Notes on Prologue
- non-bayesians say bayesian is one way of doing things
- bayesians say
- bayesian is the right way of doing things
- non-bayesian methods are approximations or an alternative when bayesian too hard to calculate
Notes on Introduction
- we believe all sorts of things and do not believe others
- even though we strictly dont have all information we need to be 100% certain
- statistics is a tool when we cannot be 100% certain
- in bayesian statistics probabilities are in the mind, not in the world
- i.e. when we obtain more information the probabilities in our mind change
- bayesian methods tell us exactly how to update our probabilities when we get new information
Notes on First Examples
- we start with prior probabilities and we update these with data to get posterior probabilities
- Bayes box is a table that helps up calculate posterior probabilities more easily
- we start by choosing values for prior probabilities and assigning to our competing hypotheses
- bayes rule
- bayes box is basically applying bayes rule lots of times, once for each hypothesis
- phone example
- we now get onto important equations