# Estimating latent mean and variance for a Gaussian

I have a latent Gaussian model with unknown parameters $$\mu$$ and $$\sigma^2$$. I can estimate these parameters using MLE and an EM-ish algorithm. However the solution is not stable; I end up in local maxima depending on the order with which I withhold data during EM. (Though the solutions are close to each other.)

So, i can run the algorithm 50 times and get 50 different estimates for $$\mu$$ and $$\sigma^2$$. I think the best estimate for the true value of $$\mu$$ is the average over all of these estimates. However I am unsure whether the best value for $$\sigma^2$$ is simply the average of all estimates for $$\sigma^2$$. Is that correct?

Edit: Now that I'm thinking about it, perhaps averaging the parameters is a bad idea, because it doesn't actually represent a maximum, and I should just choose the $$(\mu, \sigma^2)$$ that is the max of the max.

• It might be worth trying the median parameter values, rather than the average parameter values. – James Phillips Mar 19 at 23:41