The age information strongly changes the likelihood that these symptoms occurred due to Alzheimer disease. In this easily understandable and intuitive example, Alzheimer disease is an event and age is a condition associated with this event. The best example for explaining Bayesian statistics may be diagnostic tests. If we want to calculate the likelihood that one positively tested patient has the disease, one must know different expectations. First, we need to know the accuracy of the testing method. And second, we need to know the occurrence of the disease in the population. If we know that the accuracy of the test is 99% and that the disease appears in 1 out of 10 000 people, we can determine the probability that the positively tested patient is ill. One can intuitively conclude that this probability is 99%. However, this would be a mistake! The likelihood that the positively tested patient really has the disease in this case is less than 1%. ![]() ![]() Namely, the data on disease occurrence in the population, eg, prior probabilities, strongly influence the calculation. In this example, the appearance of disease is the prior probability, and the calculated probability of the illness of a positively tested person is the posterior probability.
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