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Bayes’ Theorem for Medical Tests
Understanding Bayes’ theorem for medical tests. Interpret results and the combination of more tests
Bayes’ theorem is one of the main theorems in statistics, and one of the most applied formulae in science.
Its importance grew steadily until the middle of the last century. And it is now considered essential in all statistics courses and applied in almost every field of research and not in the industry sector.
At first glance, Bayes’ theorem can seem confusing, and very often hard to grasp, and that’s already in the field of statistics that not easy per se.
However, if we analyse the thought processes leading Bayes to his theorem, we see that these are natural and logical ways of thinking.
The theorem
Bayes theorem is named after the Reverend Thomas Bayes. Around 1740 Bayes performed a thought experiment: he imagined putting his back against a flat, square table, and launching a ball onto the table without knowing where it would land.
Then, he thought of launching a second ball, this time asking his assistant if the ball landed to the left, to the right, in front of, or behind the first ball. Using this system, he was able to narrow the position of the first ball…