STAT 581

Comments to homework set 9

Question 1

The von Mises distribution (and its three-dimensional analogue the Fisher distribution) are useful distributions to describe, e.g., the preferred flight direction of migrating birds, or the magnetic orientation of rocks.

Question 2

This problem can be done using direct likelihood methods, such as the method of scoring in question 3, but the EM-approach is a natural way of attacking it.

Question 3

The method of scoring is closely related to the Newton-Raphson approach, with the difference that the latter uses observed instead of expected information. There are simulation studies indicating that the Fisher scoring method is better, in the sense of converging faster. One-step Newton-Raphson estimators are also first order efficient.