EM and mixture estimation

Following my previous post on optimization and mixtures (here), Nicolas told me that my idea was probably not the most clever one (there). So, we get back to our simple mixture model, In order to describe how EM algorithm works, assume first that both and are perfectly known, and the mixture parameter is the only one we care about. The simple model, with only one parameter that is unknown Here, the likelihood is so that we write the log likelihood as which might not be simple to maximiz..