Why is the Fisher information matrix so important, and why do we need to calculate it?
The Fisher Information matrix is extremely important. It tells how much information one (input) parameter carries about another (output) value. So if you had a complete model of human physiology, you could use the Fisher information to tell how knowledge about 1) eating habits, 2) exercise habits, 3) sleep time, and 4) lipstick color affected a person's body mass. You'd find that the entries corresponding to the first three variables would be large but that the last would be zero.