How to Find the Lowest Point in a Valley at Night

With more and more complicated models, you have to be very careful about this problem. What we sometimes find is not so much local minima, but what's called a flat spot. And that's where you get out on the likelihood, and there's just not a lot of change in any direction. This is actually a real problem in mixture modelling. That's where random i start values come from. You do one or two thousand different start values. So there'r lots of ways we can deal with that.