Statistics 102H: MLE's (Statistical Inference by S. D. Lilvey

Administrivia

MLE's and where we are in the course

• Regression: practical, most situations (more = stat 202)
• Design: important science (more = biostatistics)
• Math Stat: MLE (more = stat 432, new course)
• If you hark back for the good old days of probability (more = stat 433)

Section 4.1

Key construction

likelihood f_x(theta)

What is the difference? Real question is what is a function?

Principle: maximizing probably better than minimizing

What is large? Bigger than competitors. (I.e. is likelihood = .001 large? Yes, if next best is .000001).

Define max and arg max

Example 1: binomial

• First do it with likelihood
• Notice that there are two parts: the interesting part and the likelihood part again
• If we divided by the likelihood it would be prettier
• So: do log likelihoods
• REDO CALCULATION

Homework

• Read pages 68 - 71 of handout. Read them again! Make sure you understand the notation itself, not just the ideas.