Chapter 2: FAQs 61
What is Maximum Likelihood
Estimation?
Short Answer
Maximum Likelihood Estimation (MLE) is a statisti-
cal technique for estimating parameters in a proba-
bility distribution. We choose parameters that maxi-
mize theaprioriprobability of the final outcome actu-
ally happening.
Example
You have three hats containing normally distributed
random numbers. One hat’s numbers have mean of zero
and standard deviation 0.1. This is hat A. Another hat’s
numbers have mean of zero and standard deviation 1.
This is hat B. The final hat’s numbers have mean of
zero and standard deviation 10. This is hat C. You don’t
know which hat is which.
You pick a number out of one hat, it is−2.6. Which hat
do you think it came from? MLE can help you answer
this question.
Long Answer
A large part of statistical modelling concerns finding
model parameters. One popular way of doing this is
Maximum Likelihood Estimation.
The method is easily explained by a very simple ex-
ample. You are attending a maths conference. You
arrive by train at the city hosting the event. You take
a taxi from the train station to the conference venue.
The taxi number is 20,922. How many taxis are there in
the city?
This is a parameter estimation problem. Getting into
a specific taxi is a probabilistic event. Estimating the
