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After a couple of days of fairly intensive discussion the news inevitably moved on to other topics, but a fairly clear message had been sent to NICE that the media will rapidly pick up on any divergence from the advice of the Department of Health.

Some people may find all the other interpretations and definitions of probability are somewhat unintuitive: surely the probability of something happening is not really a "degree of belief", but something objective about the world that would be the same even if there were no human (or alien) beings around to believe it?

In Why coincidences happen we saw how the chance of a rare event occurring to someone, somewhere, depended on the number of opportunities for it to occur.

Probability theory was one of the last major areas of mathematics to be developed; its beginnings are usually dated to correspondence between the mathematicians Fermat and Pascal in the 1650's concerning some interesting problems that arose from gambling.

When we experience a surprising event and wonder about the likelihood of such a coincidence, we may be able to use probability theory to work out the chance of it happening. And whether the coincidence happens to us or to someone else, we need to take into account how many opportunities there are for it to happen.

The frequency interpretation of probability is fairly self explanatory, in that it defines a probability as a limiting frequency. If we throw a (fair) die often enough, then we will eventually find that each number comes up about a sixth of the total time. The longer we continue to throw the die, the nearer the result will come to the ideal value of 1/6 for each number. The probability of an event is then defined by the relative frequency, as the throws continue to an idealized infinity.

We have seen in The logical view: probability as objective degree of belief that "logical" probability, defined as a degree of belief which it is rational and objective to hold given the available evidence, can give rise to some contradictory results. However, in the 1920s Frank Ramsey in Cambridge [1] and Bruno de Finetti in Italy [2] independently proposed a radically different interpretation of probability which avoids these paradoxes by asserting that probability is a subjective degree of belief.

References

The view of probability as an objective degree of belief was developed in the early 20th century by people such as Harold Jeffreys and the the young John Maynard Keynes [1], and was later adopted by the influential philosopher of science, Rudolf Carnap [2]. This view is not widely held these days, either by statisticians or philosophers, though there seems to be something of recent revival (see for example Williamson 2005 [3].

References