Grammar
Likelihood - The likelihood for a hypothesis is the probability that you would have observed the data, if that hypothesis were true.
The values can be found by going through each hypothesis in turn, imagining it is true, and asking, “What is the probability of getting the data that I observed?”.
Document Structure
memory of ths sections structure
Logic
Following through this section of the paper in my own words:
- black ball white ball or two black balls sets up the problem
- we pull a black ball
- we create box with prior, likelihood, h and posterior
- priors are our sets of hypotheses
- posterior is h but amended so adds up to 1
- both
Interpretation (of posterior probabilities)
- posterior probabilities are proportional to priors and likelihoods
- a high prior helps a high posterior
- a high likelihood also helps
Bayes Rule
\(x^2\)
- bayes rule from probability theory is probability event given some other event
- bayes rule in bayesian statistics is probability a hypothesis is true given data