How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule?
I learn best visually, and I found these graph. 1. Does it furnish intuition on Theorem 2.3.5 below?
- E.g. Is the Likelihood Ratio always graphically left of Posterior and Prior? If so, why?
This can also be pictorially represented – the graph below shows the new posterior belief for a certain treatment has a reduced relative risk when the prior belief is combined with the data collected.
Blitzstein. Introduction to Probability (2019 2 ed). p 53.
Here are more details and better pictures of Theorem 2.3.5.