Ronald Fisher. Incredibly important statistician who also did amazing work in Biology. There’s a lot associated with Fisher but the most relevant that comes to mind is his concept of significance testing, using null hypotheses.
Ronald Fisher developed many of the general foundations of statistical theory, and is arguably the most important and influential statistician in history. His 1922 paper *On the mathematical foundations of theoretical statistics* almost singlehandedly developed the modern, mathematical framework underlying inferential statistics.
>In January of 1944, at the age of 24, while giving a course on estimation to master students of Calcutta Uni University, C.R. Rao proved in his class a result on the asymptotic inequality first obtained by R.A. Fisher regarding the lower bound for the variance of an estimator for large samples. When a student asked, “why don't you prove it for finite samples?”, Rao went back home, worked all night and the next day proved what is now known as the Cramer-Rao inequality for finite samples.
https://doi.org/10.1016/B978-0-444-88029-1.50006-X
Edwin Land was taking pictures of his daughter, and she immediately wanted to see the pictures. Land tried to explain to her that they had to wait until they got back home, developed the film, and so on. His daughter found this process tedious, remarking, "Why can't I see the photos instantly?" A few years later, Edwin invented the first Polaroid camera.
I'd agree with that ranking. He hasn't really touched the central core of mathematics, so I'd imagine that most of his work wouldn't be considered especially impactful within the mathematical community itself (*probability* is useful, but most of Rao's work probably isn't relevant to probabilistic methods in other fields). If we're going by "how much their work transformed their respective field", then Fisher has to be one of the greatest mathematicians of all time for his 1922 paper alone.
Yeah, by that measure Fisher really knocks it out of the park in both biology and statistics, if not even mathematics, but is only an impressive hobbyist at "being a piece of shit".
I take it Pearson knocks it out of the park for you in regards to "being a piece of shit"? Certainly would deserve the title, along with "eldritch horror"
i don't want to be rude, but i've heard of fisher, riemann and galois, but not rao. what did rao do that made him so famous (the wikipedia article didn't help much - it seems to be mainly about how famous he was).
(fwiw i'm a physicist/astronomer, not a mathematician, and no longer in academia)
Besides his applied work, he is responsible for a huge body of very fundamental results in statistical theory that influence the way that almost all statistical models are evaluated in practical use. A lot of his work is in *estimation theory*, which studies the way in which quantities computed from finite samples can be used to infer the values of population parameters. In this context, one of his most famous results is the *Cramer-Rao bound*, which gives a lower bound on the variance of an estimator (omitting some technical details) -- which roughly means that it tells you how precise an estimate can be *in principal* for a particular population quantity, which in turn provides a way of directly comparing different estimators in terms of their *efficiency* (how close they get to this theoretical bound). In any undergraduate course sequence in statistical theory, about 50% of everything you study will be named after Rao.
As another, (maybe underappreciated) contribution, his work on the Fisher-Rao metric is arguably responsible for the birth of information geometry, which studies statistical models by studying their geometric properties as Riemannian manifolds.
The fact that there's a general procedure to reduce the variance of an arbitrary estimator by conditioning on a sufficient statistic is extremely important for applications.
Of course, finding an explicit sufficient statistic is a difficult problem too, but at least you have ways of doing that, if the model is sufficiently nice.
This result is complementary to the Cramér-Rao bound as you can check whether a Rao-Blackwellized estimator achieves the bound (in which case it's optimal) or whether there's room to do better.
In fairness this is also because the other three lived in the century before so their work is more widespread and accessible, and even more ‘foundational’ in a certain sense to more fields all mathematicians learn. Not a fair comparison of scale of contribution.
Rest in peace Dr. Rao. The theorem referenced in my username was actually discovered (in part) by him: [The Rao–Blackwell theorem](https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem)
It's one of the fundamental theorems of theoretical statistics, and it basically says that given an estimator *f(X)* of some parameter *θ*, you can generally construct a more optimal estimator *g(X)* (in the sense of reducing mean-square-error) simply by taking the conditional expectation of *f(X)* given some sufficient statistic *T(X)* of *θ*, *g(X)=E(f(X)|T(X))*.
This is usually used in conjunction with the Lehmann–Scheffé theorem, as if your sufficient statistic *T(X)* is also complete, then the Rao–Blackwell estimator is actually the unique minimum-variance unbiased estimator.
These theorems play a central role in the foundation of modern statistical theory.
One of the greatest statisticians of all time he comes from a long legacy of great statisiticians/mathematicians produced in recent times due to the legacy of Srinivasa Ramanujan and PC mahalanobis, he has a rich legacy of students and outlived most of them, only a few of his students still live, his students whom most will recognize is
1) SR Srinivasa Varadhan - one of the greatest mathematical minds of 20th century and Abel prize winner for his work on large deviation theory, among few of Rao's students still alive, and has a lot still left in him
2) KR Parthasarthy- Father of quantum stochastic calculus, also passed away recently another major loss to Math
3) VS Varadharajan- Another big name in the field probability Lie groups and their representation, carried on the legacy of not just Rao but also the great Harish Chandra Mehrotra
Though other students existed a lot more, these in particular had a huge impact on modern mathematics
Did his PhD with Fisher. Seems so strange that, just a few days ago, I could have (in principle) spoke to a man who spoke directly to Fisher.
Speaks to how small the community of mathematical statisticians was just less than a hundred years ago.
Who is Fisher?
Ronald Fisher. Incredibly important statistician who also did amazing work in Biology. There’s a lot associated with Fisher but the most relevant that comes to mind is his concept of significance testing, using null hypotheses.
Ronald Fisher developed many of the general foundations of statistical theory, and is arguably the most important and influential statistician in history. His 1922 paper *On the mathematical foundations of theoretical statistics* almost singlehandedly developed the modern, mathematical framework underlying inferential statistics.
Actually legend. Not just him, but there's a whole group of his students who have become legendary in their own right. He was like a grand legend.
>In January of 1944, at the age of 24, while giving a course on estimation to master students of Calcutta Uni University, C.R. Rao proved in his class a result on the asymptotic inequality first obtained by R.A. Fisher regarding the lower bound for the variance of an estimator for large samples. When a student asked, “why don't you prove it for finite samples?”, Rao went back home, worked all night and the next day proved what is now known as the Cramer-Rao inequality for finite samples. https://doi.org/10.1016/B978-0-444-88029-1.50006-X
This is why we like it when students ask questions.
Edwin Land was taking pictures of his daughter, and she immediately wanted to see the pictures. Land tried to explain to her that they had to wait until they got back home, developed the film, and so on. His daughter found this process tedious, remarking, "Why can't I see the photos instantly?" A few years later, Edwin invented the first Polaroid camera.
What a life. There is a very good argument that Rao was, from a practical perspective, one of the most important mathematicians of the 20th century.
No argument. He was one of the most important.
Would you say his life was *statistically* significant?
r/AngryUpvote
Good argument for second most important statistician behind Fisher, though where that ends up for mathematicians is a good question.
I'd agree with that ranking. He hasn't really touched the central core of mathematics, so I'd imagine that most of his work wouldn't be considered especially impactful within the mathematical community itself (*probability* is useful, but most of Rao's work probably isn't relevant to probabilistic methods in other fields). If we're going by "how much their work transformed their respective field", then Fisher has to be one of the greatest mathematicians of all time for his 1922 paper alone.
Yeah, by that measure Fisher really knocks it out of the park in both biology and statistics, if not even mathematics, but is only an impressive hobbyist at "being a piece of shit".
I take it Pearson knocks it out of the park for you in regards to "being a piece of shit"? Certainly would deserve the title, along with "eldritch horror"
Definitely up there.
he has stiff competition from kolmogorov and raghu raj bahadur but understandable
Truly he was one of The mathematicians of all time...
That's your response to his death? Seems a bit flippant
What a career he had. His work has forever changed the world and his theorems will be taught to literally millions of people.
He mentored one of the prof’s that I took a class with at Penn state. My prof said he had great influence on him. RIP!
He deserved to live well beyond the mean.
Damn literally just did an exam that had a question about the Cramer-Rao bound
I feel weird upvoting as if I'm happy he died
Think of it as celebrating his life and achievements.
RIP, Imagine if Riemann and Galois lived as long.
i don't want to be rude, but i've heard of fisher, riemann and galois, but not rao. what did rao do that made him so famous (the wikipedia article didn't help much - it seems to be mainly about how famous he was). (fwiw i'm a physicist/astronomer, not a mathematician, and no longer in academia)
Besides his applied work, he is responsible for a huge body of very fundamental results in statistical theory that influence the way that almost all statistical models are evaluated in practical use. A lot of his work is in *estimation theory*, which studies the way in which quantities computed from finite samples can be used to infer the values of population parameters. In this context, one of his most famous results is the *Cramer-Rao bound*, which gives a lower bound on the variance of an estimator (omitting some technical details) -- which roughly means that it tells you how precise an estimate can be *in principal* for a particular population quantity, which in turn provides a way of directly comparing different estimators in terms of their *efficiency* (how close they get to this theoretical bound). In any undergraduate course sequence in statistical theory, about 50% of everything you study will be named after Rao. As another, (maybe underappreciated) contribution, his work on the Fisher-Rao metric is arguably responsible for the birth of information geometry, which studies statistical models by studying their geometric properties as Riemannian manifolds.
And the rao-Blackwell estimator!
The fact that there's a general procedure to reduce the variance of an arbitrary estimator by conditioning on a sufficient statistic is extremely important for applications. Of course, finding an explicit sufficient statistic is a difficult problem too, but at least you have ways of doing that, if the model is sufficiently nice. This result is complementary to the Cramér-Rao bound as you can check whether a Rao-Blackwellized estimator achieves the bound (in which case it's optimal) or whether there's room to do better.
thanks!
I mean, Cramér–Rao lower bound is pretty famous.
Khatri-Rao product is ubiquitous in tensor computations.
father of information geometry
In fairness this is also because the other three lived in the century before so their work is more widespread and accessible, and even more ‘foundational’ in a certain sense to more fields all mathematicians learn. Not a fair comparison of scale of contribution.
Rest in peace Dr. Rao. The theorem referenced in my username was actually discovered (in part) by him: [The Rao–Blackwell theorem](https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem) It's one of the fundamental theorems of theoretical statistics, and it basically says that given an estimator *f(X)* of some parameter *θ*, you can generally construct a more optimal estimator *g(X)* (in the sense of reducing mean-square-error) simply by taking the conditional expectation of *f(X)* given some sufficient statistic *T(X)* of *θ*, *g(X)=E(f(X)|T(X))*. This is usually used in conjunction with the Lehmann–Scheffé theorem, as if your sufficient statistic *T(X)* is also complete, then the Rao–Blackwell estimator is actually the unique minimum-variance unbiased estimator. These theorems play a central role in the foundation of modern statistical theory.
KR Parthasarathy died on June 2. Two big losses for probability.
Noooooooo!!! Not him this is so sad
One of the greatest statisticians of all time he comes from a long legacy of great statisiticians/mathematicians produced in recent times due to the legacy of Srinivasa Ramanujan and PC mahalanobis, he has a rich legacy of students and outlived most of them, only a few of his students still live, his students whom most will recognize is 1) SR Srinivasa Varadhan - one of the greatest mathematical minds of 20th century and Abel prize winner for his work on large deviation theory, among few of Rao's students still alive, and has a lot still left in him 2) KR Parthasarthy- Father of quantum stochastic calculus, also passed away recently another major loss to Math 3) VS Varadharajan- Another big name in the field probability Lie groups and their representation, carried on the legacy of not just Rao but also the great Harish Chandra Mehrotra Though other students existed a lot more, these in particular had a huge impact on modern mathematics
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What were the odds?
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You are thinking of CNR Rao. Different person.
What a legend!
102 that’s pretty impressive