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JoshuaFox comments on Open thread, May 17-31 2013 - Less Wrong Discussion
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What do people mean by this sort of probability estimate, this one from Angelina Jolie's NYTimes article? "My doctors estimated that I had an 87 percent risk of breast cancer and a 50 percent risk of ovarian cancer, although the risk is different in the case of each woman" (Italics added.)
Do they mean:
Often, if you ask someone for the probability (or frequency) of some outcome based on their experience with a given reference class, they refuse to give a number, likewise saying that "each case is different." In these cases, a fourth reason is possible, namely that they are too lazy to do the estimation.
I understand that not everyone is a Bayesian black-belt, but I am trying to figure out what implicity assumption motivates people to talk this way.
I assumed it was just a way of saying different women fall into different reference classes for the purposes of estimating breast cancer risk (e.g. an alcoholic woman with a positive BRCA1 test result and a vitamin D deficiency vs. a teetotaller with no harmful BRCA mutations and no vitamin deficiencies).
Thanks, I think that's it. She means "medical science has given us more detailed results than just a blanket probability across all female humans. Using various sorts of information, doctors can give each woman a more refined probability estimate."
There is no implicit assumption. She was apparently tested for BRCA1 based on family history, and was found positive. The correlation between BRCA1 and those cancers yields a certain percentage of risk, a calculation into which family history might also account. She links to here: http://cancer.stanford.edu/information/geneticsAndCancer/types/herbocs.html
Your third option is correct - although both effort, will and resources to acquire genetic testing are required.
Yes, you got it. She's saying "If you go to your doctor and do some tests, you can get an estimate targeted at you."
Who's they? You are reading a text written by Angelina Jolie for a general audience. She has to make certain that no woman reader who reads the story comes away with thinking that she also has a 87 percent risk.
What does a Bayesian black-belt do, when the only numbers he has are come frequentist statistics that someone else did?
Thanks, satt and zaine answered it.
Introspecting a bit, I realize that my question was motivated not sy Angelina so much as by various refusals I have encountered to give a probability/frequency estimate, even when people are well-positioned to give one.
I think it is often motivated by a tendency to withhold information in order to maintain power in human interaction; but in many cases its the first and second options above.