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Bayes’ Theorem in the 21st Century (2013) [pdf]

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Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#12

Post by Vaslo »

One of the best examples of the idea of Bayes is the Monte Hall problem. It is a good example of how prior probability (3 unopened doors) can lead to a more clear posterior-host selects an unopened door with a bad prize and you are asked whether to stay with the unopened door you chose or switch to the remaining open door. Turns out via Bayes it’s better to switch doors because you have more information now.

Tons of write ups and YouTube videos out there on it but here is one example of an explanation:

http://angrystatistician.blogspot.com/2012/06/bayes-solution...

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#13

Post by daveFNbuck »

Vaslo wrote: post #12

One of the best examples of the idea of Bayes is the Monte Hall problem. It is a good example of how prior probability (3 unopened doors) can lead to a more clear posterior-host selects an unopened door with a bad prize and you are asked whether to stay with the unopened door you chose or switch to the remaining open door. Turns out via Bayes it’s better to switch doors because you have more information now. Tons of…

Bayes' theorem also helps clear up some of the subtleties behind the Monty Hall problem. Switching is advantageous because Monty knows which door has the prize. If Monty doesn't know which door has the prize, seeing a non-prize door results in 50-50 odds that your door has the prize.

Depending on how you model Monty Hall's prior probability of revealing the prize, seeing a non-prize door can result in the probability anywhere between 0 and 2/3 of switching being advantageous.

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#14

Post by andbberger »

xcodevn wrote: post #2

I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our mode…

NUTS and Stan are quite old at this point!

Here's a more recent advance https://arxiv.org/pdf/1711.09268.pdf

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#15

Post by bo1024 »

xcodevn wrote: post #2

I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our mode…

It's fine for a company or individual trying to optimize an objective, but not as a way to do good science (which this article is about).

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#16

Post by xcodevn »

bo1024 wrote: post #15
xcodevn wrote: post #2

I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our mode…

It's fine for a company or individual trying to optimize an objective, but not as a way to do good science (which this article is about).

I strongly disagree. Bayesian inference is the only known self-consistent formal system for doing science, i.e. updating our belief system about the world based on the current evidence.

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#19

Post by laretluval »

Suppose you have a probability monad, implementing enumeration or random sampling. Like Amb but with probabilities attached.

   bayesRule :: (Prob a) -> (a -> Prob b) -> b -> Prob a
    bayesRule prior likelihood data = do
   h
I don’t actually do Haskell...just thinking out loud.

Looks like it was written similarly here http://www.randomhacks.net/files/build-your-own-probability-...

Re: Bayes’ Theorem in the 21st Century (2013) [pdf]

#20

Post by xcodevn »

formalsystem wrote: post #17

Does anyone have any examples of informative priors that they used to solve some problem at work?

See the discovery paper of gravitational waves [1] which uses informative priors from physical evidences/constraints.

[1]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.11...

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