ABSTRACT
Although the term “Bayesian inference” may not be common in everyday language, many situations in our daily lives can be described as Bayesian inference problems. Generally speaking, we face such a problem when we want to update our probability estimate for some hypothesis in the light of new evidence, for instance the hypothesis that a soccer team will win the game, given that it is behind at half time, or the hypothesis that a student at a university will pass the next exam, given that she failed before. Or imagine the following situation: You have heard that 40-year-old women have a relatively low probability of developing breast cancer within the next 10 years; about 1%. Therefore, you are not particularly worried when an acquaintance of yours who is in this age group participates in a routine screening for breast cancer. However, the x-ray picture of her breast shows a suspicious lesion that has to be followed up. You are now probably much more worried about your friend given this positive test result, because the hypothesis that she has breast cancer seems clearly more likely. In other words, you have updated your prior probability estimate for the hypothesis (the base rate for breast cancer in this age group, here 1%) in the light of the new evidence (the positive test result) to a somewhat higher posterior probability estimate for the hypothesis (the probability of breast cancer in this age group, given a positive test result).
