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.