Updating probabilities with data and moments
But what is the probability if she has a positive mammogram?
Studies show that if a woman does not have cancer, a mammogram will incorrectly claim that she does only about 10 percent of the time.
Laplace came to view probability as a waypoint between ignorance and knowledge.
The essay, the key to what we now know as Bayes's Theorem, concerned how we should adjust probabilities when we encounter new data.One classic example of this is the presence of breast cancer among women in their forties.The chance that a woman will develop breast cancer in her forties is fortunately quite low — about 1.4 percent.However, each day that he survives and the sun rises again, his confidence increases that it is a permanent feature of nature.
Gradually, through this purely statistical form of inference, the probability he assigns to his prediction that the sun will rise again tomorrow approaches (although never exactly reaches) 100 percent.The argument made by Bayes and Price is not that the world is intrinsically probabilistic or uncertain Bayes was a believer in divine perfection; he was also an advocate of Isaac Newton's work, which had seemed to suggest that nature follows regular and predictable laws.