Re:Statisticians Find They Can Agree: It’s Time to Stop Misu...
by btilly on Tuesday March 08, 2016 @01:21PM
(#11247247)
If you include into the priors information about the likelihood of the next child being born, you will indeed get different absolute probabilities. But you will not get different relative probabilities unless your available priors create a correlation between birth order and the likelihood of different genders for the next child if it comes. And therefore the probability of having the next birth cancels out of Bayes' formula and you wind up with the exact same conclusions from the observed data.
You certainly DON'T wind up with anything like the factor of 8 difference that frequentist techniques will see!
For Bayes' theorem, we need a theory of how the data is produced given the parameter of interest. Bill and Lorena's plans certainly influence what data I observe: in scenario two, I can never observe the data BBBBGGG, but in scenario one, I can. My point is that your first category is not "exact statements about the likelihood of 7 births in a row being mmmmmmmf", it is "exact statements about the likelihood of observing mmmmmmf", which is, in fact, quite different, if you admit the possibility of Bill and Lorena having particular childbearing plans.