There was a time when most people looked to religion for certainty. Priests were regarded as, if not infallible, at least worthy of special respect. Then we realised that religion did not have all the answers. Many people, when they discovered the reality of uncertainty, turned away from a religion that had promised the opposite. Even if certainty wasn't the official doctrine, many priests still offered it because that's what people wanted.

Where did the seekers of certainty turn when they deserted religion? They turned to science, ignoring the fact that many scientific discoveries had much to do with chance. Science has become the modern benchmark of truth. Scientists know that much of what they do is based on incomplete information. They have to exercise a certain amount of faith and hope when they take decisions. This faith and hope may be based to some extent on professional experience but it remains faith and hope.

Science has in some way become a religion. Scientific dogmas are defended with religious fervour and opponents are spoken of as heretics. Just as it was unacceptable for a priest to entertain any doubt, so it is that society does not want to hear the priests of science utter that inconvenient truth: 'I don't know'. Many scientists do honestly try to present the unpalatable uncertainty of their results but their message is often distorted by politicians and the media, who know that the public does not want subtlety.

Thomas Bayes

Thomas Bayes was a Presbyterian minister who died in 1761. He is famous for his mathematical paper, An essay towards solving a problem in the doctrine of chances, which was published shortly after his death. This essay contained a formula, now known as Bayes' Theorem, which became an important tool for working with conditional probability.

A good example of conditional probability can be found in the context of screening for breast cancer, a subject I have blogged about before. The probability that a woman has breast cancer, given that she has had a positive mammogram, is a conditional probability. The probability of having a positive mammogram, given that the woman has breast cancer, is a different conditional probability. People often confuse these two probabilities but they are, in fact, very different. (The first is about 1 in 10, while the second is around 9 out of 10.)

Similarly, the probability that a person is guilty based on a positive DNA test is not the same as the probability that a guilty person gives a positive DNA test. New drugs are tested in clinical trials. The standard way of evaluating trial results is to test whether a positive result could have been due to the drug. However, the probability of a positive result, given an effective drug, is not the same as the probability of an effective drug, given a positive trial result, which is what we really want to know!

Bayes Theorem helps to convert one conditional probability into the other. However, it is not popular among scientific researchers. First of all, it is more difficult to use than the fashionable methods. But, perhaps more significantly, the Bayes calculation formally recognises the potential for subjectivity, which makes many scientists uncomfortable.

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For more opinion about subjectivity in science have a look at the articles by Robert Matthews in New Scientist and Health & Beyond.

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