Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

web.ipac.caltech.edu

Post reply on HN
Print view View original

91–97 of 97 posts

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

#91

Post by platz »

Koshkin wrote: post #89
platz wrote: post #72

Earlier quoted context omitted.

They still non-trivially define/demarcate what the population actually is. That is kind of a belief because it is a choice not given by nature, and there are infinitely many choices one could choose.

Nature does not give you choice, it gives you the frequency (say, in the form of the intensity of a spectral line of an atom), and it is the base of the scientific method to listen to what nature is trying to tell you. There is nothing subjective in this process. Arguing otherwise is like saying that atheists “believe” in the non-existence of god.

Nature is telling you an infinite number of things, the process of selecting what to measure and what to exclude in the measurement is a choice.

In terms of frequentism, how you define what the population distribution you are sampling from is exactly, is a choice.

You are limiting the discussion to what happens after you've chosen how and what the population distribution consists of.. that part is itself a nontrivial and subjective process.

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

#92

Post by mturmon »

xcodevn wrote: post #84
mturmon wrote: post #77

Earlier quoted context omitted.

> ...the prior validation problem is similar to the likelihood validation problem... But priors can be much harder. Say I’m trying to estimate a wind speed from the blade velocity of a windmill. I can bring a more accurate wind speed sensor to calibrate the windmill against the wind speed, perhaps aided by basic physics. This is the likelihood portion. But what should the prior be? The typical speed at that time of d…

> I can bring a more accurate wind speed sensor to calibrate the windmill against the wind [...] But what should the prior be? [...] I have to have a crisp number — a full distribution actually, accurate out to the tails. What would you do when the sensor returns negative wind speeds due to noise or errors? The wind speed cannot be negative, or greater than speed of light. An expert in windmill can narrow down the pr…

"Bayesian framework is indeed a complete solution to inference in a formal/logical sense."

Bradley Efron, in TFA, begs to disagree:

"I wish I could report that this resolves the 250-year controversy and that it is now safe to always employ Bayes’ theorem. Sorry. My own practice is to use Bayesian analysis in the presence of genuine prior information; to use empirical Bayes methods in the parallel cases situation; and otherwise to be cautious when invoking uninformative priors. In the last case, Bayesian calculations cannot be uncritically accepted and should be checked by other methods, which usually means frequentistically."

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

#93

Post by kgwgk »

mturmon wrote: post #92
xcodevn wrote: post #84

Earlier quoted context omitted.

> I can bring a more accurate wind speed sensor to calibrate the windmill against the wind [...] But what should the prior be? [...] I have to have a crisp number — a full distribution actually, accurate out to the tails. What would you do when the sensor returns negative wind speeds due to noise or errors? The wind speed cannot be negative, or greater than speed of light. An expert in windmill can narrow down the pr…

"Bayesian framework is indeed a complete solution to inference in a formal/logical sense." Bradley Efron, in TFA, begs to disagree: "I wish I could report that this resolves the 250-year controversy and that it is now safe to always employ Bayes’ theorem. Sorry. My own practice is to use Bayesian analysis in the presence of genuine prior information; to use empirical Bayes methods in the parallel cases situation; and…

xcodevn said “in a formal/logical sense”, not “in a practical sense”.

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

#94

Post by 13415 »

daveFNbuck wrote: post #66
13415 wrote: post #63

Earlier quoted context omitted.

No method on earth necessarily gives you the right answer to a problem. You first have to represent the problem correctly, of course. Check out Scenario 2 here https://medium.com/@ProfessorF/visualizing-the-solution-to-t... for a correct tree.

Neither method guarantees the right answer, but it's a lot easier to get it wrong with a truth table.

Maybe you're right, I'm not fully convinced.

I mentioned a full truth table/decision tree because a long time ago these gave me the insight why switching is the right solution in the standard formulation of the problem, and they also illustrate why the problem is a purely deductive/logical problem whose solution does not require any inductive inference.

Then, to me it was a valuable lesson to learn that the Monty Hall problem does not reveal any perceived or real fundamental problem of probability theory.

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

#95

Post by KirinDave »

bo1024 wrote: post #82
KirinDave wrote: post #79

Earlier quoted context omitted.

Actually, it's the strength of Bayesian inference that these assumptions are made apparent. Coming to consensus on priors is the same process for arriving at consensus that all scientific inquiry must engage in. Anyone who says frequentist methods somehow more accurately represent an underlying reality are pulling a fast one.

Hmm, I think part of the question is where this debate and consensus should occur. I believe in firmly separating rigorous science from opinion and belief. To me, it follows that scientific research should focus on presenting evidence and leave it to Bayesian individuals to update their beliefs based on this evidence. Similarly I think argument or discussion about priors is not in scope for scientific research (excep…

I can't help but feel like this is a fundamental definition problem. Science is not actually distinct from consensus forming. Science does not work with raw facts, it forms models based off human observations which are themselves a kind of consensus.

Bayesian research is just more honest about what's already the case.

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

#96

Post by bo1024 »

KirinDave wrote: post #95
bo1024 wrote: post #82

Earlier quoted context omitted.

Hmm, I think part of the question is where this debate and consensus should occur. I believe in firmly separating rigorous science from opinion and belief. To me, it follows that scientific research should focus on presenting evidence and leave it to Bayesian individuals to update their beliefs based on this evidence. Similarly I think argument or discussion about priors is not in scope for scientific research (excep…

I can't help but feel like this is a fundamental definition problem. Science is not actually distinct from consensus forming. Science does not work with raw facts, it forms models based off human observations which are themselves a kind of consensus. Bayesian research is just more honest about what's already the case.

I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. So we need to new research to gather additional evidence. If every research paper tried to argue for a particular prior and posterior, rather than just gathering evidence, we would never make progress toward consensus either...

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

#97

Post by KirinDave »

bo1024 wrote: post #96
KirinDave wrote: post #95

Earlier quoted context omitted.

I can't help but feel like this is a fundamental definition problem. Science is not actually distinct from consensus forming. Science does not work with raw facts, it forms models based off human observations which are themselves a kind of consensus. Bayesian research is just more honest about what's already the case.

I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. So we need to new research to gather additional evidence. If every research paper tried to argue for a particular prior and posterior, rather than just gathering evidence, we would never make progress toward consensus either...

> I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields.

That's precisely my point. The act of presenting and refining research IS the act of building that consensus.

My statement here is not a novel thought. It's pretty much the modern philosophy of science for over a decade.

> So we need to new research to gather additional evidence.

This is simply data gathering though. Every approach starts here. I'm not sure why you suggest that people using Bayesian approaches to analysis are somehow forbidden from being informed by data (or informing priors by data).

That's exactly the same process folks use when selecting non-bayesian models. They don't spring from absolute truth, they're selected as well.

> If every research paper tried to argue for a particular prior and posterior

Given the replication crisis that's in part due to mis-application of existing models along with a lack of rigor in data collection, having research focus more tightly on the methodology for presenting data and conclusions doesn't seem like a bad outcome at all.

Post reply on HN