parameters' mode (in one simulation). Instead, when evaluating the mode at the posterior density, I get that for some parameters it is higher than for others. Why didn't the optimizer (in the cases with lower density) chose some other value to attain the higher posterior density? Could it be because my algorithm is converging before finding the global maximum? What would it be a good method to choose the "best" mode? Thank you very much for your time!