People of science. Take one.
David, you chose Thomas Bayes and Ronald Fisher.
What do both these people of science mean to you?
A huge amount.
These are two huge figures in the history of statistical inference.
Bayes, I was introduced to those ideas
when I first was a student studying mathematics.
I found them absolutely riveting.
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.
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 we've discovered the Higgs boson,
it's a five sigma discovery and that's Fisher.
That's Fisher, yes.
Now Bayes, we're going back a long time to Bayes.
When would Bayes... Bayes was extraordinary.
He was a nonconformist minister in Tunbridge Wells
and he was an amateur mathematician.
He 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 two different ways.
It was used in the idea of chance.
You know, future events. Pure unpredictability.
But it was also used when you were 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 probabilities to those is still deeply controversial.
Fisher loathed the idea.
So whilst Bayes seems like a relatively nice man,
preaching in Tunbridge Wells,
Fisher is a different kettle of fish.
Yes.
He's 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.
Which brings me to the question, you've chosen these two individuals,
so what is the difference between them?
The core of the disagreement
is whether it's reasonable to assign 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 on to a billiard table.
So Bayes' thought experiment was to take a billiard table
and throw a ball at random on to it
and I'm going to guess where it landed.
OK. So take the ball away. Yes. 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 on to 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.
Just in random directions? Just random directions.
And random speeds, I suppose. Yes, and then just...
What you should do now is tell me how many landed
on this side of the line and how many landed
on that side of the line.
Three of them are on your left as you stand like that
and two of them are over here. OK, right.
You might think then that I should estimate the line
is two fifths of the way along the table.
Yes. 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 would only say two fifths
and that's what Fisher would say just using the data.
Bays would pull it a bit towards the middle and say it's there.
And what's the difference between Fisher's approach and Bayes' approach?
Fisher's approach, he will just use the information from the data alone.
Whereas the Bayesian approach would 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.
I'm going to tell you something actually.
Because actually the answer was that I think it was about here,
which is somewhere between two fifths and three sevenths.
Between two fifths and three sevenths.
But that was roughly where the ball was.
How important is the work of Bayes and Fisher to the modern world?
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, we've 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.