I am a newbie in this area so I hope someone could explain the following problem to me in plain English.
Assume I want to use MAP to estimate some parameters on the basis of some observations. I know the method of computing MAP is: $$ \theta(x) = {\rm argmax} \ f(X|\theta) g(\theta) $$
where $g$ is the prior. However, I cannot find any answers online on how to compute this using a real world example. So here is my proposed question:
Assume you asked 100 people of who they are going to vote for in an election (out of 2 candidates A and B), and assume the end result is 60% of them saying they will vote for A. How do you estimate the result of an election using MAP if:
- candidate A is known to have a popularity of 40% and candidate B 60% (assume this to be the prior distribution)
- the popularity is unknown.
I also looked at this answer but I'm still confused: Example of maximum a posteriori estimation