People of Science with Brian Cox - Sir David Spiegelhalter
Transcript
- David: People of Science, take one.
- Brian: So David, you chose Thomas Bayes and Ronald Fisher.
- What do both these people of science mean to you?
- David: A huge amount.
- These are two huge figures in the history of statistical inference, and I teach both of them.
- Bayes, I was introduced to those ideas when I first was a student studying Mathematics and I found them absolutely riveting.
- And this idea that we could apply probabilities to facts, I’ve stuck with my whole life.
- I’ve been a Bayesian statistician, as it’s known, in my research work, and I teach both of them.
- But over that time also I’ve come to develop a huge respect for Fisher.
- He was a genius mathematician.
- Just about the entire scientific literature, or anyone who does a statistical check of a hypothesis
- you use this idea of a p-value
- Ronald Fisher invented the p-value.
- So that’s when we say, in particle physics we’ll say discovered the Higgs boson
- it’s a 5 sigma discovery, and that’s Fisher.
- David: That’s Fisher.
- Brian: Now Bayes, we’re going back a long time to Bayes.
- David: Yeah. Bayes was extraordinary, he was a nonconformist minister in Tunbridge Wells
- and he was an amateur mathematician, died in 1761.
- But then afterwards, in his papers was found a manuscript
- that then was published a couple of years later by the Royal Society.
- And this manuscript has become enormously famous and hugely influential.
- Probability around Bayes’ time was used in sort of two different ways.
- It was used in the idea of chance; future events, pure unpredictability.
- But it was also used for when you’re uncertain, say, about whether someone was guilty of a crime or not.
- In other words, uncertainty about a fact.
- Bayes put these two together and to assign probability to those is still deeply controversial.
- Fisher loathed the idea.
- Brian: So whilst Bayes seems like a relatively nice man, preaching in Tunbridge Wells, Fisher’s a different kettle of fish.
- David: Yes, what you might call a slightly ‘difficult personality’.
- He could be quite kind and generous to his students
- but if there was any suggestion that anyone would threaten him or question him, he became very aggressive indeed.
- He had a foul temper, and he just fell out with people again and again, for their whole lives.
- Brian: Well, which brings me to the question: you’ve chosen these two individuals
- so what is the difference between them?
- David: The core of the disagreement is whether it’s reasonable to assign a probability to a fact
- something that is potentially ascertainable, but we just don’t know what that is.
- Bayes said it was, and developed the calculus, the mathematics for dealing with it.
- He’s got this lovely experiment to do with balls being thrown onto a billiard table.
- So Bayes’ thought experiment was to take a billiard table and to throw a ball, at random, onto it.
- And I’m going to guess where it landed.
- Brian: OK.
- David: So take the ball away.
- Brian: Yeah.
- David: OK, I have to guess where that is.
- And the only information I’m going to get is what happens when you throw more balls onto the table
- and you’re going to tell me then, which side of that line do they lie.
- So could you do that, just start throwing balls on.
- Brian: Just in random directions?
- Brian: Just in random directions? David: Just random direction.
- David: Just random direction.
- What you should do is now tell me how many landed on this side of the line, and how many landed on that side of the line.
- Brian: Three of them are on the…on your left as you stand like that and and two of them are over here.
- David: OK, right. You might think then that I should estimate the line is two fifths of the way along the table.
- Brian: Yeah.
- David: That’s what Fisher would say, two fifths.
- Bayes would not say that. He would say it’s three sevenths of the way along the table.
- But the data only says two fifths and that’s what Fisher would say, just using the data.
- Whereas Bayes would pull it a bit towards the middle and say it’s there.
- Brian: And what’s the difference between Fishers’ approach and Bayes' approach?
- David: Fisher’s approach: he will just use the information from the data alone
- whereas the Bayesian approach will use also the fact that I know that you threw that first ball at random to lie on this table
- and that piece of information actually changes what I think.
- Brian: I’m going to tell you something actually
- because actually the answer was, that I think it was sort of about here
- which is somewhere between two fifths and three sevenths, so it’s about right!
- David: Between 40% - two fifths - and three sevenths.
- Brian: But that was roughly where the ball was so…
- How important is the work of Bayes and Fisher to the modern world?
- David: Bayesian ideas are everywhere.
- Your spam filter is probably a Bayesian spam filter
- all sorts of image processing techniques
- a huge amount of machine learning algorithms will be based on Bayesian methodology.
- And Fisherian methods, again, staggeringly important.
- Every scientific paper you read is going to have a p-value at the end of it
- But it’s all to do with how data changes our judgment, our knowledge, what we can learn from data
- and that’s what the modern world’s about.
Sir David Spiegelhalter discusses how the work of amateur mathematician Thomas Bayes and statistician Ronald Fisher – who was also a leading proponent of the now completely discredited eugenics movement - helped to shape the current thinking of probability.
Explore our Google Arts and Culture Collection on Bayes and Fisher -
See our collected archive papers of Fisher & Bayes' work -
With special thanks to the Oxford and Cambridge Club.
About the Royal Society
91TV is a Fellowship of many of the world's most eminent scientists and is the oldest scientific academy in continuous existence.
/
Subscribe to our YouTube channel for exciting science videos and live events.
Find us on:
Bluesky:
Facebook:
Instagram:
LinkedIn:
TikTok: