Scene 1

A Quick Tour of Maximum-Likelihood Estimation

Scene 2

A tool for understanding where our observations may have come from

Scene 3

“Given the data, where did they come from?”

Scene 4

Scene 5

S  is a set of parameters that describe the parent distribution from which  D  is most likely to have come.

The mean      Some measure of spread, say      The kurtosis (skew)

Scene 6

…where do we set the       so that the likelihood                  is maximized?

Scene 7

Analytically: Usually not so easy (solve y = f(x) for x) Computationally: OK most of the time

Scene 8

Brute-force: Work within the hypercube of volume

Scene 9

L := + inf S_l  :=  0   For  s  in S1 x S2 x S3  do:      l := Likelihood(S, D);       if (l < L) then:            L = l;             s _l  = s; Return L,  s_l         # ML and location

Scene 10

There may be more than one choice of S that maximizes L     | S_i | may be large    Heuristics such as assuming the parent distribution is of a certain type may quickly lead to the wrong answer   “The parent distribution is obviously binomial”  “That 5% event will  never  happen. As a result, we make a  Gaussianity  assumption.”

A Quick Tour of Maximum-Likelihood Estimation

Scene 1 (0s)

Scene 2 (6s)

Scene 3 (34s)

Scene 4 (1m 4s)

Scene 5 (1m 21s)

Scene 6 (1m 39s)

Scene 7 (2m 19s)

Scene 8 (2m 42s)

Scene 9 (3m 14s)

Scene 10 (4m 0s)

Scene 11 (4m 47s)