A to Z Bayes - Part 1: The Basics
Let's Experiment
Step 1: Figuring out the hypothesis space
Before we've even seen the data all we could've told is that the dice can have the number of faces as any integer between 2 and infinity. And each such possibile reality is called as a hypothesis (plural - hypotheses). The set of all hypotheses is called as the hypothesis space and we need to figure out which one is the most probable hypothesis among them.
Hypothesis Space and Prior Probabilities of each hypothesis.
For example the prior probability for the hypothesis '10 sided dice' is approx 0.04.
Note that all the heights must sum to 1.
For example the prior probability for the hypothesis '10 sided dice' is approx 0.04.
Note that all the heights must sum to 1.
Since we couldn't have all the infinite integers we chose the last hypothesis as *'any dice with greater than 28 sides'*