DISCUSSION FOR ASSIGNMENT 3

For data set 1, convergence to what is certainly the global maximum
from three starting points was very rapid, requiring only one or two
interations.  However, when started with mu=0 and sigma=5, convergence
was very slow.  After 30 iterations, the parameters were far from the
MLE.  A longer run finally converged to the same result as the other
runs after over 1400 iterations.  This behaviour apperas to be a
consequence of the distribution when sigma is large being almost
uniform over the circle, which provides little push toward the MLE.

For data set 2, some starting points lead to rapid convergence on what
appears to be the true MLE, at mu=5.18 and sigma=1.577.  Other
starting points moved to around mu=2.01 and sigma=3.2.  However, this
may not be a true local minimum, since the EM algorithm was still
slowly moving, and continued to slowly move even after thousands of
iterations.

For data set 3, the three starting points I chose all converged to
what appears to be the true MLE, at mu-1.488 and sigma=1.505.  Two of
these runs converged in about 20 iterations, but the third run
(started at mu=5 and sigma=0.5) took about 70 iterations to converge.