Everything Is Predictable

That’s what Bayesian statistics gives the scientist; a vehicle for scepticism, a way to say “I don’t believe this theory.”

Imagine you do some study to test some hypothesis – we won’t say what it is yet – and you get a p-value of 0.02. How likely is it that your hypothesis is true? It’s an annoying fact that a large number of people who definitely should know better would say that the probability is 98 per cent. The chance of seeing those results by chance is one in fi

Again, the most common error was that they assumed a p-value gave the probability that the results were due to chance. This is (as we’ve been discussing for quite some time now) completely backwards. What p-values tell you is how likely you are to see that data, given a hypothesis.

What is the chance of seeing this result, given some hypothesis? If you’ve ever read any stories about science in the media, you’ll probably recognise the phrase ‘statistical significance’. You may also have come across ‘p-values’. A p-value is the likelihood of seeing results at least as extreme as those you’ve seen, given the null hypothesis, whi

But what does that mean? Can I say that bigfoot people are cleverer, or not? What Fisher did was suggest that we should choose some arbitrary level at which we say ‘OK, it’s pretty unlikely that we’d see results this extreme given the null hypothesis, so I’m going to behave as though it’s a real effect.’ Fisher himself said that a p-value of 0.05 –

‘Necessarily,’ wrote David Howie, a historian of statistics, ‘these inferences were tentative. They were advanced not with certainty but with degrees of confidence that were updated or modified to account for new information.’95 That is: they were done in a Bayesian fashion. Each time Jeffreys got new information, he updated his prior confidence in

His insight in probability theory was that probabilities are beliefs; our beliefs, if we act on them, are themselves a kind of bet. As Ramsey put it: ‘All our lives, we are in a sense betting. Whenever we go to the station, we are betting that a train will really run, and if we had not a sufficient degree of belief in this, we should decline the be

Jeffreys himself wrote: ‘[E]very scientific advance involves a transition from complete ignorance, through a stage of partial knowledge based on evidence becoming gradually more conclusive, to the stage of practical certainty.’ The uncertain parts of science, he said, are ‘the most interesting part’.96

No] testimony is sufficient to establish a miracle,’ wrote Hume, ‘unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish.’